© t madas. fact © t madas to convert any fraction into decimal form, carry out the division: to...

$: © T Madas. Fact © T Madas To convert any fraction into decimal form, carry out the division: To convert any decimal into a fraction, write it as a fraction$
© T Madas

© T Madas

Fact

© T Madas

To convert any fraction into decimal form,carry out the division:716 7 16= ¸ 0.4375=

To convert any decimal into a fraction,write it as a fraction out of 10, 100, 100 etc: 7

100.7=

38100

0.38 =

4061000

0.406 =

31022.3=

51

5=

4641

464 =

2310=

Note that recurring decimals need some algebraic manipulation before converting

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The rule for Addition & Subtraction of fractions is:

a bc c± a b

c±=

For example:4 27 7

+ 67

=

5 16 6

- 23

=46

=

When the denominators of the fractions are different we must find a common denominator before adding or subtracting them.

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The rule for Addition & Subtraction of fractions is:

a bc c± a b

c±=

For example:4 27 7

+ 67

=

5 16 6

- 23

=46

=

2 75 15

+ =15 15

+ =6 7 1315

3 58 12

+ =24 24

+ =9 10 1924

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Multiplication of fractions follows the rule:

a cb d

´ = acbd

=a c´b d´

For example:4 25 3

´ 815

=

5 24 9

´ 518

=1036

=

3 25

´ 21

´35

= 65

=

What is the physical meaning of fraction multiplication?

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Find of 23

15

2 153

´

Find of 15

23

1 25 3

´

215

=

215

=

This is in analogy of multiplication of decimals:

0.7 x 0.8 finds 0.7 of 0.8or 0.8 of 0.7

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Division of fractions follows the rule:

a cb d

¸ ab

= adbc

=dc

´

Two fractions such that one is obtained by turning the other “upside down”

Reciprocals

Reciprocals are said to be inverses of each other with respect to the operation of multiplication

The reciprocal of is because:

23

32

32 13 2

´ =

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a cb d

¸ ab

= adbc

=dc

´


Reciprocals


The reciprocal of is because:

58

85

5 8 158

´ =

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a cb d

¸ ab

= adbc

=dc

´


Reciprocals


The reciprocal of is 3 because:

13

1 3 13

´ =

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a cb d

¸ ab

= adbc

=dc

´


Reciprocals


The reciprocal of 7 is because:

17

17 17

´ =

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a cb d

¸ ab

= adbc

=dc

´


Reciprocals


The reciprocal of 2.33 is because:

12.33

12.33 12.33

´ =

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a cb d

¸ ab

= adbc

=dc

´

Examples of fraction division:4 25 3

¸ 45

= 32

´ 1210

= 65

=

3 24

¸ 34

= 12

´ 38

=

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Three adverts appear on a page of a newspaper.

The 1st advert covers 1/4 of the page.

The 2nd avert covers 1/8 of the page.

The 3rd advert covers 3/16 of the page.

What fraction of the page is not covered by adverts?14

18+ +

316 =

x 2

x 2

x 4

x 4

416

216+ +

316= 9

16

If is covered by adverts

then is not covered by adverts.

916

716

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1. How many quarters in 2 ?


3. How many tenths in 2 ?


5. How many twelfths in 1 ?

12

34

31035

13

342 =11

4

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12

34

31035

13

342 =11

4123 = 7

2 =144

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12

34

31035

13

342 =11

4123 = 7

2 =144

3102 =23

10

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12

34

31035

13

342 =11

4123 = 7

2 =144

3102 =23

10351 = 8

5 =1610

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12

34

31035

13

342 =11

4123 = 7

2 =144

3102 =23

10351 = 8

5 =1610

131 = 4

3 =1612

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A rectangle is 6⅝ cm long by 3½ cm wide.1. Calculate it perimeter.2. Calculate its area.

6⅝ cm

3½

cm to find the

perimeter:586 1

23+ 586 1

23++ =

Method 1

5819+ 5

8+ =

10819+ =5419+ =

÷ 2

÷ 2

1419+ =1

1420 cm

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6⅝ cm

3½

cm to find the

perimeter:586 1

23+ 586 1

23++ =

Method 2

538

72+ 53

872++ =

1068

142+

x 4

x 4=

1068

568+ =

1628 =

2820

1420 cm

=

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6⅝ cm

3½

cm

to find the area:5

86 123x =

538

72x =

37116

31623 cm2

= 37 116

2 3

5 3

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Roulla used half of her exercise book in the autumn term.So far this term she has used a further one sixth of it.

1. What fraction of her exercise book has she used so far?2. How many pages does her exercise book have if she has 30 pages left?

12

16+

x 3

x 3= 3

616+ = 4

6 = 23

÷ 2

÷ 2

If she has used of her exercise book

she must have of it left.

If of her exercise book is 30 pages

then the entire exercise book must have 90 pages

23

13

13

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Johnny spent his monthly allowance as follows:

of it on lunch and food snacks

of it on two music CDs

of it on a new book

1. What fraction of his monthly allowance has he got left?2. If he is left with £6 what is his monthly allowance?

251316

25

13+ +

16 =

x 10

x 10

x 6

x 6

x 5

x 5

1230

1030+ +

530= 27

30 = 910

÷ 3

÷ 3

Johnny has spent of his monthly allowance

so he must have of his monthly allowance left.

If of his monthly allowance is £6

then his monthly allowance must be £60

910

110

110

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Edmonton is 3⅝ miles away from Southgate.Barnet is 2¾ miles away from Southgate.How much further from Southgate is Edmonton than Barnet?

583 3

42– = 298

114– = 29

8228– = 7

8

x 2

x 2

Edmonton is ⅞ of a mile further from Southgate than Barnet is.

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Ethan works day and night shifts in alternating weeks.He works:5 days for 7¾ hours per day during his “day-shift” week.5 nights for 6½ hours per night in his “night-shift” week.Calculate how many hours he works a fortnight.

Week 1:5 x 3

4 =7 5 x314 = 155

4 = 3438

Week 2:5 x 1

2 =6 5 x132 = 65

2 = 1232

Adding the two figures:3

438 1232+ =70 1

41+ = 1471

Ethan works 71¼ hours every fortnight

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[You may shade the shapes below to help you with your answer]

Calculate4 12÷3

4

124 3

4÷ = 92

34÷ = 9

243x = 36

6 = 6

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Bethany uses ⅝ metres of ribbon to wrap up a gift box.How many identical gift boxes can she wrap using a 7½ metre roll of ribbon?

127 5

8÷ = 152

58÷ = 15

285x = 120

10 = 12

Bethany can wrap up 12 such boxes

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There is of the original amount left

1. What fraction of the original amount of juice remains in the carton?

2. Who drunk the most juice? [you must show full workings]

Tony drank of a full carton of orange juice.

His sister Alice drank of what was left.

13

34

If Tony drank of a full carton there is of a full carton left.

Therefore Alice drank of of a full carton

The operation that finds “something” of “something” is:multiplication

13

34

23

23

34

23x = 6

1212= Alice drunk half the carton

13

12+

x 2

x 2= 2

636+ = 5

6

x 3

x 3

16

[who drank the most?]

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Let us solve the problem pictorially

Tony drunk of a full carton

Alice drunk of what was left

We are left with of a full carton

Tony drunk of a full carton

Alice drunk of a full carton

Which is the same as

1334

16

1336

12

1. What fraction of the original amount of juice remains in the carton?

2. Who drunk the most juice? [you must show full workings]

Tony drank of a full carton of orange juice.

His sister Alice drank of what was left.

13

34

© T Madas

13.548

6.7524

The school day in Northgate School starts at 08:45 and finishes at 15:30.What fraction of a 24 hour day does the school day take up? [Give your answer in its simplest form.]

08:45

09:00

15:00

to

to

to

09:00

15:00

15:30

15 minutes

6 hours

30 minutes

6 hours, 45 minutes6¾ hours6.75 hours

=x 2

x 2= 27

96932=

x 2

x 2

÷ 3

÷ 3

6752400

6.7524 =

x 100

x 100= 27

96932=

÷ 25

÷ 25

÷ 3

÷ 3

© T Madas

To make a litre of a certain fruit punch, fruit juices are mixed in the following proportions:

1. What fraction of a litre corresponds to kiwi fruit juice?

2. What is the ratio of these juices as apple : cranberry : kiwi ?

3. What fraction of a litre from each fruit juice is contained in 2½ litres of this fruit punch?

total: 1 litre

of a litrekiwi

of a litrecranberry

of a litreapple

amounttype of juice

5124

15

1960

512

415+ =

x 4

x 4

x 5

x 5

2560

1660+ = 41

60

1 4160– =60

604160– = 19

60

© T Madas





total: 1 litre

of a litrekiwi

of a litrecranberry

of a litreapple

amounttype of juice

5124

15

1960

512

415: :

x 4

x 4

x 5

x 5

1960

2560

1660: : 19

60

x 60 x 60 x 60

25 : 16 : 19

© T Madas





total: 1 litre

of a litrekiwi

of a litrecranberry

of a litreapple

amounttype of juice

5124

15

1960

=

=

=

=

of a litrex

of a litrex

of a litrex

of a litrex5124

15

1960

5252

52

52

2524

2030

23

95120

1924

52

=

=

© T Madas

´ 358

34

1

58

2

272

Calculate the area of the following trapezium:

=34

1 74

=272 16

7

=58

2 218

( )´12

74 + 21

8=A ´ 16

7

( )= ´12

148

+ 218

´ 167

= 12

´ 167

5= 25 cm

© t madas. fact © t madas to convert any fraction into decimal form, carry out the division: to...

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multiplication of fractions

division of fractions

convertingthe rule

examples of fraction

cm3 cmto

analogy of multiplication

decimal form

recurring decimals