mat 080 study guide & assignments

MATH 070 STUDY GUIDE & ASSIGNMENTS (Revised: Summer 2012)

CERTIFY mode is where you will complete your Hawkes assignments.

You may use the PRACTICE mode in a lesson before attempting to certify in the lesson.

Most lessons require 80 - 85% of the assignment to be correct to certify.

After you have certified in a lesson, a certificate will appear on the monitor, indicating that you

have successfully certified in that lesson.

If you do not receive a certificate, you should practice more problems and then attempt to certify

the lesson again.

Your homework is not complete until you have submitted your certificate electronically on or

before the lesson’s due date.

Hawkes certificates are automatically submitted if you are connected to the internet. If you are not

connected to the internet, save your certification on a portable storage device and go to

http://www.hawkeslearning.com/ROCKINGHAMCOMBO to submit your assignments at a later

date when you have access to the internet.

Some assignments are to be completed using paper and pencil. These are located in the textbook

or in the RCC Moodle site for this course.

STUDENT NAME: ______________________________________________________

HAWKES COURSE ID: ROCKINGHAMCOMBO

MY HAWKES ACCESS CODE IS: _________________________________________

UNIT 0: Prerequisite Unit

Lesson Section Topic Homework Assignments

1 WS Order of Operations with Whole

Numbers Worksheet A, #1-10.

2 Text &

WS Operations with Fractions

2nd Ed: Page 70, #3, 5, 6, 8,

15, 16, 17, 21, 23, 24.

Worksheet A, #11-23.

3 WS Operations with Decimals Worksheet A: #24-32.

http://www.hawkeslearning.com/ROCKINGHAMCOMBO

UNIT 2: Introduction to Algebra

Lesson Section Topics Homework Assignments

1 2.1c Evaluating algebraic expressions Hawkes 2.1c

Worksheet A, # 1-7

2 2.1a

Variables and Algebraic

Expressions, Terms and Coefficients Hawkes 2.1a and 2.1b

Worksheet A, #8-13 2.1b Simplifying Expressions

3 Distributive Property Hawkes – Ch. 2 Review

Worksheet A, #14-23

4 2.2 Translation of Verbal Expressions

Hawkes 2.2

2nd

Ed., Page 114, Translate and

simplify if possible # 21, 24, 25, 29, 30,

33, 35, 36.

Worksheet A, #24-28

Review

UNIT 2 TEST

UNIT 1: Real Numbers

Lesson Section Topic Homework Assignments

1 1.1a Introduction to Real Numbers Hawkes 1.1a and 1.1b

Worksheet A: #1,2, 3 1.1b Absolute Value

2 1.2 Addition of Real Numbers Hawkes 1.2

Worksheet A: #4-13

3 1.3 Subtraction of Real Numbers Hawkes1.3

Worksheet A: #14-20

4 1.4 Multiplication & Division of Real Numbers Hawkes 1.4

Worksheet A: #21-28

5 1.8 Order of Operations Hawkes 1.8

Worksheet A: #29-34

Review

UNIT 1 TEST

UNIT 3: Linear Equations


1

2.3a Solutions to Equations, Linear

Equations of Form Ax+B=C

Hawkes 2.3a, 2.3b, 2.4

Worksheet A, #1-5 2.3b

2.4

2 2.5

Linear Equations involving

Parentheses and of Form

Ax+B=Cx+D

Hawkes 2.5

3 WS A Equations with Fractions Worksheet A, #6-15

4 Text - 3.1 Literal Equations 2

nd Ed. Page 186, #29, 31, 33, 36, 37, 38, 40,

41, 43, 46, 47, 49, 54, 55, 56, 57, 58, 59, 60.

5 3.4 Linear Inequalities & Graphs Hawkes 3.4

6 2.6a Applications – Direct

Translation Hawkes 2.6a

7 WS B Applications - Geometry Worksheet B, #1-10

Review

UNIT 3 TEST

UNIT 4: Graphing Linear Equations


1 4.1 Cartesian Coordinate

System

Hawkes 4.1

2nd

Ed: Page 264, #3,5,6.

2 4.2 Graphing Lines

Hawkes 4.2

2nd

Ed: Page 279,

Graph by making a table of values: #7, 11, 15, 16,

18, 27, 31, 33, 35, 36, 38, 43, 45, 47.

Worksheet A, #1 - 6.

3 Text - 4.3 Slope and Slope-Intercept

Form

2nd

Ed: Page 290, #1-8

Worksheet A, #7-18.

4 4.4a Equations of Lines Hawkes 4.4a

5 4.6 Linear Inequalities Hawkes 4.6

2nd

Ed: 32, #9, 11, 13, 17, 19, 23.

6 Using Linear Graphs LAB 4

Review

UNIT 4 TEST

UNIT 5: Exponents and Scientific Notation


1 WS A Definition of Exponents Worksheet A, #1-20.

2 Rules of Exponents – Non-negative

exponents Hawkes, Chapter 5 Review

3 WS B Definition of Negative Exponent Worksheet B, #1-25.

4 5.1, 5.2a Rules of Exponents – Integer exponents Hawkes, 5.1, 5.2a

5 5.2b, WS C Scientific Notation Hawkes, 5.2b

Worksheet C, #1-10.

6 Unit Analysis LAB 5

Review

UNIT 5 TEST

UNIT 6: Polynomials


1 5.3, 5.4 Identifying Polynomials; Addition and

Subtraction of Polynomials Hawkes 5.3 and 5.4

2 5.5, 5.6a,

5.7a

Multiplication of Polynomials, FOIL,

Division by Monomials Hawkes 5.5, 5.6a and 5.7a

3 WS A Order of Operations with Polynomials Worksheet A, #1-12.

4 6.1b Greatest Common Factor Hawkes 6.1b

5 6.2 Trial & Error – Leading Coefficient 1 Hawkes 6.2

6 6.3a, 6.4a Trial & Error, Difference of Squares Hawkes 6.3a and 6.4a

Review

UNIT 6 TEST

MATH 070 UNIT 0 WORKSHEET A Evaluate each expression.

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

Perform the indicated operations.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

26.

27.

28.

29.

30.

31.

32.

ANSWERS:

MATH 070 UNIT 1 WORKSHEET A

1. Find the opposite of each number:

2. Simplify.

3. Evaluate:

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

26.

27.

28.

29.

30.

31.

32.

33.

34.

L

E

S

S

O

N

1

L

E

S

S

O

N

2

L

E

S

S

O

N

3

L

E

S

S

O

N

4 L

E

S

S

O

N

5


ANSWERS:

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

26.

27.

28.

29.

30.

31.

32.

33.

34.

L

E

S

S

O

N

1

LESSON 2

LESSON 3

LESSON 4

LESSON 5


Evaluate each expression using the indicated values.

1.

2.

6.

7.

;

3.

4.

5.

Simplify each expression.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

Translate and simplify if possible.

24.

25.

26.

27.

28.

Answers:

MATH 070 UNIT 3 WORKSHEET A Determine whether the given number is a solution to the equation.

1.

2.

3.

4.

5.

It is often easier to solve an equation involving fractional coefficients if the fractional coefficients are eliminated. This can be done by multiplying each side of the equation by the common denominator of the fractions. NOTE: Eliminating fractions can be used only when solving equations and inequalities.

Example:

Exercises: Eliminate fractions before solving each of the equations below.

6. x

3 = -2 7.

2

3x

5

2 =

-1

2 8. x

2

3 =

-1

4 9.

x

5 2 = 3

10. x

2 + 4 =

1

3x 1 11.

1

2x 7 =

3

5x + 4 12.

3

2x + x + 2x – 4 = 7

13. 2

1(x + 3) =

4

x 14.

2

1x –

10

1

5

x x = 3 15.

3

x + 2 =

4

3x – 3

ANSWERS: 6) x = -6 8) x = 5

12 10) x = -30 12) x = 3 14) x =

2

15

Multiply both sides of the

equation by the common

denominator of 12.

Subtract 9x from both sides.

Add 72 to both sides.

Divide both sides by negative 3.

11

MATH 070 UNIT 3 WORK SHEET B

The perimeter of a geometric figure is a measure of the distance around the figure. When the sides of a geometric figure are line segments, the perimeter of the figure can be found by adding the lengths of the sides.

Triangle a b c Perimeter = a + b + c EXAMPLE 1: The perimeter of a rectangle is 26 ft. The length of the rectangle is 1 ft. more than twice the width. Find the length and width of the rectangle. SOLUTION: Draw a picture of your figure. 1. Name and represent the unknowns with variables. 2x + 1 Name Representation x x Width: x Length: 2x + 1 2x + 1 2. Add the lengths of the sides of the rectangle and set the sum equal to the perimeter. (x) + (2x + 1) + (x) + (2x + 1) = 26 (x + 2x + x + 2x) + (1 + 1) = 26 6x + 2 = 26 6x = 24 x = 4

3. To find the length & width, substitute the value of x, which is 4, into the representation of the length and width.

Length: 2 x + 1 Width: x = 2(4) + 1 = 4 = 9 ANSWER: The length is 9 ft. and the width is 4 ft.

12

In a triangle, the sum of the measures of all three angles is 180O. B

) A C (

A + B + C = 180o

Two special triangles are show below.

A right triangle has one right angle (90O

). The other two angles are acute (less than 90O

). An isosceles triangle has two equal angles and two equal sides. Two equal sides and two equal angles

90o ) ( Right triangle Isosceles triangle

EXAMPLE 2: In a certain right triangle, the measure of one of the acute angles is twice the measure of the smallest angle. Find the measure of the other two angles.

SOLUTION: Draw your picture. x

1. Name and represent the angles:

smallest = x second = 2x 90o

right = 90o 2x

2. Substitute the values into the angles of a triangle formula and solve the equation.

A + B + C = 180 x + 2x + 90 = 180 3x + 90 = 180 3x = 90

x = 30o

3. To find the other two angles, substitute the value of x, which is 30o, into their representatives.

smallest: x second: 2x

= 30o = 2(30) = 60

o

ANSWER: The measures of the other two angles are 30o and 60

o.

13

Exercises: 1. In an isosceles triangle, two sides are equal. The length of one of the equal sides is 3 times the

length of the third side. The perimeter is 21 m. Find the length of each side. 2. The perimeter of a rectangle is 42 m. The length of the rectangle is 3 m less than twice the

width. Find the length and width of the rectangle. 3. The perimeter of a triangle is 110 cm. One side is twice the second side. The third side is 30

cm more than the second side. Find the length of each side. 4. The perimeter of a rectangle is 48 m. The width of the rectangle is 8 m less than the length.

Find the length and width of the rectangle.

5. In an isosceles triangle, the measure of one angle is 5 less than three times the measure of one of the equal angles. Find the measure of each angle.

6. The measure of the first angle of a triangle is twice the measure of the second angle. The

measure of the third angle is 10 less than the measure of the first angle. Find the measure of each angle.

7. The measure of the first angle of a triangle is three times the measure of the second angle. The

measure of the third angle is 33 more than the measure of the first angle. Find the measure of each angle.

8. In an isosceles triangle, the measure of one angle is 12 more than twice the measure of one of the equal angles. Find the measure of each angle.

9. The measure of one angle of a right triangle is 3 less than twice the measure of the smallest angle. Find the measure of each angle.

10. In a triangle, the measure of one angle is 5 more than the measure of the second angle. The

measure of the third angle is 10 more than the measure of the second angle. Find the measure of each angle.

ANSWERS:

1) 9m, 9m, 3m 3) 20 cm, 40 cm, 50 cm 5) 37, 37, 106

7) 63, 21, 96 9) 31, 59, 90

14

MATH 070 UNIT 4 WORK SHEET A

PART I: Graphing Lines

Graph each line. Give a table of values.

PART II: DETERMINING SLOPE FROM THE GRAPH

The slope of a line can be determined from its graph. The slope formula requires two points, whose

coordinates can be read from the graph. These coordinates are substituted into the slope formula,

m =

12

12

xx

yy

.

Example 1: Find the slope of the line graphed.

Let P1 = (-1, -3) and

P2 = (2, 1)

m =

12

12

xx

yy

=

)1(2

)3(1

=

3

4

Exercises: Find the slope of each line. 7. 8. 9..

15

10. 11. 12.

ANSWERS: 7. 4

5 9.

2

1 11. –1

PART II DETERMINING SLOPE FROM THE EQUATION OF THE LINE

The slope of a line can also be found directly from its equation. Once any two points on the line have

been determined, the slope formula, m =

12

12

xx

yy

, is used.

Example 1: Find the slope of the line 3x – 2y = 8 by finding two points.

Solve for y. 3x 2y = 8

-2y = -3x + 8

2

y2

=

2

8x3

y = 2

3x 4

Find two points. x y

0 -4 Let P1 = (0, -4) and

2 -1 P2 = (2, -1).

Use the slope formula. m =

12

12

xx

yy

=

02

)4(1

=

2

3

Observe that in Example 1, the slope is

Furthermore, when we solve for y = mx + b, the coefficient of x is

16

Any time an equation can be written in the form y = mx + b, the slope of the line is

m, the coefficient of x.

Example 2: Find the slope of the line 7x 3y = 10 by solving for y.

Solve for y. 7x 3y = 10.

3y = 7x + 10

3

y3

=

3

10x7

y = 3

x7

3

10

The slope is

, the coefficient of x.

Exercises: Find the slope of each line using the method in example 2.

13. 17.

14. 18.

15.

16.

ANSWERS: 13. –2 15. 5

7 17.

17

MATH 070 LAB 4: USING LINEAR GRAPHS

PART I: While surfing the Internet, you find a site that claims to sell DVD’s at cheap prices with a monthly membership fee of $8. Unfortunately, the site does not tell you how much they charge for each DVD, but it does give you the following information:

Number of DVD’s Ordered 1 2 3

Total Cost (Includes S & H, Excludes membership fee)

$15 $24 $33

a. Let x = the number of DVDs ordered in one month and y = the monthly cost.

Complete the table of values for x = 1, 2, and 3

b. Plot the points from the table on the graph below and connect the points.

c. Note that the points form a straight line. Therefore,

the rate of change is constant. Find the slope of the line.

d. Find the equation of the line using the point-slope form for the equation of a line.

X Y

1

2

3

50 45 40 35 30 25 20 15 10

5 1

2 3 4 5

18

e. Use the simplified equation from part d to find the cost if 9 DVDs are ordered.

PART II: An educator wants to see how student performance on the MAT 070 final exam affects the student’s performance in the next math course. The following data was collected for fifteen of her MAT 070 students after they completed their next math course.

MAT 070 Final Exam Grade

Next Math Course Final Average

61 80

76 84

100 96

70 85

65 70

40 70

97 90

85 89

43 62

88 85

73 76

56 70

85 79

76 80

88 80

19

1. Plot the data points using the x-axis for the MAT 070 final exam grade and the y–axis for the grade in the next math course.

2. Draw the line which best fits the data points. (Note: The line will not pass

through all of the points.)3. Find the equation of the line as follows:

a) Find the coordinates of two points on the line.

b) Calculate the slope of the line using the points from part a.

100 95 90 85 80 75 70 65 60 55 50 45 40 35 30 25 20 15 10

5 5

10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100

20

c) Determine the equation of the line using the point-slope form of a line and parts a & b.

Use the equation from part 3c to answer Questions 4 and 5. 4. If a student scores an 82 on the MAT 070 Final Exam, predict the final grade the student will receive in the next math course. 5. If the student received a grade of 90 in the next math course, determine what score the

student was likely to have earned on the MAT 070 Final Exam.

21

MATH 070 UNIT 5 WORK SHEET A The meaning of exponents can be used to simplify expressions involving products, quotients, and powers of variable expressions raised to positive integer exponents. Recall that in an exponential expression such as x3, x is the base, and 3 is the exponent which indicates how many times the base is used as a factor. That is,

x3 = x x x

3 factors To expand an exponential expression, write the expression in factored form.

Example 1: Expand (-5x4)(2x2) Solution: (-5x4)(2x2) = (-5 2)(xxxx xx) Example 2: Expand (-3a2b)3 Solution: (-3a2b)3 = (-3a2b)(-3a2b)(-3a2b)

= (-3)(-3)(-3)(aa aa aa)(b b b)

Example 3: Expand y12x

4xy2

4

Solution: y12x

4xy2

4

=

x x y12

x y y y y4

To simplify an exponential expression, write the expression in factored form. Then write the result in exponential form.

Example 1: Simplify (-5x4)(2x2) Solution: (-5x4)(2x2) = (-5 2)(xxxx xx)

=

Example 2: Simplify (-3a2b)3 Solution: (-3a2b)3 = (-3a2b)(-3a2b)(-3a2b)

= (-3)(-3)(-3)(aa aa aa)(b b b)

=

Example 3: Simplify y12x

4xy2

4

Solution: y12x

4xy2

4

=

x x y12

x y y y y4 =

22

EXERCISES: Simplify each expression.

1. (8m2)(5m) 8. (-2nt3)2 15. 3m22

m11

2. (-7w2)(-3w4) 9. (-a3b)2 16.

4

32

a

a

3. (-3a3)(-3a3) 10. (cd)3(cd3) 17.

2

32

ab

abba

4. (xy2)(x4y2) 11. (4k2)(-3k)2 18.

3

2

6

32

x

xx

5. (2bc)(-b5c) 12. 2

4

3

6

x

x 19.

4

2

y2

y4

6. (pq2r)(p2q)(r3q2) 13. 3

5

5

15

n

n

20.

2

4

p4p2

p6

7. (z4)2 14. 5

4

z

z

ANSWERS:

1. 40m3 11. 36k4

3. 9a6 13. -3n2

5. -2b6c2 15. 2m2

1

7. z8 17. a2b2

9. a6b2 19.

2y

8

23

MATH 070 UNIT 5 WORKSHEET B

RULES OF EXPONENTS: Let x and y denote rational numbers and let a and b denote

integers.

1. xa x

b = x

a + b 5.

a

y

x

=

a

a

y

x y 0

2. xa x

b = x

a-b x 0 6.

x

0 = 1

3. (xa)

b = x

ab 7. x

-a =

ax

1

4. (x y)a = x

a y

a

EXAMPLES:

Simplify the following:

a) (-2)-4

b) 2

4

3 c) (x

5) (x

-4) d)

4

5

x

x

e) (x-5

)4 f) (x

2 y)

-3 g)

3

y

x h) (2x)

3

Solutions:

a) (-2)-4

= 42)(

1

=

16

1

b) 2

4

3 =

2

2

4

3

= 2

2

3

4 =

9

16

c) x5 x

-4 = x

5 + 4 = x

1 = x

d) 4

5

x

x

= x –5 4

= x-9

= 9

1

x

e) (x-5

)4 = x

-5 4 = x

-20 =

20

1

x

f) (x2 y)

-3 = (x

2)

-3 y

-3 = x

-6 y

-3 =

6

1

x

3

1

y =

36

1

yx

g)

3

y

x =

3

y

x 3

= 3

3

x

y

h) (2x)3 = 2

3 x

3 = 8x

3

(OVER)

24

EXERCISES:

1. 6-2

2. 2

4

3 3.

6

2

1 4.

3-2

1

5. x8 x

11 6.

11

8

x

x 7. (x

8)

11 8.

3

y

x

9. (a-8

) (a3) 10.

3

8

a

a

11. 8

3

a

a 12.

42

x

13. (x-3

)2 14. (a

-8)

-2 15. (3a

-1)

2 16. (3a

-1)

-2

17. (2x3 y) (3x

4 y

-2) 18.

3

42

7

14

yx

yx 19. (3p

-2) (p

8)

20. 63

32

ba

ba

21.

4

b

a 22. 4x

0 (2y)

0

23. x-8

x-12

24. (2x)3 (4x)

2 25.

432

5

x

x

ANSWERS:

1. 36

1 3.

64

1 5. x

19 7. x

88

9. 5

1

a 11. a

11 13.

6

1

x 15.

2

9

a

17. y

x 76 19. 3p

6 21.

4

4

a

b 23. x

4

25. 3

40

x

25

MATH 070 UNIT 5 WORKSHEET C

28.63 x 10

-8 is in neither scientific notation nor decimal notation. The following illustrates

one method of converting to scientific notation.

Example - Convert to scientific notation.

EXERCISES:

Convert to scientific notation:

1. 286. 3 x 105 2. 26.34 x 10

-12

3. 0.412 x 10-6

4. 0.81 x 1011

Perform the operation and write the answer in scientific notation:

5. (8.6 x 10-8

) (4.3 x 103) 6. (4.78 x 10

4) (–1.3 x 10

18)

7. 8

15

105

108.4

x

x 8.

3

2

101.8

104.6

x

x

9. (0.38 x 102) (–1.7 x 10

9) 10.

4

5

100.3

103.6

x

x

ANSWERS:

1. 2.863 x 107 3. 4.12 x 10

-7

5. 3.698 x 10-4

7. 1.68 x 107

9. –6.46 x 1010

26

MAT 070 LAB 5 UNIT ANALYSIS

The metric system is a measurement system used by most of the world. All of the conversions

use the same place values that are used in the base-ten numeration system. The purposes of this

lab are to teach

the metric prefixes

unit analysis.

The base unit of length in the metric system is the meter (m) which is just a little longer than a

yard. All multiple and submultiple units are based on powers of ten. Greek prefixes (kilo,

hecto, and deka) are used for multiple units and Latin prefixes (deci, centi, and milli) are used

for submultiple units. The following table shows the metric prefixes, their meanings, and their

symbols.

PREFIX MEANING SYMBOL kilo 1000 k

hecto 100 h deka 10 da

deci 0.1 d

centi 0.01 c milli 0.001 m

Combining the prefixes with the base unit of meter, one

obtains

Most people prefer not to work with decimals. The decimals can be cleared in the

submultiple units as follows.

1 dm = 0.1 m 1 cm = 0.01 m

10(1 dm) = 10 (0.1 m) 100(1 cm) = 100 (0.01 m)

10 dm = 1 m 100 cm = 1 m

Similarly, 1000 mm = 1 m.

The conversions now read

Unit analysis is used to convert among the units. Setting up a unit analysis conversion is

much like reading a road map. The following diagram shows a possible arrangement for the

metric units of length along with routes connecting them.

1 km = 1000 m 10 dm = 1 m

1 hm = 100 m 100 cm = 1 m

1 dam = 10 m 1000 mm = 1m

1 km = 1000 m 1 dm = 0.1 m

1 hm = 100 m 1 cm = 0.01 m

1 dam = 10 m 1 mm = 0.001 m.

27

1.234 hm

Note that a conversion fact enables a route. One can go

from any prefix to the base unit and from the base to any

prefix unit.

The following are the steps used to perform unit analysis.

1. Use the diagram to write “travel” directions.

2. List the appropriate conversions.

3. Form a chain of multiplication to cancel unwanted units and be left with the desired unit.

4. Perform the multiplication or division to get the answer.

Example: Convert 1234 dm to hectometers.

Step 1. dm m hm

km hm

mm m dam

cm dm

Step 2. 10 dm = 1 m and 1 hm = 100 m

Step 3. Note that the quantity is being multiplied by 1 each time!

Step 4. hm1000

1234 =

Metric conversions cannot involve more than two moves (given prefix to base and base to

desired prefix). When either the given unit or the desired unit is the base, there is only one

move.

Example: 0.84 km = ______ m

Step 1 km m (one move)

Step 2 1 km = 1000 m

1234 1 1

1 10 100

dm m hmx x

dm m

28

Step 3 0.84 1000

1 1

km mx

km

Step 4

EXERCISE SET 1: Use unit analysis to perform the following conversions. Be sure to

show and label all steps.

1. 58 m = _____dam 2. Convert 1.23 hm to meters

3. Convert 0.7 m to decimeters 4. 78.54 m = _____km

5. 0.3 cm = _____mm 6. 34.98 mm = ____ dam

7. 84.5 km = ____ dam 8. 0.008 dm = _____ mm

ANSWERS TO ODD PROBLEMS:

1. 5.8 dam 3. 7 dm 5. 3 mm

7. 8450 dam

One of the big advantages of the metric system is that the conversions for length, mass, and

capacity work the same way. In other words, the same prefixes are used with all base metric

units. The purposes of this lab are to

introduce the base metric units for mass and capacity

review unit analysis as a tool to perform metric to metric conversions

demonstrate the power of unit analysis in U.S. to metric and metric to U.S.

conversions.

The base metric unit of mass is the gram (g). A nickel has mass of approximately 5 grams.

The base metric unit for capacity is the liter (L), which is just a little more than a quart. The

conversion charts for mass and capacity are identical to the chart for length, except that meter

is replaced with gram or liter.

840 m

29

MASS

1 kg = 1000 g

1 hg = 100 g

1 dag = 10 g

10 dg = 1 g

100 cg = 1 g

1000 mg = 1 g

CAPACITY

1 kL = 1000 L

1 hL = 100 L

1 daL = 10 L

10 dL = 1 L

100 cL = 1 L

1000 mL = 1 L

As with length, one uses unit analysis to do conversions.

Example: Convert 0.025 kg to grams

Step 1 kg g

Step 2 1 kg = 1000 g

Step 3 0.025 1000

1 1

kg gx

kg

Step 4

Example: Convert 24.7 dL to milliliters.

Step 1 dL L mL

Step 2 10 dL = 1 L and 1000 mL = 1 L

Step 3 24.7 1 1000

1 10 1

dL L mLx x

dL L

Step 4

There are no exact conversions between the common U.S. units and the metric units;

however, one can use the following bridges to get approximate answers.

QUANTITY

BRIDGE

Length 1 in = 2.54 cm

Capacity 1 L = 1.06 qt

Mass/Weight 1 kg = 2.2 lbs

25 g

2470 mL

30

Example: Michael is 4 ft 7 in tall. Express his height in centimeters.

1 ft = 12 inches; therefore 4 ft. = 48 inches and 4 ft 7 in = 55 in. Now use unit analysis to

convert to centimeters.

Step 1 in cm

Step 2 1 in = 2.54 cm

Step 3 55 2.54

1 1

in cmx

in

Step 4

Example: Joanne bought a Mini-Cooper that has a gas tank capacity of 37 liters. To the

nearest tenth, how many gallons of gas will the tank hold?

One needs to know that a gallon is four quarts.

Step 1 L qt gal

Step 2 1 L = 1.06 qt and 4 qt = 1 gal

Step 3 37 1.06 1

1 1 4

L qt galx x

L qt

Step 4

Example: Mrs. Hurley has a holiday recipe that calls for 12 ounces of jasmine tea. Her

internet source sells only by the gram. How many grams of the tea should she order?

The 12 ounces must be converted to grams. The English to metric bridge given earlier is 1

kg = 2.2 lb. One must recall that 1 lb = 16 oz. Now, unit analysis can be used to perform

the conversion.

Step 1 oz lb kg g

Step 2 1 lb = 16 oz, 1 kg = 2.2 lbs, and 1 kg = 1000 g

139.7 cm

9.8 gal

One must get to the bridge unit, cross the bridge, and then go to the desired unit.

31

Step 3 12 1 1 1000

1 16 2.2 1

oz lb kg gx x x

oz lb kg

Step 4

EXERCISE SET 2 (problems 1-16): Use unit analysis to perform the indicated conversions.

1. 5000g = ______kg 2. 14.6 kg =_____g 3. 18 mg = _____g

4. 493 L = _____Kl 5. 5.1 kg = _____cg 6. 800.37 mL = ____hL

7. 47.1 dL = _____daL 8. 0.0034 hL = ___ cL 9. 8 in = ______cm

10. 0.4 lb = _____g

11. The standard width of a bowling lane is 41 in. Express this width in centimeters.

12. Your chemistry professor mixes the contents of two beakers containing 2.5 L and 700

mL of a liquid. What is the combined amount in liters?

13. A prehistoric bird had a wingspan of 8 m. Express this wingspan in feet.

14. In 1989, an oil tanker in Alaska spilled 10 000 000 gal of oil in Prudhoe Bay. What

is the quantity of this spillage expressed in kiloliters?

15. A passenger car is generally considered small if the distance between its front and

back wheels is less than 95 inches. What is this distance expressed in meters?

16. One of the heaviest babies ever born was an Italian boy who weighed 360 oz. at birth.

What was the baby’s mass in kilograms?

ANSWERS:

1. 5 kg 3. 0.018 g 5. 510,000 cg

7. 0.471 daL 9. 20.32 cm 11. 104.14 cm

13. 26.25 ft 15. 2.41 m

341 g

32


ORDER OF OPERATIONS To simplify polynomial expressions, one follows the rule for the order of operations. Example: Simplify (2x – 1)(x – 3) – 2(x – 1)2 + 3x2 – 2(x + 4)

1. Work inside symbols of inclusion

(2x –1)(x – 3) – 2(x – 1)2 + 3x2 – 2x - 8 2. Raise to powers (2x – 1)(x – 3) – 2(x2 – 2x + 1) + 3x2 – 2x - 8

3. Multiply

(2x2 – 7x + 3) – (2x2 - 4x + 2) + 3x2 – 2x - 8 4. Add and subtract

(2x2 – 7x + 3) + (-2x2 + 4x – 2) + 3x2 – 2x - 8

ANSWER: 3x2 – 5x – 7 Exercises: Simplify: 1. 2(x – 3) – 4(2x – 1) 7. (2x +3)(x – 2) – (x + 1) (2x – 3) 2. x(2x + 3) + 2x(x – 1) 8. (x + 2)2 – x(2x – 1) 3. x2(2x – 3) – x(x2 – 3x + 4) 9. (x + 2)2 – (x – 1)2 4. 5x3(x – 1) – 2x2(x2 + 3x – 2) 10. x(x – 4) – (x – 2)2 5. 3x(x – 1) + 5x(2x – 3) 11. 4x – (2x – 3)2 + 8x2 6. (x – 1)(x + 1) + (x + 2)(x – 2) 12. 3x – (4x – 5)(x – 2) + x(3x – 1) Answers: 1. –6x – 2 7. –3 3. x3 – 4x 9. 6x + 3 5. 13x2 – 18x 11. 4x2 + 16x – 9 REVISED August 30, 2011

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