ch 01

1

There are many factors that affect the environment of our planet. One of these is world population.

The data supplied in the table give the estimated or projected world population for the middle of the year. In which ten-year period did (or will) the world population increase the most?

In which ten-year period is the percentage increase the largest?

This chapter refreshes your skills in working with numbers expressed as fractions, decimals, percentages or in index form and applying those skills to real-life situations.

Number skills

Year World population

1950 2 555 078 074

1960 3 039 332 401

1970 3 707 610 112

1980 4 456 705 217

1990 5 283 755 345

2000 6 080 141 683

2010 6 823 634 553

2020 7 518 010 600

2030 8 140 344 240

2040 8 668 391 454

2050 9 104 205 830

MQ9 Vic ch 01 Monday, September 17, 2001 10:17 AM

2

M a t h s Q u e s t 9 f o r V i c t o r i a

Order of operations

Anton has calculated the answer to 5

+

6

×

4 as44, while Marco insists that the answer is 29.Who is correct?

In mathematics, it is important to ensure thateverybody obtains the same result from a calcu-lation; so the order in which mathematical oper-ations are worked is important.

The order of operations requires that:1 all brackets are evaluated first, beginning

with the innermost brackets2 then, all multiplication and division are

evaluated, working from left to right3 and finally, any addition and subtraction,

working from left to right.

To obtain the correct answer to the calculation 5

+

6

×

4, we must complete theoperations of

+

and

×

in the correct order. That is,

×

first then

+

.5

+

6

×

4

=

5

+

24

=

29

In other examples you will need to read the question carefully to interpret the correctorder of operations and the correct way to write the calculation.

Evaluate each of the following without using a calculator.a 4 + 12 − 5 + 6 b 4 + 12 − (5 + 6) c 6 + 21 ÷ 7 d [4 × (5 + 8)] ÷ 2

THINK WRITE

a Write the calculation. a 4 + 12 − 5 + 6Perform the addition and subtraction from left to right.

= 16 − 5 + 6= 11 + 6

Write the answer. = 17b Write the calculation. b 4 + 12 − (5 + 6)

Evaluate the bracket first. = 4 + 12 − 11Perform the addition and subtraction from left to right and write the answer.

= 5

c Write the calculation. c 6 + 21 ÷ 7Perform the division. = 6 + 3Perform the addition. = 9

d Write the calculation. d [4 × (5 + 8)] ÷ 2Remove the brackets by working the innermost bracket first.

= [4 × 13] ÷ 2= 52 ÷ 2

Divide and write the answer. = 26

1

2

3

1

2

3

1

2

3

1

2

3

1WORKEDExample


C h a p t e r 1 N u m b e r s k i l l s 3

Order of operations

1 Evaluate each of the following without using a calculator.a 3 + 12 − 5 + 6 b 7 + 5 − 11 + 2 − 3 c 10 − 2 − 3 + 4 d 18 − 11 + 4 + 12 − 14 e 25 + 5 − 10 + 2 − 10 f 32 − 8 + 6 − 7 − 5 g 10 × 6 × 4 × 2 h 18 × 4 × 3 × 0 i 80 ÷ 4 ÷ 5j 25 ÷ 5 × 6 k 8 × 2 ÷ 4 × 3 l 72 ÷ 2 ÷ 6 × 3m 16 + 2 × 5 n 80 ÷ 2 + 28 o 12 − 14 × 0p (4 + 6) × 8 q (35 − 11) ÷ 6 r (7 + 2 − 3) × 8s 12 ÷ (9 − 3) t 75 ÷ (12 + 13)

Mum bought 2 packets of Easter eggs to hide in the garden for her 4 children to find. Each packet contained 20 eggs. While she was hiding them, the dog ate 4 eggs, Dad ate 3, and 1 was squashed. If all the other eggs were found, and each child found the same number of eggs, how many eggs did each child have?

THINK WRITE

Write a mathematical sentence showing what happened. Find the total number of eggs and subtract the number that were eaten or squashed. Then divide by the number of children looking for eggs. [2 × 20 − (4 + 3 + 1)] ÷ 4Use order of operations to solve the problem.

= (2 × 20 − 8) ÷ 4= [40 − 8] ÷ 4= 32 ÷ 4= 8

Write the answer in a sentence. Each child found 8 eggs.

1

2

3

2WORKEDExample

rememberEvaluate in the following order.1. Brackets first, beginning with the innermost pair, then working through to the

outermost pair.2. Multiplication and division in order from left to right.3. Addition and subtraction in order from left to right.

remember

1AWWORKEDORKEDEExample

1

Mathcad

Order ofoperations

Mathcad

Ascending anddescending

order


4 M a t h s Q u e s t 9 f o r V i c t o r i a

2a What is 12 × (4 + 2) ÷ 8 equal to?

b What is 36 ÷ 3 ÷ 4 + 2 equal to?

c What is 8 × 5 + 3 × (8 − 5) is equal to?

3 Evaluate each of the following.a 8 × 9 − 10 × 6 b 14 × (3 + 2) ÷ 7 c 72 ÷ (2 + 7 × 1)d 80 ÷ 5 − 60 ÷ 6 e 35 × (8 + 4 − 6 × 2) f (13 − 3) × 2 + 4 × 6g (17 − 12) ÷ 5 × 2 h (14 + 7 − 8) × 6 i [14 + (2 × 6 − 3)] × 4j [(2 + 1) × 7 − 3 × 5] − 6 ÷ 3 k {[(3 + 9) ÷ 12] + 4 × 4} − 17l {40 − [(8 + 2) × 3 − 5]} ÷ 5 m 16 ÷ 4 + 24 ÷ 6 + 5 × 5 − 19n 108 ÷ 4 × (4 − 4) × 4 o {11 + (4 + 3) × 2 + 5 × 6 + (8 – 2) × 5} × 4p [16 × 3 ÷ 2 + 40 ÷ 4 × 2 − 3 × 11 + 14] ÷ 5 + (6 × 2 + 4) × 2 − (7 × 5 + 2)

4 Takiko has brought 3 packs of nut biscuits to share with the 20 members of her class. Ifeach pack contains 12 nut biscuits and 3 girls and 5 boys are allergic to nuts or don’t eatbiscuits, so don’t have any; how many nut buscuits will each of the other class membersreceive?

5 The Wimbletons wanted to buy atennis racquet for each of their3 children. The normal price ofa racquet is $100 but the shopis offering a special deal. If tworacquets are bought at the sametime, the price is reduced by $25for each one. If the Wimbletonsbuy one at the normal price and twoon the special deal, how much do theypay altogether? Write an equation toshow how you could have found the answer.

A 10 B 12 C 9 D 8 E 1

A 2 B 72 C 50 D 5 E 10

A 49 B 192 C 59 D 129 E 339

Mathca

d

Addingwhole numbers DIY

mmultiple choiceultiple choice

Mathca

d

Subtracting whole numbers DIY

Mathca

d

Multiplying whole numbers DIY

Mathca

d

Dividing whole numbersDIY

WWORKEDORKEDEExample

2



IntegersIntegers include positive whole numbers, negative whole numbers and zero. They canbe represented on the number line.

The rules for using integers are:

Rule 1 When adding integers with the same sign, keep the sign and add; −3 + −2 = −5.

Rule 2 When adding integers with different signs, find the difference and use the signof the number further from zero; –3 + 4 = 1.

Rule 3 When subtracting integers, add the opposite; 5 − −7 = 12.

Rule 4 When multiplying integers, the following rules are obeyed.

(a) Positive × Positive = Positive 5 × 8 = 40

(b) Positive × Negative = Negative 5 × −8 = −40

(c) Negative × Positive = Negative −5 × 8 = −40

(d) Negative × Negative = Positive −5 × −8 = 40

Rule 5 When dividing integers, use the same rules as for multiplication.

(a) 16 ÷ 2 = 8

(b) 16 ÷ −2 = −8

(c) −16 ÷ 2 = −8

(d) −16 ÷ −8 = 2

–5 –4 –3 –2 –1 0 1 2 3 4 5

Calculate each of the following without the use of a calculator and using the correct order of operations.a −15 × −5 ÷ 3 b 7 + −5 − −8 c 4 − 60 ÷ (−4 − 6)

THINK WRITE

a Write the calculation. a −15 × −5 ÷ 3Multiplication and division are the only operations; so work from left to right.

= 75 ÷ 3= 25

b Write the calculation. b 7 + −5 − −8Addition and subtraction are the only operations; so work from left to right.

= 2 − −8= 2 + 8= 10

c Write the calculation. c 4 − 60 ÷ (−4 − 6)Work the brackets. = 4 − 60 ÷ −10Perform the division.Perform the subtraction.

= 4 − −6= 4 + 6= 10

1

2

1

2

1

2

34

3WORKEDExample



Integers

1 Calculate each of the following without the use of a calculator and using the correctorder of operations. a −7 + 12 b −14 + 7 c −18 − 8 d 25 − 24 − 2e −2 − 3 − 6 f −7 − 11 + 5 g 14 − 15 + 11 h 13 − 19 − 6 + 9i 10 × 2 ÷ 5 j 6 × −3 × −2 k −4 × −3 × −5 l 64 ÷ −16 ÷ 4m −12 × 4 ÷ 16 n −120 ÷ −10 × 2 o 36 ÷ −6 × −5 p −6 × −1 × −10 ÷ 4

2 Calculate each of the following without the use of a calculator and using the correctorder of operations.a 8 + −7 + −3 b 15 − 18 + −8 c 6 + −7 + −10 d 6 − −7e −5 − −2 f 7 − −2 − 7 g 4 + −8 − −5 h −7 − −13i −9 + −9 − −9 j 4 + −6 + −2 − −1 k −3 − 6 − −10 + −5

3a −7 − 8 + 2 − 3 is equal to:

b −12 × −8 ÷ −4 × 2 is equal to:

c 9 + −5 − −4 + 2 − −1 is equal to:

A −2 B −16 C −14 D −20 E 0

A 12 B −12 C 48 D −48 E 316

A 9 B 1 C 23 D 11 E −1

Insert operation signs to make this equation true.5 K 3 K 4 K 1 = −2(Trial and error is a suitable method.)THINK WRITE

The answer (−2) is less than the first number in the question; so try subtraction.

5 − 3 − 4 − 1 = −3 ≠ −2

The result of the first try (−3) is a little too small; so change the last sign to +.

5 − 3 − 4 + 1 = −1 ≠ −2

The result of the second try (−1) is too big; so try multiplying the last digit, which is 1, remembering to use the order of operations.

5 − 3 − 4 × 1 = 5 − 3 − 4= −2

1

2

3

4WORKEDExample

remember1. When adding integers with the same sign, keep the sign and add.2. When adding integers with different signs, find the difference and use the sign

of the number further from zero.3. When subtracting integers, add the opposite; for example 5 – –7 = 12.4. When multiplying and dividing integers, like signs give positive answers,

unlike signs give negative answers.5. When using order of operations, evaluate brackets before multiplication and

division, then evaluate addition and subtraction.

remember

1BWWORKEDORKEDEExample

3aSkillSH

EET 1.1


3b

SkillSH

EET 1.2

Mathca

d

Order of operations with integers


EXCEL

Spreadsheet

Arithmetic timer


C h a p t e r 1 N u m b e r s k i l l s 74 Calculate each of the following without the use of a calculator and using the correct

order of operations.a −3 + 3 × 3 b −9 − 2 × 6 c 15 ÷ 5 − 5 d 7 × 0 − 5e 6 × (0 − 6) f −14 × 2 − 2 × 10 g 2 − 6 × 3 h 8 + 2 × −5i 3 × 8 − 5 × 7 j 12 × −3 − 4 k 0 × 3 × −6 + 6 l −90 ÷ −5 − 26m 5 × (−3 + 5) + 7 n 128 ÷ −16 + 3 × −5 o (3 + 7) ÷ −2 + −4p −60 ÷ −4 × 3 − 43 q 28 ÷ −2 × (2 − 5) r 56 ÷ 7 + 70 ÷ −10s 94 ÷ 2 + 3 × −3 t 14 − 4 × (5 + −6)

5a What does 5 × −4 − 10 × −6 equal?

b What does 5 × (−4 − 10) × −6 equal?

c (–2 – –4) × (8 × 5 − 4) is equal to:

d –64 ÷ 8 – –8 is equal to:

e The correct operation signs to make 2 K −5 K −2 K −5 = −3 a true statement are:

6 Insert operation signs to make these equations true:a 5 K 6 = 11 b 7 K −4 = −28 c −18 K −2 = 9d −7 K −3 = −4 e 3 K 4 K 5 = 2 f 7 K 2 K 3 = 17g −5 K −4 K 10 = 2 h 6 K 3K 3 = 0 i 8 K 5 K 2 = −2j 2 K 3 K 5 K 4 = 26 k 16 K 8 K 8 = −6 l 12 K 18 K 2 = 21m 12 K 18 K −2 = 21 n −8 K 4 K −2 = 0 o 10 K 3 K 4 K 2 = 0p 5 K 2 K −3 K −3 = 2

7 Thanh stands on a cliff top 68 m above sea level and drops a stone into the water. It stops on the bottom 27 m below sea level. How far has the stone fallen?

8 The temperature range in Melbourne on 29 April was 7°C. If the maximum temperaturewas 15°C, what was the minimum temperature?

A −40 B 40 C 80 D −80 E 180

A 420 B −420 C 180 D −180 E −40

A 244 B −216 C 16 D −48 E 72

A 4 B −4 C 0 D −16 E 16

A ×, −, − B ×, +, + C ×, ÷, + D −, +, × E −, ×, +


3c



4

GAMEtime

Number skills— 001



Golf scoresIn golf, par is the number of strokes considered necessary to complete a hole in expert play. A birdie is a score of one stroke under par and a bogey is one stroke over par. An eagle is a score of 2 strokes under par while 3 strokes under par is called an albatross. A double bogey is 2 strokes over par and a triple bogey is 3 strokes over par.1 Use integers to represent:

a par b a birdie c a bogey d an eaglee an albatross f a double bogey g a triple bogey.

2 Which score for a hole would be the most difficult to achieve?3 Leon and Dion have finished a round of 18 holes with the following information

shown on their scorecards.

What integer represents each person’s final score as a number of strokes over, under or at par?

4 Who wins this round of golf?5 Two professional golfers achieve overall final scores for 18 holes of −8 and −6.

a What does this mean?b Who achieved a better score for this round of golf? c How many strokes did each player make for the 18 holes if the course is

considered to be a par 71 course?

Leon Dion

parsbirdiesbogeyseaglesdouble bogeysalbatrossestriple bogeysFinal score

4361202

parsbirdiesbogeyseaglesdouble bogeysalbatrossestriple bogeysFinal score

6240213



Estimation and roundingRounding to a given number of decimal placesMs Shopper’s bill at the supermarket comes to $94.68 and she pays $94.70. MrShopper’s bill is $83.72 and he pays $83.70. The bills have been rounded to the nearest5 cents because the 5-cent is the smallest coin used. Ms Shopper’s bill has beenrounded up because 68 cents is closer to 70 cents than to 65 cents. Mr Shopper’s billhas been rounded down because 72 cents is closer to 70 cents than to 75 cents.

Measuring distances is another one of the many practical situations where it isnecessary to round an answer to a given number of decimal places. For example, thedistance between two towns is given to the nearest kilometre. It is not practical oruseful to the average motorist that the distance between Melbourne and Sydney by acertain route is 1024.352 km. We give the distance simply as 1024 km.

The accuracy of measurement is limited by what is practical and by the accuracy ofthe instrument being used to take the measurement. For example, with your ruler it wouldnot be possible to measure anything more accurately than to the nearest millimetre.

The measurement 5.6713 cm ≈ 5.7 cm because 5.6713 is closer to 5.7 than it is to5.6. The rounded answer, 5.7, is the closest approximation to the exact answer.

To round an answer to a given number of decimal places, consider only the first digit after the required number of decimal places.

If that digit is 0, 1, 2, 3 or 4, then leave it and all following digits out of the answer. If that digit is 5, 6, 7, 8 or 9, then the last digit to be written is increased by

1 and all else is left out.

Many calculators are able to round off using theFIX function.

On some scientific calculators, you need to press first.

On a TI graphics calculator, press , arrowdown to the second row, then arrow across tohighlight the number that corresponds to the requirednumber of decimal places. Press to set thisrounding condition. To undo this operation, press , arrow down to highlightFLOAT and press .

Any rounded answer is not an exact answer but a close approximation.

Note: The more decimal places, the closer the approximation is to the exact answer.

MODEMODE

ENTERMODE

ENTER

Round 15.439 657 to: a 1 decimal place b 3 decimal places.THINK WRITEa Write the number. a 15.439 657

Look at the second decimal place to determine whether to leave it or to round it up. The digit is 3; so rewrite the number without all digits after the first decimal place.

≈ 15.4

b Write the number. b 15.439 657Look at the fourth decimal place to determine whether to leave it or to round it up. The digit is 6; so increase the third decimal place by 1. Note: Adding 1 to 9 gives 10, thus 439 becomes 440 and the zero must be included.

≈ 15.440

1

2

1

2

5WORKEDExample



There were 70 000 people at the Melbourne Cricket Ground for Australia’s one-day match against the West Indies.

Rounding to a given number of significant figuresAlthough the caption describes a crowd of 70 000, in reality there may have been70 246 people. The number has been rounded to 1 significant figure because the restof the number, 246, has no impact on our image of the size of the crowd. When usingvery large or very small numbers, rounding to a given number of significant figures isoften used.

To round to 1 significant figure means having only 1 non-zero digit beginning fromthe left with the other digits being zeros. The number 367 rounded to 1 significantfigure is 400 because 367 is closer to 400 than to 300.

To write 452 correct to 2 significant figures, we need to consider whether 452 iscloser to 450 or 460. It is closer to 450, and 4 and 5 are the 2 significant figures.

The method of deciding whether to leave or round up is the same as rounding to anumber of decimal places.

Round 347 629 to: a 1 significant figure b 3 significant figures.THINK WRITEa Write the number. a 347 629

Look at the second significant figure to determine whether to leave it or to round it up. The digit is 4, so rewrite the number, replacing all digits after the first significant figure with zeros.

≈ 300 000

b Write the number. b 347 629Look at the fourth significant figure to determine whether to it leave or to round it up. The digit is 6 so write the answer by adding 1 to the third digit and replace all other digits with zeros.

≈ 348 000

1

2

1

2

6WORKEDExample


C h a p t e r 1 N u m b e r s k i l l s 11Note: The more significant figures taken, the closer the approximation is to the exactanswer.

When the first non-zero significant figure appears after the decimal point, any zerosbefore that figure are not significant.

EstimationRounding is also used when making an estimation or mental approximation of ananswer. Estimation is a method of checking the reasonableness of an answer or a calcu-lator computation. We can estimate an answer by rounding the numbers in the questionto simple numbers that can be calculated mentally.

Round 0.004 502 6 to 3 significant figures.

THINK WRITE

Write the number. 0.004 502 6The first significant figure is the 4. Round to 3 significant figures beginning with the 4. The last zero must be included in the answer because it is one of the significant figures.

≈ 0.004 5012

7WORKEDExample

Estimate answers to the following without calculating the exact answer.a 31 × 58 b 46 679 + 2351 × 65

THINK WRITE

a Write the calculation. a 31 × 58Round each number to 1 significant figure. ≈ 30 × 60Perform the mental calculation. = 1800

b Write the calculation. b 46 679 + 2351 × 65Round each number to 1 significant figure. ≈ 50 000 + 2000 × 70Perform the mental calculation. = 50 000 + 140 000

= 190 000

1

2

3

1

2

3

8WORKEDExample

remember1. When rounding to a given number of decimal places, count only those places

after the decimal point.2. When rounding to a given number of significant figures, begin counting from

the first non-zero digit.3. A quick mental estimation can be used to check the accuracy of calculations.4. Rounding is often used to convey a concept of size rather than an exact number.

remember



Estimation and rounding

1 Round the following to: i 1 decimal place ii 2 decimal places iii 3 decimal places.a 5.893 27 b 67.805 629 c 712.137 84 d 81.053 72 e 504.896 352

2 Round the following to 0 decimal places. (To 0 decimal places means to the nearestwhole number.)a 25.68 b 317.19 c 1027.8 d 19.53

3 Round the following to 1 decimal place.a 3047.2735 b 24.7392 c 8.2615 d 19.9804

4 Round the following to: i 1 ii 2 iii 3 iv 4 significant figures.a 574 248 b 430 968 c 28 615 d 1 067 328 e 458 610

5 Round the numbers in question 2 to 2 significant figures.

6 Round the following correct to 3 significant figures.a 0.085 246 b 0.000 580 4 c 0.000 008 067 3d 0.006 765 73 e 0.000 026 973 f 0.000 352 1

7 Estimate answers to the following without calculating the exact answer.a 183 ÷ 58 b 78 × 11 c 632 + 169 d 1010 ÷ 98e 17 × 19 f 476 ÷ 8 + 52 g (51 + 68) × 12 h 68 + 19 × 9i 5 × (78 − 59) j 42 × 8 + 18 × 5 k 176 ÷ 18 + 689 ÷ 7l m 473 × 248 n 657 − 239 ÷ 49o 12 345 + 549 × 146

8a The number 49.954 correct to 1 decimal place is:

b The number 3 056 084 correct to 3 significant figures is:

c The number 0.008 065 3 correct to 3 significant figures is:

d A number rounded to 2 decimal places is 6.83. The original number could have been:

9 Each of the 178 students who attend the Year 9 Social has to pay $55. If the cost ofhiring the band is $1000, estimate how much money would be available to pay for thesupper and the security people.

A 49.9 B 49.0 C 50 D 50.0 E 50.1

A 3 050 000 B 3 056 000 C 3 057 000 D 306 E 3 060 000

A 0.008 B 0.008 065 C 0.008 06 D 0.008 07 E 0.806

A 6.835 B 6.831 C 6.8372 D 6.85 E 6.8

1CWWORKEDORKEDEExample

5

EXCEL

Spreadsheet

Rounding and significant figures DIY


6

Mathca

d

Rounding


7


8Mathca

d

Estimation

397


WorkS

HEET 1.1

MA

TH

SQUEST

C H A L L

EN

GE

MA

TH

SQUEST

C H A L L

EN

GE

1 In 1832, a young runner named Mensen Ehrnot reportedly ran nearly8950 km over a 59-day period. On each of those days he ran 16 hoursand rested for 8 hours. Estimate how many kilometres he ran, onaverage, per hour.

2 In the hundred consecutive whole numbers from 1 to 100, how manytimes does each of the ten digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 occur?


C h a p t e r 1 N u m b e r s k i l l s

13

1

Evaluate 9

−

13

−

14.

2

Evaluate 8

−

8

÷

4.

3

Evaluate (13

+

5

×

7)

÷

12.

4

Evaluate

−

25

+ −

10

− −

50.

5

Evaluate

−

84

÷

12

×

3.

6

Evaluate

−

18

+

(

−

9

+

11)

×

14.

7

Insert signs to make the following equation true. 5

K

21

K

7

K

5

=

20

8

Round 1.746 582 to 4 decimal places.

9

Round 0.006 059 9 to 4 significant figures.

10

Give an estimate for 78

+

43

+

55

−

86.

Decimal numbers

Decimal numbers are so much a part of everyday life that we need to be able to usethem, put them in order and convert them to simple fractions and percentages.

When using either your graphics calculator or a scientific calculator, enter the calcu-lation as written and the calculator will perform the calculation using the correct orderof operations. There are, however, many things that we need to be able to do ourselveswith decimals without the aid of a calculator.

Ordering decimal numbers

Ascending order means from lowest to highest and descending order means fromhighest to lowest. This is done by first writing each number with the same number ofdecimal places, adding zeros where necessary. We then look at the left-most digit. Thegreater this digit, the greater the decimal number. If the left-most digits are the same,we move to the next digit, and so on.

1

Write the following decimal numbers in ascending order:0.66, 0.606, 0.6.THINK WRITE

Write the numbers. 0.66, 0.606, 0.6Write all numbers with the largest number of decimal places, in this case 3, then compare.

0.660, 0.606, 0.600

Write the original numbers in ascending order after looking at the second and third decimal places.

0.6, 0.606, 0.66

12

3

9WORKEDExample

MQ9 Vic ch 01 Wednesday, September 19, 2001 8:34 AM


Finite or terminating decimal numbersFinite decimal numbers have a fixed or finite number of decimal places and can bewritten as a fraction with a denominator that is a multiple of 10. If the decimal numberhas 1 decimal place, the denominator of the fraction is 10; if there are 2 decimal places,the denominator is 100; if there are 3 decimal places, the denominator is 1000 and soon. In each case the numerator is the decimal number without the decimal point. Thesefractions are simplified where possible.

Converting decimal numbers to percentagesTo convert a decimal number to a percentage, we multiply the decimal number by 100and include the % sign.

Convert each of the following to fractions in simplest form:a 0.65 b 1.2 c 0.6275.THINK WRITEa Write the decimal number. a 0.65

There are 2 decimal places, so write as a fraction with a denominator of 100 and simplify by cancelling. (You may use a calculator to simplify.)

=

Write the answer. =

b Write the decimal number. b 1.2

There is 1 decimal place, so write as a fraction with a denominator of 10 and simplify by cancelling. (You may use a calculator to simplify.)

=

Write the answer as a mixed number. = 1

c Write the decimal number. c 0.6275

There are 4 decimal places, so write the fraction with a denominator of 10 000 and simplify. (You may use a calculator to simplify.)

=

Write the answer. =

1

2 6513

10020-------------

31320------

1

2 126

105--------

315---

1

2 6275251

10 000400----------------------

3251400---------

10WORKEDExample

Convert 0.357 to a percentage.THINK WRITE

Write the decimal number. 0.357Multiply the decimal number by 100 by moving the decimal point 2 places to the right. Remember to include the percentage sign.

= (0.357 × 100)%= 35.7%

12

11WORKEDExample



Decimal numbers

1 Calculate each of the following.a 6.56 + 3.214 b 4.87 − 2.493 c 5.6 × 7.04d 5.75 ÷ 0.25 e (4.5 + 2.1) × 3.5 f (8.6 − 4.4) ÷ 7g 4.8 − 2.16 ÷ 0.18 h 3.2 × (6.4 + 0.78) i 7.2 ÷ 0.12 × 6j 7.2 ÷ (0.12 × 6) k 5.8 × (3.1 ÷ 0.4) l 6.2 + 3.5 × 2

2 Calculate each of the following, rounding your answers to 2 decimal places.a 6.46 × 2.356 b 8.12 × 5.4 ÷ 9.6 c 8 ÷ 0.35 + 2.1d (6.509 + 4.804) ÷ 0.341 e 3.2 × 4.057 − 13.91 ÷ 2.43

3 Write each of the following sets of decimal numbers in ascending order.a 0.66, 0.4, 0.71 b 2.3, 0.23, 23 c 0.7, 1.32, 1.04d 1.02, 1.1, 1.22 e 0.5, 0.56, 0.06 f 0.323, 0.4, 0.35

4 Write each of the following sets of decimal numbers in descending order.a 0.24, 0.204, 0.2004 b 0.062, 0.081, 0.11 c 0.7, 0.77, 0.707d 0.082, 0.09, 0.0802 e 1.2304, 1.23, 1.204 f 0.359, 0.39, 0.3592

5a The expression 6.43 × 2.356 ÷ (2.1 − 0.365) correct to 2 decimal places is equal to:

b The false statement is:

c The expression −0.9 + 6.5 × 0.004 − 1.2 ÷ 0.6 is equal to:

d A good estimate for 5.2 × 0.2 + 1.18 ÷ 0.012 is:

6 Convert each of the following to fractions in simplest form.a 0.9 b 0.6 c 0.16 d 0.27 e 0.78f 0.15 g 0.08 h 1.5 i 2.84 j 0.125k 0.484 l 0.963 m 0.775 n 0.0625 o 0.8875

7 Convert each of the following to percentages.a 0.72 b 0.31 c 0.89 d 0.57 e 0.9f 0.06 g 0.782 h 0.6175 i 0.0094 j 1.35k 1.602 l 11 m 2.3 n 5.75 o 2.485

A 0.36 B 6.85 C 87.31 D 8.73 E 6.84

A 0.67 < 0.7 B 0.506 < 0.51 C 0.735 > 0.73D 0.203 < 1.3 E 0.085 > 0.85

A −1.074 B −2.874 C −2.64 D −20.874 E −0.84

A 101 B 11 C 110 D 99.373 E 1010

remember1. To order decimal numbers, write each with the same number of decimal places

and compare.2. To write finite decimal numbers as fractions, make the denominator an

appropriate multiple of 10 and simplify where possible. The number of zeros in the denominator should be the same as the number of digits after the decimal point.

3. To convert a decimal number to a percentage, multiply by 100 and include the percentage sign.

remember

1D

SkillSH

EET 1.4

SkillSH

EET 1.5

SkillSH

EET 1.3Mathcad

Operationswith

decimalnumbers


9


SkillSH

EET 1.6

SkillSH

EET 1.7


10

EXCEL Spreadsheet

Convertingdecimals to

fractions


11

EXCEL Spreadsheet

Convertingdecimals topercentages



8a In simplest form and as a fraction 0.3125 is equal to:

b As a percentage 0.0875 is equal to:

c The number 0.656 25 is equal to:

9 Francis is paid $11.50 an hour for babysitting. If he works for 7 hours over theweekend, how much does he earn altogether?

10 Yvette babysits for 5 hours after school each Friday. She is paid $10 an hour. a How much does

she earn each week?

b If she banks $3.25 of the money each week, how much does she have left to spend?

A B 31.25 C D 31 E

A 0.875% B 8.75% C 87.5% D % E 875%

A B C D E


312510 000---------------- 5

16------ 1

4--- 13

40------

780------

1320------ 53

80------ 11

16------ 21

32------ 5

8---

MA

TH

SQUEST

C H A L L

EN

GE

MA

TH

SQUEST

C H A L L

EN

GE

1 Allison, Bhiba, Chris and Dinesh ordered one box of apples to shareequally between them. However, no one was present when the box wasdelivered. Allison arrived and took of the apples. Later, Bhiba cameand took of the apples left in the box. Then Chris came and did thesame. Finally Dinesh arrived and took his rightful share of theremaining apples. If 9 apples remained in the box, how many appleswere in the box originally?

2 Mitchell has mown 0.6 of the lawn. He still has 50 m2 of lawn to mow.What is the total area of the lawn?

3 A train 0.5 km long is travelling at a speed of 80 km/h. How long will ittake the train to go completely through a tunnel which is 1.5 km long?

14---

13---



Answer the decimal questions tofind the puzzle’s code.

= as a decimal = 8.6– 4.9

= 2.8 + 3.6=

= 5.26 + 1.87=

= 0.5 × 8.4=

= 1.1 × 0.8=

= 0.2 × 20=

= 6 × 0.8=

= 4.5× 1.2

= 6.3 ÷ 0.63=

= 1.64 ÷ 0.4=

= 12 ÷ 0.5=

= 1.2 – 0.8=

= 5 × 0.3=

=

= as a decimal

=

=

=

= 10% as a decimal

= 12.7– 9.87

= 1.6– 0.95

= 7.63– 3.23

= 2.374+ 3.926

= 0.67+ 0.53

= 0.87+ 1.33

= 8.34– 6.54

3–4

= as a decimal

=

=

=

= as a decimal

= as a decimal

=

= as a decimal

=

7––20

17––4

4–5

3–8

23––50

5–2

= 0.3 + 0.4= =

= 22% as a decimal=

= 51% as a decimal=

= 60% as a decimal=

= 93% as a decimal=

5.4

4.1

2.5

0.93

4.0

0.75

3.7

7.13

1.8

0.88

0.46

0.6

2.2

0.1

0.375

0.51

4.8

4.2

0.22

1.5

24

0.65

0.4

10

0.8

0.7

6.3

1.2

6.4

4.25 2.83

4.4

0.35

What type of crWhat type of creatureature is a KAe is a KATYDIDTYDID and wher and where are are its ears?e its ears?



FractionsThere are many essential skills that you will need with fractions. You can review themin the exercise below and by the matching SkillSHEET. You should be able to simplifyfractions and convert between improper fractions and mixed numbers. You should alsobe able to use your calculator efficiently.

As with any calculation involving fractions, if youwish to have an answer expressed as a fraction theneach calculation needs to end by pressing ,selecting 1: Frac and pressing .

For example, to simplify on your graphics calcu-lator, enter 28 ÷ 44 then press choose option1: Frac, then press . This can be seen in thescreen at right.

Note: The graphics calculator gives all answers as improper fractions and will not giveanswers as mixed numbers.

It is important that we know how to perform calculations using fractions both withand without a calculator.

Without a calculator, we would simplify by dividing both the numerator and the

denominator by the highest common factor (HCF) of both. The HCF of 28 and 44 is 4.

=

Graphics CalculatorGraphics Calculator tip!tip! Obtaining an answer expressed as a fraction

MATH

� ENTER2844------

MATH

� ENTER

2844------

2844------ 287

4411----------=

711------

Evaluate the following.a + b × c 2 ÷

THINK WRITE

a Write the fraction calculation. a +

Write both fractions with the same denominator by using equivalent fractions.

= +

Add the fractions and simplify the answer by writing it as a mixed number.

=

= 1

b Write the fraction calculation and cancel where applicable.

b ×

Multiply numerators and multiply denominators.

=

34--- 5

6--- 3

4--- 5

6--- 1

4--- 3

5---

134--- 5

6---

2 912------ 10

12------

3 1912------

712------

131

4----- 5

62-----

2 58---

12WORKEDExample



To perform the calculations in worked example 12 ona graphics calculator, the following steps need to befollowed:(a) Enter 3 ÷ 4 + 5 ÷ 6, press , choose

1: Frac then press . The result is givenas . The graphics calculator gives all answers asimproper fractions.

(b) Enter 3 ÷ 4 × 5 ÷ 6, press , choose 1: Frac then press .(c) Enter (2 + 1 ÷ 4) ÷ (3 ÷ 5), press , choose 1: Frac then press .

Writing fractions with the same denominator allows us to compare the size of fractions.

THINK WRITE

c Write the fraction calculation. c 2 ÷

Change the mixed number to an improper fraction. = ÷

Times and tip, (change the division sign to a multiplication sign and tip the second fraction) and cancel.

= ×

Multiply numerators and multiply denominators; then simplify the answer by writing the fraction as a mixed number.

=

= 3

114--- 3

5---

2 94--- 3

5---

393

4----- 5

31-----

4 154------

34---

Graphics CalculatorGraphics Calculator tip!tip! Fraction calculations

MATH

� ENTER1912------

MATH � ENTERMATH � ENTER

Find of 98.

THINK WRITEWrite the calculation. of 98

Change the ‘of’ to ×, write the whole number over 1 and cancel if applicable.

= ×

Multiply numerators and multiply denominators. = 42

37---

137---

2371----- 9814

1-----------

3

13WORKEDExample

Write the fractions , , in ascending order.

THINK WRITEWrite the fractions. , ,

Write all fractions as equivalent fractions by finding the lowest common denominator, in this case 18.

= , ,

Rewrite the original fractions in the correct order. = , ,

23--- 8

9--- 5

6---

123--- 8

9--- 5

6---

21218------ 16

18------ 15

18------

323--- 5

6--- 8

9---

14WORKEDExample



Another way of writing fractions in order is to convert each fraction to a decimalnumber before comparing them.

Converting fractions to decimal numbersTo convert a fraction to a decimal number, divide the numerator by the denominator.

Converting fractions to percentagesTo convert a fraction to a percentage, multiply the fraction by 100 and include the % sign.

Convert to a decimal number.

THINK WRITEWrite the fraction.

Divide the numerator by the denominator.0.875

8 7.000

Write the fraction and the equivalent decimal number. = 0.875

78---

178---

2 )

3 78---

15WORKEDExample

Convert to a percentage.

THINK WRITEWrite the fraction.

Multiply by 100, include the percentage sign and cancel if applicable.

= ( × )%

Multiply the numerators and multiply the denominators. = %

Simplify by writing as a mixed number. = 57 %

2340------

12340------

223402-------- 1005

1-----------

31152

---------

412---

16WORKEDExample

remember1. To write fractions in simplest form, divide the numerator and the denominator by the

highest common factor (HCF) of both.2. To change improper fractions to mixed numbers, divide the numerator by the denominator

and express the remainder as a fraction in simplest form.3. To change a mixed number into an improper fraction, multiply the whole number by the

denominator, add the numerator and write the result over the denominator.4. To add or subtract fractions, form equivalent fractions with the same denominator, then

add or subtract the numerators.5. To multiply fractions, cancel if possible, then multiply the numerators, multiply the

denominators and simplify if appropriate.6. To divide fractions, times and tip, then simplify if possible.7. To add, subtract, multiply or divide mixed numbers, change the mixed numbers to improper

fractions first. (When subtracting, an alternative method is to make the second fraction into a whole number after writing the fractions with the same denominator.)

8. To write fractions in order, express them as equivalent fractions and compare.9. To find a fraction of an amount, multiply the fraction by the amount.

10. To convert a fraction to a decimal number, divide the numerator by the denominator.11. To convert a fraction to a percentage, multiply the fraction by 100 and include the % sign.

remember



Fractions

1 Write the following fractions in simplest form.

a b c d e

f g h i j

k l m n o

2 Convert the following to mixed numbers in simplest form.

a b c d e

f g h i j

3 Convert the following mixed numbers to improper fractions.

a 3 b 4 c 9 d 5 e 3

f 5 g 2 h 1 i 5 j 3

4 Evaluate the following.

a + b − c × d ÷

e + f − g × h ÷

i − + j 2 + 3 k 5 − 4 l 3 × 1

m 6 ÷ 3 n (4 + 3 ) × o − − + p × − ÷ − ÷

5 Find the following.

a of 72 b of 28 c of 36 d of 81 e of 65

f of 117 g of 150 h of 98 i of 192 j of 480

6 Write each of the following sets of fractions in ascending order.

a , , b , , c , ,

d , , , e , , , f 1 , 1 , 1 ,

g , , , h , , i − , − ,

j − , − , − k , − , , − l − , , , − ,

7 Convert each of the following fractions to a decimal number.

a b c d

e f g h

i j k l 1

1E

SkillSHEET 1.10

SkillSH

EET 1.12

SkillSH

EET 1.13

SkillSH

EET 1.11

SkillSH

EET 1.9

SkillSH

EET 1.8Mathcad

Simplifyingfractions8

12------ 24

30------ 14

28------ 72

81------ 45

50------

3549------ 24

64------ 14

22------ 21

36------ 36

108---------

108144--------- 75

500--------- 16

20------ 25

100--------- 33

99------

225------ 31

7------ 49

4------ 37

6------ 21

9------

6816------ 55

20------ 80

15------ 98

10------ 94

12------

34--- 4

5--- 1

3--- 5

6--- 9

10------

67--- 9

11------ 5

8--- 13

20------ 14

17------


12 14--- 3

5--- 2

3--- 5

12------ 2

7--- 3

4--- 8

15------ 5

6---

GC program

Fractions57--- 2

5--- 9

10------ 5

12------ 7

10------ 11

14------ 5

8--- 2

5---

78--- 5

9--- 1

10------ 1

4--- 1

3--- 2

5--- 9

10------ 7

8--- 1

6---

34--- 1

2--- 1

4--- 3

5--- 4

5--- 1

6--- 2

3--- 5

6--- 1

2--- 1

3--- 1

4--- 1

5---


13 58--- 3

4--- 5

6--- 2

3--- 1

5---

49--- 7

10------ 1

7--- 11

12------ 3

16------


14 14--- 1

2--- 3

8--- 3

10------ 1

3--- 7

20------ 1

6--- 3

20------ 1

5---

710------ 2

3--- 13

20------ 1

2--- 2

5--- 7

20------ 11

25------ 19

50------ 1

4--- 5

6--- 7

12------ 11

16------

730------ 3

15------ 1

3--- 2

5--- 5

18------ 5

19------ 5

17------ 1

8--- 1

5--- 1

4---

1925------ 31

40------ 79

100--------- 1

10------ 1

9--- 1

8--- 1

7--- 2

3--- 7

10------ 2

3--- 3

4--- 4

5---


15

EXCEL Spreadsheet

Convertingfractions to

decimals

GC program

Convertingfractions to

decimals

34--- 4

5--- 9

20------ 14

25------

3140------ 7

100--------- 5

16------ 3

80------

310------ 141

200--------- 5

32------ 1

2---


22


8

Convert each of the following fractions to a percentage.

a

b

c

d

e

f g h

i

j

k

l

9a

The fraction is equal to:

b

The expression (

−

−

)

×

(

−

) is equal to:

c

The false statement below is:

d

The fraction as a decimal number is:

e

The fraction as a percentage is:

10

Easisell High had 100 boxes of lollies to sell to raise money for the Children’sHospital. If Year 9 sold of the boxes and Year 10 sold of what was left:

a

how many did each year level sell?

b

how many boxes were left for the other year levels to sell?

c

what fraction of the total was left for the other year levels to sell?

11

Alexa made a cake forthe family to share. Assoon as it was iced,Mum and Alexa eachate of it, Dad ate ,and Freddi and Elliotate each. Whatfraction of the cakewas left for the nextday?

A B C D E

A

−

B

−

C

−

1

D

−

1

E

0

A

>

B

<

C

<

D

>

E

>

A

0.58

B

1.6

C

0.625

D

62

E

5.8

A

0.6%

B

66.67%

C

66 %

D

66 %

E

67%

EXCEL

Spreadsheet

Converting fractions to percentages


1614--- 1

5--- 3

8--- 7

16------

79100--------- 18

25------ 59

80------ 11

20------

Mathca

d

Converting fractions to decimals or percentages

56--- 7

9--- 5

7--- 4

11------

mmultiple choiceultiple choice112192---------

916------ 25

48------ 13

24------ 5

8--- 7

12------

511------ 5

12------ 5

8--- 5

9---

5759504------------ 25

9504------------ 317

3168------------ 857

3168------------

15--- 3

20------ 2

3--- 3

4--- 5

8--- 4

7--- 4

5--- 3

4--- 5

6--- 5

7---

58---

12---

23---

511------ 2

3---

12--- 1

5---

16--- 1

4---

112------


C h a p t e r 1 N u m b e r s k i l l s

23

Percentages

In this section, we will be converting percentages to decimal numbers and to simplefractions. We will be finding the percentage of an amount, expressing one amount as apercentage of another, finding the full amount given some other amount as a percentageof it, and increasing and decreasing amounts by a given percentage.

Converting percentages to decimal numbers

To convert a percentage to a decimal number, divide the percentage by 100.

% means ‘out of 100’.

Converting percentages to fractions in simplest form

To convert a percentage to a fraction in simplest form, place the percentage over100 and simplify where appropriate. If the percentage includes a fraction, change toan improper fraction then divide the percentage by 100 and simplify whereappropriate.

Finding a percentage of an amount

To find a percentage of an amount, change the percentage to a fraction, the ‘of’ to

×

and perform the operation.

Convert 56.25% to a decimal number.

THINK WRITE

Write the percentage. 56.25%Divide the percentage by 100. The number will be smaller so change the position of the decimal point 2 places to the left.

= 0.562512

17WORKEDExample

Convert 22 % to a fraction in simplest form.

THINK WRITE

Write the percentage. 22 %

Change the percentage to an improper fraction and divide by 100.

= ÷ 100

= ×

Simplify. =

29---

129---

2 2009

---------

2009

--------- 1100---------

329---

18WORKEDExample



Expressing one amount as a percentage of anotherTo express one amount as a percentage of another is the same as to convert a fraction toa percentage. Write a fraction with the first amount as the numerator and the secondamount as the denominator, then multiply the fraction by 100.

Finding the full amount, given a percentage of itIf Fred knows that his cheque for $50 000 was 25% of his uncle’s estate, can he workout the value of the estate? To do this, first calculate 1% of the total amount, thenmultiply by 100 to find 100% of the amount. This is known as the unitary method ofpercentages.

Find 34% of 950.THINK WRITE

Write the calculation. 34% of 950

Change the percentage to a fraction, the ‘of’ to × and perform the operation.

= ×

= 17 × 19= 323

1

234

1002----------- 95019

1--------------

19WORKEDExample

Write 2.4 as a percentage of 12.8.THINK WRITE

Write a fraction with the first amount as the numerator and the second amount as the denominator.

Change the fraction to a percentage by multiplying by 100 and including the %.

= ( × )%

Simplify. = 18.75%

Note: The answer could also be left as a fraction.

12.412.8----------

2 2.412.8---------- 100

1---------

3

20WORKEDExample

Find the number, if 62% of the number is 186.THINK WRITE

Write the given information. 62% is 186.Find 1% by dividing both the percentage and the number by the percentage. (That is, ÷ 62.)

1% is 3.

Find 100%, or the whole amount, by multiplying the percentage and the number by 100.

100% is 300.

Write the answer in a sentence to show what is meant.

62% of 300 is 186.

12

3

4

21WORKEDExample



Increasing and decreasing by a given percentageTo increase an amount by a given percentage, add the increase to 100% to find a newpercentage and then find the new percentage of the original amount. Similarly, todecrease an amount by a percentage, subtract the decrease from 100% and find the newpercentage of the original amount.

Alternatively, the percentage increase could be found and added to the original amount.To decrease an amount by a given percentage, subtract the decrease from 100% to

find a new percentage and then find the new percentage of the original amount. Forexample, to decrease 300 by 17% is to find 83% of 300. The answer must be less thanthe original amount because it has been decreased.

Increase 300 by 17%.

THINK WRITE

Add the increase to 100% to find the new percentage of 300.

(17 + 100)%= 117%

Write the calculation using the new percentage which is greater than 100% because it is an increase.

117% of 300

Write the percentage as a fraction out of 100, multiply by the amount and cancel if appropriate.

= ×

Simplify. = 351Write a sentence. If 300 is increased by 17%, it becomes 351.

1

2

31171001----------- 3003

1-----------

45

22WORKEDExample

remember1. To convert a percentage to a decimal number, divide by 100.

2. To convert a percentage to a fraction in simplest form, divide by 100 or write the percentage as a fraction out of 100, then simplify.

3. To find a percentage of an amount, divide the percent by 100 and multiply by the amount.

4. To express one amount as a percentage of another, divide the first amount by the second and multiply by 100.

5. If we need to find an amount, given the percentage of that amount, find 1% and multiply the result by 100.

6. To increase an amount by a given percentage, add the percentage to 100% and find the resulting percentage of the amount.

7. To decrease an amount by a given percentage, subtract the percentage from 100% and find the resulting percentage of the amount.

remember



Percentages

1 Convert each of the following percentages to a decimal number.a 62% b 41% c 38% d 93%e 10% f 2% g 36.7% h 21.25%i 250% j 315.7% k 800% l 0.6%

2 Convert each of the following percentages to a fraction in simplest form.a 97% b 42% c 40% d 70%e 55% f 50% g 25% h 30%

i 62 % j 33 % k 47 % l 8 %

m 81 % n 28 % o 44 % p 16 %

3 Find the following.a 71% of 8 b 65% of 320 c 52% of 1700d 13% of 54 e 83% of 27 f 24% of 175

g 12.5% of 104.48 h 42.5% of 55 i 58 % of 15.6

j 88 % of 3.69 k 23 % of 150 l 33 % of 300

4 Write each of the following as a percentage, giving your answer as an exact decimalnumber where appropriate.a 45 out of 60 b 27 out of 100 c 6 out of 20d 32 out of 50 e 37.5 out of 60 f 0.3 out of 12g 21 out of 48 h 9.6 out of 15 i 18 out of 25j 0.63 out of 1.25 k 15.5 out of 60 l 62.8 out of 80

5a The percentage 123.5% as a decimal number is:

b As a fraction in simplest form 67 % is:

c Which of the following is largest?

d What is 23 % of 45?

e What percentage of 60 is 35?

6 Find the number in each of the following examples.a 12% of the number is 156 b 23% of the number is 368c 15% of the number is 690 d 82% of the number is 328e 16% of the number is 1.44 f 120% of the number is 5.4 g 13% of the number is 32.5 h 68% of the number is 138.72i 2.5% of the number is 22.5 j 31 % of the number is 37.5

A 1.235 B 12.35 C 0.1235 D 12 350 E 123.5

A B C D E

A 57% B 0.6 C D 61% E

A 10.4625 B 10.575 C 10.44 D 10.5 E 10.4

A 58 % B 171 % C 58.3% D 21% E 25%

1F

SkillSH

EET 1.14 WWORKEDORKEDEExample

17

Mathca

d

Percent-ages


18

12--- 1

3--- 1

2--- 1

3---

EXCEL

Spreadsheet

Converting percent-ages to fractions and decimals

911------ 4

7--- 4

9--- 2

3---


19

13---

89--- 1

2--- 1

3---

EXCEL

Spreadsheet

Finding the percentage of an amount


20

EXCEL

Spreadsheet

One amount as a percentage of another


14---

2740------ 11

16------ 53

80------ 269

400--------- 2

3---

2950------ 49

80------

15---

13--- 3

7---


21

14---


C h a p t e r 1 N u m b e r s k i l l s 277 Increase each of the following numbers by the given percentage.

a 45 by 15% b 5800 by 42% c 65 by 20%d 72 by 70% e 106 by 53% f 670 by 3%g 880 by 62 % h 2.5 by 27% i 84 by 41 %

8 Decrease each of the following numbers by the given percentage.a 45 by 15% b 76 by 35% c 120 by 40%d 2722 by 53% e 6530 by 30% f 104 by 7%g 1.2 by 11% h 640 by 42 % i 96 by 16 %

9a If 20% of a number is 80, what is the number?

b If 480 is decreased by 27 %, the result is:

c If 60 is increased by 15%, by what percentage does the result have to be decreasedto obtain 54?

10 If Fred knows that his cheque for $50 000 was 25% of his uncle’s estate, what was thevalue of his uncle’s estate?

11 The Sunflower Clothing Store was having a 15% off sale. If Sam wanted to buy a newpair of jeans, how much would they cost if the original price was $75?

A 400 B 16 C 25 D 96 E 64

A 612 B 132 C 348 D 72.5 E 1745

A 15% B 21 % C 25%% D 78 % E 20%


22

EXCEL Spreadsheet

Increasing ordecreasing by a

percentage12--- 2

3---

12--- 2

3---

mmultiple choiceultiple choiceGAMEtime

Number skills— 0021

2---

1723------ 6

23------

WorkS

HEET 1.2


28


G R E G M c I N T Y R E — P r o d u c t i o n M a n a g e r

Name: Greg McIntyreProfession: Production ManagerQualifications: Certificate of Business Studies (Advertising)Employer: Idea Communications

I decided to undertake the Business Studies (Advertising) course because I was interested in advertising and commercial art. It was also recommended to me by my high school art teacher. At Idea Communications I oversee all work produced in the art studio and by outside suppliers. I check that production specifications are complied with, that budgets are adhered to and deadlines are met. All new jobs require ‘opening’ which entails filling in production brief forms, estimating costs and preparing schedules. Quotations are obtained for all outside supplier costs. A choice is made, but not always because of cost, and orders are issued.

A lot of the work I do involves calculations with fractions, decimals and percentages. For example:1. Estimates involve calculating the number

of hours each task or job will involve, multiplying by the hourly rate for staff required, adding outside costs (printer,

photographers and so on) and adding GST.

2. Schedules are produced by working backwards from the delivery deadline. I determine the sequence of tasks, how long each task will take and the studio members required. All staff time sheets must correlate with the task and the time allocated. Work is often ‘juggled’, depending on priority, to ensure that deadlines are met.

3. Invoice approvals are checked against purchase orders and take into account unquoted items such as freight, tax and corrections.

It seems to me that mathematical skills are vital to a productive enterprise of any kind. Computers and calculators are a useful aid, but without an understanding of the principles, not much can be achieved.

Questions1. What does ‘opening’ a new job entail at

Idea Communications?2. Why is it more beneficial for Greg to ‘work

backwards from the delivery deadline?’3. What other courses offer an advertising

certificate or degree?

Career profile



1 Evaluate −3 − 4 ÷ −2 × (6 − 9).2 Evaluate + − .

3 Evaluate × ÷ .4 Round 0.003 950 01 to 4 significant figures.5 Convert 67% to a decimal.6 Express as a percentage. 7 Write 0.62 as a simple fraction.8 Evaluate 49.312 − 183.8 + 701.6511.9 Change 5 to an improper fraction.

10 Decrease $349 by 83%.

Index notation, square roots and higher order roots

Index notationAn index is a power to which a number is raised. It isthe number of times that the base number is multi-plied together. In the case of 24, 2 is the base and 4 isthe index.

On a calculator this is calculated by using the ^function or the xy function. The keys to press on agraphics calculator to calculate 24 are 2^4 ENTER.

Interesting timesCandice has the choice of investing $1000 at 6 % p.a. or at 6.65% p.a.1 Write 6 % as a decimal number.2 Write 6.65% as a decimal number.3 Which of the two interest rates is greater?4 Using the greater interest rate, how much interest would Candice earn in 1 year?5 If she kept the money (including the interest) in the bank for 3 years, how much

would she have at the end of the 3 years? (Hint: It is not $1200.00.)

23---

23---

247--- 1

4--- 11

14------

1120------ 15

22------ 5

6---

1720------

67---

Express as a fraction in simplest form.THINK WRITE

Write the calculation.

Remove the brackets (optional). =

Simplify both numerator and denominator. =

49---

3

1 49---

3

2 43

93-----

364729---------

23WORKEDExample



Fractions need to be entered using the ÷ key. However,to ensure that both the numerator and the denominatorare raised to the given power, enter the fraction withbrackets. If you wish the answer to be expressed as afraction, remember to press and select1: Frac before pressing . The screen at rightshows the calculation for worked example 23.

Square rootsThe square root of a number is a value which, when multiplied by itself, gives the original number. For example = 8 because 8 × 8 = 64.

Taking the square root of a number is the oppositeoperation to squaring a number. That is, 82 = 64 and

= 8.Generally, on a scientific calculator you would

enter 64 then the key. On a graphics calculator,you would press [ ] then 64 and .

Higher order rootsThe cube root of a given number is a value, which when written 3 times and multiplied,is equal to the given number. For example, = 3 because 3 × 3 × 3 = 27.

The fourth root of a given number is a value which, when written 4 times and multi-plied, is equal to the given number. For example, = 5 because 5 × 5 × 5 × 5 = 625.

On a scientific calculator this is done by using the or key.

To find the cube root of a number, press ,select 4: (, enter the number under the root signand press .

The screen to the right shows the calculations forthe following cube roots: , , .

Graphics CalculatorGraphics Calculator tip!tip! Simplifying fractionsraised to a power

MATH

� ENTER

64

64

2nd ENTER

Evaluate and write the answer, correct to 2 decimal places.

THINK WRITE

Write the given square root.Use a calculator to find the square root.Round the answer as required. ≈ 21.40

458

1 45823

24WORKEDExample

273

6254

x x1y---

Graphics CalculatorGraphics Calculator tip!tip! Finding cube roots and higher order roots

MATH3

ENTER

273 21973 12.563


C h a p t e r 1 N u m b e r s k i l l s 31To find a higher order root, press the number of the

root required (4 for fourth root, 5 for fifth root and soon) then , select option 5: , enter the numberunder the root sign and press . (Note: This optioncan also be used with square roots and cube roots.)

The screen at right shows the calculations for thefollowing higher order roots: , , .

The square root of a fraction can be evaluated by finding the square root of both thenumerator and the denominator. This also applies to higher order roots.

On a graphics calculator, would be entered as

2nd [ ] 36 ÷ 49). Press and select 1: Frac(to express your answer as a fraction) then press

.

MATH x

ENTER

6254 7815 426

Calculate correct to 3 decimal places.

THINK WRITE

Write the given root term.Use a calculator to find the answer.Write the answer correct to 3 decimal places.

= 3.651

6495

1 6495

23

25WORKEDExample

Express as a fraction.

THINK WRITE

Write the given square root.

Rewrite as the square root of both the numerator and the denominator.

=

Evaluate, keeping the answer in fraction form. =

3649------

13649------

2 36

49----------

367---

26WORKEDExample

3649------

MATH �

ENTER

remember1. Use a calculator to evaluate numbers with indices and to find square roots and

higher order roots.2. If the number is a fraction, calculate the numerator and denominator

separately.

remember



Index notation, square roots and higher order roots

1 Calculate the following.a 27 b 35 c 106 d 44 e 53

f 1.72 g 2.54 h 3.13 i 3.052 j 0.83

2 Express the following as fractions in simplest form.

a b c d e

f g h i j

3 Evaluate the following.

a b c d e

f g h i j

4 Evaluate the following, correct to 2 decimal places.

a b c d e

f g h i j

5 Calculate the following.

a b c d

6 Calculate the following, correct to 3 decimal places.

a b c d

7 Express the following as fractions in simplest form.

a b c d

e f g h

8 Calculate the following:a 24 + 53 b 6.12 – 2.13 c 0.84 × 1.23 d 64 ÷ 43

9a To 3 significant figures, is:

b Rounded to 3 decimal places, (1.2)5 is equal to:

10 A large number can be expressed in the form 3.56 × 104. What is the number?

11 The planet Jupiter is approximately 7.78 × 108 km from the sun. Write the number of kilometres as a whole number.

A 67.7 B 16.617 C 67.698 D 17.0 E 16.6

A 2.488 B 2.49 C 1.037 D 1.04 E 6

1G

SkillSH

EET 1.15


23 45---

2 23---

3 12---

6 310------

4 712------

2

89---

5 12---

7 34---

3 67---

4 35---

5

EXCEL

Spreadsheet

Square roots DIY

441 0.09 81 1.44 2116

0.0529 676 132.25 0.0576 7.29

Mathca

d

Index notation, square roots and higher order roots DIY


24 465 65.87 2354 0.986 19.9

8624 1.75 56.78 21.45 5.6

WWORKEDORKEDEExamplexample

25 13.8243 5.378 245 70.72814 7296

468 8693 149.06425 89757

WWORKEDORKEDEExamplexample

26 181------ 9

16------ 121

169--------- 4

121---------

289729--------- 0.36

9.61---------- 0.25

1.44---------- 0.49

2.25----------

mmultiple choiceultiple choice45833

EXCEL

Spreadsheet

Scientific notation DIY

WorkS

HEET 1.3



Calculator computationsA calculator can be used to compute more difficult examples. Generally we enter thecalculation as it is seen; however, we have to remember to bracket everything which isunder a square root sign as well as bracketing the numerator and denominator in a frac-tional calculation.

Calculate the following, expressing the answers correct to 3 decimal places.

a b

THINK WRITE

a Write the calculation. a

Perform the calculation using either a scientific or graphics calculator. (On a graphics calculator, press

[ ] 6.5 ^ 2 + 1.7 ^ 3), then .)

Write your answer correct to 3 decimal places.

= 6.868

b Write the calculation. b

Perform the calculation using a calculator.(On a graphics calculator, press (3.5 ^ 4 − 9.8 ^ 3) ÷ [ ] 10.7 ^ 2 − 53) then .)

Write your answer correct to 3 decimal places.

= −100.889

6.52 1.73+3.54 9.83–

10.72 53–-----------------------------

1 6.52 1.73+2

2ndENTER

3

13.54 9.83–

10.72 53–-----------------------------

2

2ndENTER

3

27WORKEDExample

remember1. Use a calculator to evaluate more difficult examples.

2. Rounding to a given number of significant figures begins at the first non-zero digit.

3. Rounding to a given number of decimal places begins with the first digit after the decimal point.

remember



Calculator computations

1 Calculate the following, expressing the answers correct to 3 decimal places.

a b c

d e f

g h i

j −6.53 + 2.66 k l

m n o

2 Calculate the following, correct to 4 significant figures.

a b c 5.32 − 4.43

d e f

g h i

3

a What is , correct to 4 significant figures, equal to?

b What is , correct to 2 decimal places, equal to?

A 24.40 B −5.026 C 21.03 D −13.69 E 22.65

A 17.66 B −0.68 C 7.84 D 5.15 E 20.08

World populationAt the start of the chapter we looked at estimates of the world population over a 100-year period.1 Calculate the increase in population for each 10-year period.2 Which 10-year period has the largest increase in population?3 What is the predicted increase in population from 1950 to 2050?4 Round each of the populations given in the table to 2 significant figures.5 Use your answers to part 4 to calculate the percentage increase in

population for each 10-year period.6 Which 10-year period has the highest percentage increase in population?7 What is the predicted percentage increase in population from 1950 to 1960?8 Write a few sentences describing your results. How does the increase in

world population affect the environment?9 Parts 5, 6 and 7 used rounded results to calculate the percentage increase.

Design a spreadsheet to perform these calculations with the original population figures.

1H

Mathca

d

Calculator computations DIY


27 516 204– 516 204– 516 204–

65 97–3 9.6 4.1 6.8+× 7.823

46.721 18.6–---------------------- 5.9 2.4–

3.7--------------------- 1

9.7------- 1

3.4-------+

–2.7 3.9–4.6 3.2–×–

--------------------------- 1

59 75+----------------------

65 35+72 98–------------------ 75 9.2+

61 3.7–------------------------ 416 324–

5.8 7.2+----------------------------

147 29–------------------ 56 99+

28 11+------------------

1.282 3.15+ 122 82 72–+2 12 6××

------------------------------- 4.64 2.15–3.43 1.95–-------------------------

25.82 4.12–5.93 6.44–

--------------------------------- 150 29.3–4.12

------------------------- 9632.7

-------------× 96.5 67.5+5.1 2.8–( )2

-------------------------------


49.63 5.6 3.1–×–

5.1 2.78–( ) 1.63 1.05+( )

Year World population

1950 2 555 078 074

1960 3 039 332 401

1970 3 707 610 112

1980 4 456 705 217

1990 5 283 755 345

2000 6 080 141 683

2010 6 823 634 553

2020 7 518 010 600

2030 8 140 344 240

2040 8 668 391 454

2050 9 104 205 830



Use a calculator to answer thequestions to find the puzzle’s code.

7.512

20.898

4.875 13.452 8.1675 26.544 38.064 35.811 13.0801 19.115 7.875 7.75

8.52 20.79 17.8092 33.384 10.56 12.405 43.169 19.272

14.846 25.776 16.41 13.367 14.606 11.64 27.341 26.821 16.453 5.90625 4.12

2.375.068.98+

=

2.38465.0784.9424+

=

2.685.45x

=

3.6724.85x

=

21.32.5

=

=18.9

3.2=

=

15.73 – 8.218=

the average of2.7, 3.6, 9.4 and3.8

=

=

=

the mean of21.8, 15.24,7.62 and 31.8

=

=

the mean of6.78, 13.24,8.91 and 3.74

=

=

the sum of 3.74,8.94, 0.87, 2.64,3.17 and 1.43

=

=

the sum of 8.34,9.27, 5.416,18.203 and 1.94

=

=

the average of16.74, 13.29and 4.89

=

=

the sum of 8.73,9.21, 2.643, 8.4,2.976 and 1.425

=

=

6.2 + 3.05 + 1.79+ 8.43 + 0.95+ 3.781 + 2.62

=

=

the differencebetween 7.054and 21.9

=

=

the product of2.75 and 3.84

=

=

34.293 less17.84

=

=

84.7 less57.359

=

=

10.34 multipliedby 1.265

=

=

12.4 ÷ 1.6=

=

16.48 ÷ 4=

=

18.9 ÷ 2.4=

=

18.237 – 4.87=

=

72% of 35.8=

=

38% x 35.4=

=

81% of 25.8=

=

24% of 158.6=

=

5.28 x 3.65=

=

103.8 x 0.345=

=

21% of 126.4=

=

Which piece of Which piece of Australian curAustralian currrency ency ffeatureatures scenes fres scenes from aom aviation historviation history?y?



ApplicationsThe skills learnt in this chapter can now be applied to problems relating to real-lifesituations. In this part the problems will be simplified to basic mathematicalexpressions so we can use mathematical skills to determine the answers.

The temperature at Mt Buller drops steadily at night by 1.8°C per hour. The temperature at 6 pm is 4.5°C. What is the temperature at 2 am?

THINK WRITEFind the number of hours between 6 pm and 2 am.

Hours between 6 pm and 2 am: 6 + 2 = 8

Write a mathematical expression for the total drop in temperature.

Temperature drop: 8 × 1.8

Write a mathematical expression for the temperature drop from 4.5°C.

Temperature at 2 am: 4.5 − 8 × 1.8

Use the order of operations to solve the problem.

= 4.5 − 14.4= −9.9

Write the answer in a sentence. The temperature at 2 am is −9.9°C.

1

2

3

4

5

28WORKEDExample

In a school of 460 students, half of them buytheir lunch from the canteen, while bring lunch from home. The rest do not eat lunch. How many students do not eat lunch?

THINK WRITE

Find the number of students who buy lunch. Students who buy lunch: × = 230

Find the number of students who bring their lunch.

Students who bring lunch: × = 184

Find the number who eat lunch by adding these amounts.

Students who eat lunch: 230 + 184 = 414

Find the number who do not eat lunch by subtracting these amounts from the total number of students.

Students who don’t eat lunch: 460 – 414 = 46

Write the answer in a sentence. The number of students who do not eat lunch is 46.

25---

112--- 460

1---------

225--- 460

1---------

3

4

5

29WORKEDExample



Applications

1 a The temperature in Young drops steadily by 1.7°C per hour. The temperature at5 pm is 8°C. What is the temperature at 2 am?

b The temperature in Doblin at 4 am is −5°C. The temperature rises steadily by 2.6°C per hour. What is the temperature at 10 am?

c The winter temperature at Dubbo drops from 13°C at 3 pm to −6°C at 4 am. Howmany degrees does the temperature drop?

d If the minimum temperature in Canberra on Monday is −7°C and it rises by 16°C tothe maximum temperature, what is the maximum temperature that day?

e The temperature range on Tuesday in Milday was 24°C. If the maximum tempera-ture was 10°C, what was the minimum temperature?

Tessa’s wage is increased by 3.2%. If her old wage is $675 per week, what is her new wage?

THINK WRITE

Find the new percentage by adding the percentage increase to 100%, which is the original wage.

100% + 3.2% = 103.2%

Find the new wage. New wage: 103.2% of 675= 696.60

Answer the question in a sentence. The new wage is $696.60.

1

2

3

30WORKEDExample

remember1. Read the question carefully.2. Highlight or underline important information.3. Write a mathematical expression or calculation for the given situation.4. Use mathematical skills to evaluate the expression.5. Write a sentence to answer the question.

remember

1I


28


2 a

Roger wins $150 on a poker machine but then loses $340 the restof the night. How much worse off is he than when he started?

b

A bank statement shows a balance of

−

$53.76. Fran deposits$156.80. What is the new balance?

3 a

What is the cost of 36 litres of petrol at 71.9c per litre?

b

Potatoes cost $1.80 per kilogram. How much will 8 kilograms of potatoes cost?

c

Donna buys 5 exercise books at $1.35 each and 4 pens at 45c each. What is herchange from $10?

d

Tony is paid $15.60 per hour. How long must Tony work in order to earn $140.40?

e

Steve earns a salary of $41 000 per annum. What is his weekly salary if 1 year is52.143 weeks?

f

Janice pays for the following amounts of petrol on a trip from Sydney toMelbourne: 23 L at 81.9c per L, 36 L at 85.8c per L, 31 L at 90.5c per L. What wasJanice’s total petrol bill for the journey?

g

A certain body is 68% fluid. The body’s volume is 5.8 L. How much of this body is fluid? Give the answer in millilitres.

4

A school has 570 students. For sport of the students choose soccer, choose foot-ball and the rest play tennis. How many play tennis?

5 a

Yan has a choice of of $40or of $39. Which choicewould give him more money?

b

Of the 1881 people who livein Galaxy, are women. Howmany of the inhabitants aremen?

c

At a factory, 1 out of 150light bulbs are faulty. If thefactory makes 1200 lightbulbs, how many are faulty?

d

Teri is paid $480 per week.Of this, goes to rent, tofood, to other essentialsand the rest is saved. Howmuch per week does Terisave?

e

In a biscuit mixture, issugar. If there are 120 gramsof sugar in the mixture; howmany grams of mixture isthere?

6

Jay earns $12.50 per hour and works a 35-hour week. He obtains a 4.5% pay increase.What is his new weekly wage?


29

310------ 1

3---

35---

23---

49---

920------ 2

5---

110------

38---


30


C h a p t e r 1 N u m b e r s k i l l s 397 a In a township, 68% of the people go to church. There are 5500 people in the town.

How many go to church?b In an election, 43% vote Liberal, 41% Labor, 8% Democrat and the rest vote for

minor parties.i What percentage of voters vote for minor parties?ii If there are 15 500 registered voters, of which 95% vote at the election, how

many voters do not vote for either of the 2 major parties (Liberal or Labor)? c Roald achieves 39 out of 60 for a test while Serena achieves 25 out of 40. Who per-

formed better and by what percent?d A car is discounted by 15%. If the

customer pays $16 150, what was the price of the car before it was discounted?

8 The distance from Earth to our closest neighbouring galaxy, the Large Magellanic Cloud, is approximately 1.608 × 1018 km. Write this distance as a basic numeral.

9a The temperature at Fresia is 4.8°C

at midday. The temperature falls steadily by 1.3°C per hour. What is the temperature in Fresia at 1 am the following morning?

b At a school, of Year 9 students study history, study geography and the reststudy commerce. If there are 180 students in the whole of Year 9, how manystudents study commerce?

c The Johnson family pay council rates at 1.008 12 cents in the dollar. If their land isvalued at $60 000, how much do they pay in rates?

d Jeans are discounted by 20%. The discounted price is $30 less than the usual price.How much are the discounted jeans?

A −12.2° B –12.1° C −12° D −9.5° E 3.11°

A 153 B 80 C 27 D 21 E 45

A $60 487.20 B $604.87 C $6048.70 D $604.90 E $60.50

A $24 B $45 C $120 D $150 E $50


35--- 1

4---



Copy the sentences below. Fill the gaps by choosing the correct word or expression from the word list that follows.

1 The order of operations is first, followed by multiplication ordivision left to right, then finally addition or subtraction, left to right.When using a scientific calculator, work the whole question from left toright.

2 Rounding to a given number of decimal places begins with the first digitafter the decimal .

3 Rounding to a given number of figures begins with the firstnon-zero digit of the complete number.

4 To convert a decimal number to a fraction, place the digitsover 10, 100, 1000 . . . (depending on the number of decimal places), andsimplify if appropriate.

5 To convert a fraction to a decimal number, divide the by thedenominator.

6 To convert a decimal number to a percentage, multiply the number by 100.

7 To convert a percentage to a decimal number, thepercentage by 100.

8 To convert a fraction to a percentage, multiply the by 100.

9 To convert a percentage to a fraction, put the over 100 andsimplify if appropriate (or divide by 100 if the percentage has a fraction).

10 To find a percentage of an amount, divide the percentage by 100 andmultiply by the .

11 To express one amount as a percentage of another, divide the firstamount by the second amount and multiply by .

12 To find the full amount, given some other quantity is a percentage of theamount, determine 1% by dividing, then by 100 to find thefull amount.

13 To increase an amount by a given percentage, the percentageto 100% and find that percentage of the amount.

14 To an amount by a given percentage, subtract the percentagefrom 100% and find that percentage of the amount.

summary

W O R D L I S Tadddecreasedividepoint

decimalsignificantnumeratorbrackets

100multiplypercentagefinite

amountfraction



1 Evaluate each of the following.a (16 + 12) ÷ 7 b 7 × 6 − 12 ÷ 3 c [3 × (7 − 5)] ÷ 2 d 12 + 8 × 5 ÷ 4

2 Evaluate each of the following.a 5 × 9 + (60 − 6) ÷ 9 b −6 − 4 × −2c [(8 × −4 + 7) + 7] ÷ −3 d 36 ÷ −6 − 4 × −5 + 6

3 Insert operation signs to make the equation true: 6 K −5 K 3 K 2 = −12

4 Round 5689.7143 to:a 2 decimal places b 2 significant figures.

5 Round 2156.586 to:a the nearest ten b the nearest tenth.

6 A rounded number is 13.50. The original number could have been:

7 Evaluate these expressions.a 0.375 + 4 × 9.06 b 14.4 ÷ 1.2 − 0.65 × 23

8 Convert each of the following decimal numbers into a fraction in simplest form.a 0.875 b 0.24 c 0.55 d 0.365 e 0.248f 0.13 g 0.75 h 0.575 i 0.372 j 0.4

9 Evaluate these expressions.a + × b × ( − ) ÷

10 Convert each of the following to a percentage.a 0.71 b 2.4 c d

11Which of the following statements is false?

12 Evaluate the following.a of 56 b 65% of 590 c 0.89 of 420

13 Convert each of the following to a decimal number.a 12% b 34.6% c d

14 Convert each of these percentages to a fraction in simplest form.a 52% b 130% c 28 %

15 Decrease 240 by 24%.

16 If 45 is 3% of a number, what is the number?

17 Place the following in ascending order.

a 57%, 0.6, b , 0.245, 23 %

A 13.5 B 13.52 C 13.507 D 13.495 E 13.4938

A < B > C < D < E >

1A

CHAPTERreview

1B

1B1C

1C

1Cmmultiple choiceultiple choice

1D

1D

1E14--- 3

5--- 5

8--- 2

3--- 7

12------ 1

4--- 5

18------

1E1516------ 1

6---

1Emmultiple choiceultiple choice

34--- 19

25------ 5

16------ 3

10------ 13

40------ 7

20------ 8

11------ 18

25------ 6

7--- 17

20------

1F37---

1F78--- 33

4------

1F47---

1F1F1F29

50------ 6

25------ 1

2---



18 Place the following in descending order.

a , 82%, 0.83 b , 41%, 0.416

19 Evaluate each of the following.

a b c

20 Evaluate each of the following.a 2.52 × 3.53 b 2.5 × 102 × 3.5 × 103

21 Calculate each of the following correct to:i 3 decimal places ii 3 significant figures.

a b

22The temperature in Warialda at 7 pm is 3.5°C and at 3 am is −3.7°C. What is the average drop in temperature per hour between the two readings?

23In the first semester test Dominic scored 37 out of 50, while in the second semester test he scored 59 out of 80. Which of the following statements correctly compares his second semester result with his first semester result?

24 Rhonda pays $27.93 for petrol. If the price of petrol is 66.5 cents per litre, how many litres did Rhonda put into her car?

25 A dam is 58% full. It presently holds 302 470 L. How many more litres of water will fill the dam to 100% of capacity?

26 Simon visits his parents in a country town 1575 km away from his home. He drives of the way the first day and intends to reach the town the next day.a How far does he need to drive

on the second day? b Simon drives for 12 hours

on the first day. What is his average speed on that day?

c Simon’s car averages 15 km per litre of petrol. What is his petrol cost for the trip if the price of petrol is 69.9 cents per litre?

A 0.72° B 0.02° C 0.025° D 0.9° E 0.8°

A increased by % B decreased by % C same result

D increased by 28.7% E decreased by 28.7%

1F 45--- 5

12------

1G1296 4.2025 1.3313

1G

1H87 54+87 54–------------------ 789 614–3

654 437–----------------------------

1I mmultiple choiceultiple choice

1I mmultiple choiceultiple choice

14--- 1

4---

1I

1I

1I 1625------

testtest

CHAPTERyyourselfourself

testyyourselfourself

1


ch 01

Education

order of d

correct order of operations

number of eggs

following order

victoria d

correct answer

numbers diy b

use order of operations