Algebra Summer Math Packet

Pre‐Algebra Summer Math Packet

To help students retain math concepts and skills we are requiring students to complete this Pre‐Algebra

Summer Math Packet. The skills required to answer the questions in this packet are ones that should

have been mastered by students in previous math courses. Some of the skills are also covered in the

first chapter of the Pre‐Algebra textbook. The packet contains a brief review and example problems for

each skill.

Students should complete all of the questions for each lesson.

Please note:

1. Working through these problem sets is mandatory.

2. All work should be completed on separate sheets of paper. Answers should be written on the

packet.

3. Students should bring completed problems sets with them to turn in on the first day their math

class meets next school year.

a. Students do not need to print out the answer pages that are included with the packet.

4. Students should check their work upon completion.

a. The answers to the questions are located at the back of this packet. If a student

answers a question incorrectly, he/she should return to the work shown, attempt to find

the source of the error(s), and correct the problem.

5. Students should NOT use calculators on any portion of this packet.

6. Students will be given a homework grade for completion of this packet.

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7McDougal Littell Middle School Math

Remediation Book Lesson 1.4

Whole Numbers, Decimals,and Integers

Lesson 4: Adding and Subtracting Decimals

SECTION

1

To add and subtract decimals, line up the decimal points. Then add or subtractas with whole numbers and bring down the decimal point.

Practice: First Try

Add.

1. 3.68 2. 0.07 3. $25.49 4. $12.491 0.94 1 17.82 1 $ 3.47 1 $ 2.79

5. 10.53 6. 30.03 7. $10.30 8. $.081 1.06 1 2.09 1 $62.50 1 $.95

9. $5.50 1 $.89 10. 12.8 1 4.41 11. 59.38 1 21.51

Subtract.

12. $12.00 13. 8.762 14. 10.394 15. $19.992$ 6.50 2 0.381 2 0.898 2 $ 8.64

16. 8.30 17. 52.52 18. $20.50 19. $14.992 5.73 2 25.25 2 $10.25 2 $ 5.50

20. 17.001 2 5.5 21. $20 2 $14.98 22. 25.17 2 19.62

HINTWhen adding or subtracting decimals, be sure the decimal point in the answer is directly below the decimal point in the problem.

EXAMPLE 1

Line up the decimal points vertically.Write zeros as needed. Add.Line up the decimal points.

Line up the decimal points vertically.Subtract.Line up the decimal points.

6.451 8.80 15.25

EXAMPLE 2

$12.502 $ 1.25 $11.25

Add. 6.45 1 8.8

Subtract. $12.50 2 $1.25

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SECTION

1 Whole Numbers, Decimals, and Integers

Lesson 6: Multiplying with Decimals

When multiplying with decimals, the number of decimal places in theproduct is equal to the total number of decimal places in the factors.

EXAMPLE 1 Multiply. 6.253 3 8

6.253 Count 3 decimal places in the factor: 6.253.3 8 50.024 The product has 3 decimal places.

2 4 2

HINTThe number of digits to the right of the decimal point in the product is the sum of the number of digits to the right of the decimal point in the factors.

EXAMPLE 2 Multiply. $14.50 3 0.06

$14.50 2 places

3 0.06 1 2 places

$.8700 4 places

2 3

$.87

Practice : First Try

Multiply.

1. 3.2 2. 0.05 3. 0.7 4. 3.013 5 3 9 3 6 3 9

5. 3.1 6. 1.25 7. 4.5 8. 0.63 0.3 3 4.4 3 0.8 30.09

9. $16.49 10. $8.69 11. $3.50 12. $12.003 5 3 28 3 0.04 3 0.9

13. 0.2 3 82 14. 3.986 3 3 15. 0.06 3 5

16. 92.6 3 1.32 17. 0.99 3 1.5 18. 0.374 3 0.3

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Lesson 8: Dividing with Decimals

SECTION

1

If the divisor is a whole number, write a decimal point in the quotientdirectly above the decimal point in the dividend.

If the divisor is a decimal number, move the decimal point to the rightuntil the divisor is a whole number. Then move the decimal in the dividendthe same number of places to the right. Write a decimal point in the quotientdirectly above the new decimal point in the dividend.

Practice: First Try

Divide.

1. 2 qw 6.34 2. 5 qw 97.15 3. 0.3 qw 9.81 4. 0.04 qw 10.6

5 3 4 5 20

EXAMPLE 1 Divide. $1.98 by 4. Round to the nearest cent.

0.4954 qw 1.980 20 19 216 38 236 2 0 22 0 0

Round the quotient to the nearest cent.

$.495 $.50

Check 0.4953 4 1.98

0 3 4 5 0

4 3 4 5

9 3 4 5 36

Write zeros as needed to keep going.

The decimal point in the quotient is above the decimal point in the dividend.

EXAMPLE 2 Divide. 318 4 0.6

5300.6 qw 318.0 6 qw 3180 230 18

218 00 200 0

5 3 6 5 30

3 3 6 5 18

0 3 6 5 0

Rewrite

Check 5303 0.6 318.0

Move this decimal until thedivisor is a whole number.

Then move this decimal point the same number of places. Write zeros as needed.

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167

Algebra

Lesson 1: Writing Expressions

SECTION

6

A variable is any letter that represents an unknown number.

A numerical expression has numbers and operations.

A variable expression also has variables.

It is sometimes called an algebraic expression.

Practice: First Try

Write symbols for the given words.

1. the sum of eight and six 2. twenty divided by fi ve

3. the product of x and y 4. two times a number

5. fi ve times three 6. the sum of nine and two divided by 7

7. 8 times the sum of b and 3 8. 6 divided by the difference of x and 1

9. the difference of nine and fi ve 10. the product of ten and forty

EXAMPLE 1 Here are some numerical expressions.

Words Symbols

four times ten 4 • 10 4 3 10 4(10)

the sum of two and fi ve 2 1 5 (2 1 5)

nine divided by the difference of six and one

9 4 (6 2 1) 9

}6 2 1

EXAMPLE 2 Here are some variable expressions.

Words Symbols

the product of seven and n 7 • n 7 3 n 7(n)

a minus b plus four a 2 b 1 4

the quotient of a number and two x 4 2 x}2

McDougal Littell Middle School MathRemediation Book Lesson 6.1

HINTNotice in the examples shown here that some operations can be represented by more than one symbol.

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Practice: First Try

Evaluate the expression.

1. y 2 4 when y 5 9 2. a 1 7 when a 5 11

3. 3x when x 5 5 4. z}2 when z 5 18

5. n2 when n 5 4 6. 9 2 p3 when p 5 1

7. m 1 n}5 when m 5 4 and n 5 10 8. 2x 1 y when x 5 3 and y 5 1

9. a2 2 b2 when a 5 6 and b 5 4 10. s 1 50 • t when s 5 13 and t 5 3

Algebra

Lesson 6: Evaluating Expressions

SECTION

6

EXAMPLE 1 Evaluate 2x 2 4 when x 5 5.

2x 2 4 5 2(5) 2 4 5 10 2 4 5 6

Substitute 5 for x. Use the order of operations.

To evaluate a variable expression, substitute the given value for the variable(s). Then use the order of operations to evaluate.

EXAMPLE 2 Evaluate 14 1 n2 when n 5 6.

14 1 n2 5 14 1 62 5 14 1 36 5 50

Substitute 6 for n. Use the order of operations.

EXAMPLE 3 Evaluate 3a2 2 b when a 5 2 and b 5 5.

Substitute 5 for b.

3a2 2 b 5 3(2)2 2 5 5 3(4) 2 5 5 12 2 5 5 7

Substitute 2 for a. Use the order of operations.

HINTIf using a calculator to evaluate, don’t assume it will do order of operations correctly.

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Algebra

Lesson 5: Order of Operations

SECTION

6

Some expressions have more than one operation. A set of rules called the order of operations tells us how to evaluate them.

When an expression has more than one operation, do the operations in the following order.

Order of Operations

1. Evaluate expressions inside parentheses.

2. Evaluate expressions with exponents.

3. Multiply and divide from left to right.

4. Add and subtract from left to right.

Practice: First Try

For each expression, tell which operation you would do fi rst.

1. 43 1 9 2 3 2. 20 2 (4 1 7) 3. 24 4 6 1 7

4. 6 2 1 1 5 5. (3 2 1) 1 42 6. 24 2 32

Evaluate the expression. Use the order of operations.

7. 10 3 (6 2 2) 8. 52 2 (4 1 3) 9. 12 4 4 3 23

10. (12 1 4) 4 22 11. (9 2 1)(2 1 6) 12. 8 1 7 2 1 • 4

EXAMPLE (5 − 2) 1 62 • 4

Parentheses

5 3 1 62 • 4

Exponents

5 3 1 36 • 4

Multiply, Divide

5 3 1 144

Add, Subtract

5 147

You can use the sentence “Please excuse my dear Aunt Sally” to help you remember the order of operations.

HINTIf there is addition and subtraction in the same expression, do them from left to right. For example, in 18 2 4 1 2, do the subtraction fi rst. In 18 1 2 2 4, do the addition fi rst. The same is true for multiplication and division.

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SECTION

1

EXAMPLE 1 Graph –6 and –1 to compare them.

26 is less than –1. 21 is greater than 26.

26 , 21 21 . 26

Two numbers are opposites if they are the same distance from 0 on a number line, but are on opposite sides of 0. The absolute value of a number is the distance between the number and 0 on a number line. The absolute value of a number n is written | n |.

EXAMPLE 2 The numbers 23 and 3 are opposites.

The absolute value of 23 is 3.

The absolute value of 3 is 3.

Write |23| 5 3 and |3| 5 3.

Practice: First Try

Complete with <, >, or 5.

1. 24 _____ 25 2. 22 _____ 2 3. 1 _____ 23

4. 27 _____ 24 5. 0 _____ 26 6. 28 _____ 0

Write the absolute value of each integer.

7. | 5 | 5 _____ 8. | 22 | 5 _____ 9. | 24 | 5 _____

10. | 4 | 5 _____ 11. | 21 | 5 _____ 12. | 0 | 5 _____


Lesson 11: Integers

The set of numbers in the box are integers.Negative integers are less than 0, and positive integers are greater than 0. Zero is an integer that is neither positive nor negative.

You can graph integers on a number line.

HINTThe numbers increase as you move from left to right on a number line.

4210�1�2�3�4 3

10�1�2�3�4�5�6�7

3 units 3 units

4210�1�2�3�4 3

. . . , 24, 23, 22, 21, 0, 1, 2, 3, 4, .

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Lesson 12: Adding Integers

SECTION

1

EXAMPLE 1

You can use absolute value or a number line to add integers.

Add. –3 + (–2)

Find absolute values: U23U 5 3 and U22U5 2

Add absolute values: 3 1 2 5 5

Attach a negative sign: –5

Write the sum: –3 + 1–22 = –5

HINTTo add two negative integers, add their absolute values. The answer is negative.

EXAMPLE 2 Add. –5 + 2


Subtract absolute values: 5 – 2 = 3

Attach a negative sign: –3

Write the sum: –5 + 2 = –3

HINTTo add a negative integer and a positive integer, subtract their absolute values. The answer has the sign of the integer with the greater absolute value.

EXAMPLE 3 Add. –3 + 5


Subtract absolute values: 5 – 3 = 2

The answer is positive: 2

Write the sum: –3 + 5 = 2

HINTUse a number line to check your answer.

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24McDougal Littell Middle School MathRemediation Book Lesson 1.12

Practice

Add. Use the number line if it helps you.

1. 4 1 121 2 5 _____ 2. 22 1 122 2 5 _____ 3. 5 1 128 2 5 _____

4. 23 1 3 5 _____ 5. 24 1 123 2 5 _____ 6. 25 1 7 5 _____

7. 26 1 2 5 _____ 8. 1 1 126 2 5 _____ 9. 21 1 129 2 5 _____

10. 24 1 9 5 _____ 11. 23 1 125 2 5 _____ 12. 8 1 127 2 5 _____

Extend Your Skills

13. When Alison went to bed, the temperature was –8°C. If it drops 10 degreesovernight as predicted, what will be the temperature?

14. In an electronic game, Nate scored the following points: 120, 230, 210, 150,240, 220, 220, 110. What was his fi nal score?

15. What is the sum of any integer n and its opposite?

16. What is the sum of any integer n and zero?

Puzzle

Write the integers –4, –3, –2, –1, 0, 1, 2, 3, 4 in the magic square. Every horizontal,vertical, and diagonal sum must equal zero. Two numbers have already been written for you.

�10 �9 �8 �7 �6 �5 �4 �3 �2 �1 0 1 2 3 4 5 6 7 8 9 10

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Subtract. 2 2 6

Use addition: 2 1 1–62 = 24

Write the difference: 2 2 6 5 24


Lesson 13: Subtracting Integers

SECTION

1

EXAMPLE 1

To subtract an integer, you add its opposite. Rewrite the subtraction expressionas addition. Then follow the rules for addition of integers.

The opposite of a negative number is positive, and the opposite of a positivenumber is negative.

Practice : First Try

Match each subtraction expression with its addition expression.

1. 3 2 1–82 2. 3 2 8 3. 23 2 8 4. 23 2 1–82

A. 3 1 1–82 B. 23 1 8 C. 3 1 8 D. 23 1 1–82

Subtract. Use the number line if it helps you.

5. 24 2 7 5 _____ 1 _____ 5 _____ 6. 1 2 8 5 _____ 1 _____ 5 _____

7. 3 2 1–12 5 _____ 1 _____ 5 _____ 8. 272 1–225 _____ 1 _____ 5 _____

HINTTo add integers, see pages 23–24.

Subtract. 4 2 1–22

Use addition: 4 1 2 = 6

Write the difference: 4 2 1–22 5 6

EXAMPLE 2

Subtract. 24 2 2

Use addition: 24 1 1–22 = 26

Write the difference: 24 2 2 5 26

EXAMPLE 3

�10 �9 �8 �7 �6 �5 �4 �3 �2 �1 0 1 2 3 4 5 6 7 8 9 10

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Lesson 14: Multiplying and Dividing Integers

SECTION

1

When you multiply two positive numbers or two negative numbers, the product is positive.

When you multiply a positive number and a negative number, the product is negative.

Use the same sign rules when you divide with positive and negative numbers.

Multiply.

2 3 8 5 16 positive 2 3 128 2 5 –16 negative

positive positive positive negative

22 3 128 2 5 16 positive 22 3 8 5 216 negative

negative negative negative positive

EXAMPLE 1

Divide.

12 4 3 5 4 positive 12 4 123 2 5 –4 negative

positive positive positive negative

212 4 123 2 5 4 positive 212 4 3 5 24 negative

negative negative negative positive

EXAMPLE 2

Practice: First Try

Multiply.

1. 4 3 124 2 5 _____ 2. 26 3 5 5 _____ 3. 27 3 122 2 5 _____

4. 6 3 10 5 _____ 5. 211 3 3 5 _____ 6. 28 3 121 2 5 _____

Divide.

7. 40 4 125 2 5 _____ 8. 12 4 122 2 5 _____ 9. 29 4 123 2 5 _____

10. 214 4 121 2 5 _____ 11. 232 4 8 5 _____ 12. 81 4 129 2 5 _____

HINTBefore you multiply or divide, look at the signs and determine what the sign of the answer will be.

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Algebra

Lesson 18: Points in the Coordinate Plane

SECTION

6

You can locate points in a coordinate plane. A horizontal x-axis and a vertical y-axis intersect at the origin, dividing the plane into four quadrants,numbered I, II, III, and IV.

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III

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y-axis

x-axis

To locate a point in the coordinate plane, use an ordered pair. The numbersin an ordered pair (x, y) are coordinates, with the x-coordinate followed by the y-coordinate.

In the coordinate plane above, locate point A. Starting at the origin, count 3 units left and 2 units up. Point A is located at (23, 2).

EXAMPLE

Practice: First Try

Use the coordinate plane above. Write the coordinates for each point.

1. B 2. C 3. D

4. E 5. F 6. G

Draw a coordinate plane. Draw and label each point at thelocation indicated.

7. U (21, 4) 8. V (3, 3) 9. W (0, 23)

10. X (25, 22) 11. Y (2, 0) 12. Z (4, 23)

HINTWhen drawing a coordinate plane always label the axes and the origin.

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202McDougal Littell Middle School MathRemediation Book Lesson 6.18

Practice: Second Try

Write the coordinates for each point.

1. A 2. B

3. C 4. D

5. E 6. F

7. G 8. H

9. I 10. J

Write the point for the given coordinates.

11. (5, 23) 12. (24, 23)

13. (0, 0) 14. (2, 4)

15. (3, 24) 16. (0, 3)

17. (23, 25) 18. (22, 0)

19. (3, 0) 20. (25, 3)

Extend Your Skills

Imagine a neighborhood on a coordinate grid, with your home at the origin and the top of the page as due north.

21. If you travel 3 blocks west, then 5 blocks north to get to school, what quadrant is your school in?

22. If you travel 2 blocks east, then 1 block south to get to your friend’s house, what quadrant is your friend’s house in?

23. If you travel 2 blocks west, then 4 blocks south to get to the store, whatquadrant is the store in?

Puzzle

Draw a coordinate plane. Draw points as indicated. Then connect them in order using straight lines. What fi gure do you get?

(23, 3) to (3, 0) to (23, 23) to (0, 3) to (3, 23) to (23, 3)

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Algebra

Lesson 12: Solving One-Step Equations

SECTION

6

EXAMPLE

HINTSee Lessons 10, 11 for more practice on solving one-step equations.

One-step equations can be solved using any of the four basic operations.

Use the inverse operation, or opposite operation of what is in the equation.

Operation Inverse Operation

Addition Subtraction

Subtraction Addition

Multiplication Division

Division Multiplication

You can use all four operations to solve one-step equations.

Using Addition

a – 2 5 10a – 2 1 2 5 10 1 2 Add.

a 5 12Check: 12 2 2 5 10

Using Subtraction

y 1 2 5 10y 1 2 2 2 5 10 2 2 Subtract.

y 5 8Check: 8 1 2 5 10

Using Multiplicationn}2

5 10n}2

• 2 5 10 • 2 Multiply.n 5 20

Check: 20}2

5 10

Using Division

2x 5 102x}2

5 10}2

Divide.

x 5 5Check: 2(5) 5 10

Practice: First Try

Solve the equation. Check your solution.

1. x – 1 5 8 2. m 2 6 5 6 3. c 1 3 5 7 4. 6d 5 24

5. r}2

5 9 6. 2n 5 6 7. 9z 5 27 8. h 4 3 5 7

9. y 1 9 5 15 10. a}6

5 5 11. c 2 19 5 20 12. t 1 8 5 18

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Algebra

Lesson 13: Solving Two-Step Equations

SECTION

6

Use two operations to solve a two-step equation. To determine which operation to undo fi rst, use the order of operations in reverse.

Practice: First Try

Solve each equation. Check your solution.

1. 3y 2 4 5 5 2. 2a 1 5 5 13 3. m}4

2 1 5 6

4. b}9

2 3 5 1 5. 6c 2 7 5 11 6.y}5

1 12 5 18

EXAMPLE 1

EXAMPLE 2

Solve the equation.

2x 2 1 5 7

2x 2 1 1 1 5 7 1 1 Add 1 to each side.

2x 5 8 Simplify.

2x}2

5 8}2 Divide each side by 2.

x 5 4 Simplify.

Check: 2(4) 2 1 5 7 ✓

HINTFirst, use addition or subtraction. Then, use multiplication or division.

Solve the equation.

n}5 1 2 5 6

n}5 1 2 2 2 5 6 2 2 Subtract 2 from each side.

n}5 5 4 Simplify.

n}5 • 5 5 4 • 5 Multiply each side by 5.

n 5 20 Simplify.

Check: 20}5 1 2 5 6 ✓

HINTRemember to check your solution in the original equation.

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Answer Key

Section 1 Whole Numbers, Decimals, and IntegersLesson 4 (pp. 7–8)

Practice:

First Try

1. 4.62 2. 17.89 3. $28.96 4. $15.28 5. 11.59 6. 32.12 7. $72.80 8. $1.03 9. $6.39 10. 17.21 11. 80.89 12. $5.50 13. 8.381 14. 9.496 15. $11.35 16. 2.57 17. 27.27 18. $10.25

19. $9.49 20. 11.501 21. $5.02 22. 5.55

Second Try

1. 6.62 2. $15.22 3. 16.3 4. $13.17 5. 45.3 6. 0.523 7. $12.11 8. 26.53 9. 34.4 10. $27.24 11. 195.54 12. 69.12 13. 9.79 14. $15.27 15. $40.66

16. 7.26 17. 8.72 18. $9.02 19. $14.25 20. $21.50 21. 46.23 22. 6.564 23. 8.429

24. 45.77 25. $10.05 26. 106.75 27. 36.31 28 a. $24.59 28 b. $5.41 29. $115.25

Puzzle

Fill up the 0.3 liter container first. Pour it into the 0.5 liter container. Fill up the 0.3 liter container again, andfill up the rest of the 0.5 liter container, and you will have 0.1 liter left over in the 0.3 liter container.

Answer Key


Practice:

First Try

1. 16.0 2. 0.45 3. 4.2 4. 27.09 5. 0.93 6. 5.5 7. 3.6 8. 0.054 9. $82.45 10. $243.32

11. $.14 12. $10.80 13. 16.4 14. 11.958 15. 0.3 16. 122.232 17. 1.485 18. 0.1122

Second Try 1. 0.06 2. 406.5 3. 27.09 4. 76.35 5. 61.82 6. 7.4772 7. 0.002 8. 15.4008 9. $81.00 10. $11.88 11. $57.00 12. $13.50 13. 92.4 14. 115.8 15. 0.2 16. 2.928 17. 2.985 18. 225.72 19. $.10 20. $63.00 21. $4.49 22. $18.96 23. $1.24 Puzzle

7.14

3 3

1.25

3 4.4

7.2

3 0.5

13.50

3 6

14.25

3 4

0.75

3 0.2

57 3.6 21.42 81 0.15 5.5

Answer Key

Section 1 Whole Numbers, Decimals, and Integers

Lesson 8 (pp. 15–16)

Practice:

First Try

1. 3.17 2. 19.43 3. 32.7 4. 265

Second Try

1. 1.63 2. 15.6 3. 0.011 4. 150.5 5. 40.3 6. 0.3 7. 170 8. 100 9. 8.57 10. 84.15 11. 0.8466 12. 381 13. 7 14. 52.7 15. 4.1 16. 3.5 17. 700 18. $8.11 19. $3.22 20. $16.25 21. $5.50 22. $2.07 23. $4.33 24. $22.50 25. $0.43

26. You multiply the divisor and the dividend by the same multiple of 10, which moves the decimal point. Puzzle problems a and c

Answer Key

Section 6 AlgebraLesson 1 (pp. 1672168)

Practice:

First Try

1. 8 1 6 2. 20 4 5 3. xy 4. 2n 5. 5 3 3 6. (9 1 2) 4 7 7. 8(b 1 3) 8. 6 4 (x 21)

9. 9 2 5 10. 10 3 40

Second Try

1. 12 2 7 2. 4 1 2 3. 10 4 5 4. 3 3 18 5. m 1 9 6. 10 2 m 7. gh or g(h) 8. 20 4 n

9. 10x 10. 3 1 y 11. 2(5 1 5) 12. 50 2 4(7) 13. n 4 6 14. x 2 y

15. ten plus four 16. twelve divided by three 17. five times two 18. a number minus seven

19. nine times z 20. one divided by the sum of x and y 21. a 1 5 22. 3c 23. h 28

Puzzle

gr82cu! (Great to see you!)

Answer Key


Practice:

First Try

1. 5 2. 18 3. 15 4. 9 5. 16 6. 8 7. 6 8. 7 9. 20 10. 163

Second Try

1. 17 2. 24 3. 5 4. 26 5. 7 6. 3 7. 9 8. 1 9. 36 10. 270 11. 6 12. 57

13. 16 in., D 14. 60 cm2, B 15. 14 ft2, C 16. 81 m2, A

Puzzle

AT ONCE

Answer Key


Practice:

First Try

1. exponent 2. parentheses (1) 3. division 4. subtraction 5. parentheses (2) 6. exponents

7. 40 8. 18 9. 24 10. 4 11. 64 12. 11

Second Try

1. 38 2. 24 3. 10 4. 4 5. 4 6. 10 7. 91 8. 5 9. 21 10. 45 11. 0 12. 6

13. 65 14. 7 15. 7 16. 31 17. 7 18. 1 19. 9 20. 29 21. 25 22. 7 23. 1 24. 3

25. The first letter of each word matches. Answers will vary for phrases students make up on their own.

26. The cost is $78. To evaluate the expression, you must do the multiplication first, then the addition.

Puzzle

Possible answers: (1 1 2) 3 3 2 (4 1 5) 5 0; 52 1 4 3 3 3 2 1 1 5 50, 5 3 (4 1 3 1 2 1 1) 5 50

Answer Key


Practice:

First Try

1. . 2. , 3. . 4. , 5. . 6. , 7. 5 8. 2 9. 4 10. 4 11. 1 12. 0

Practice:

Second Try

1. . 2. . 3. 5 4. , 5. . 6. , 7. 8 8. 25 9. 26 10. 7

11. 1 12. 22 13. 6 14. 1 15. 5 16. 6 17. 7 18. 1

19. Check graph. 27, 25, 24, 22, 21, 0, 2, 3, 5, 6

20. Absolute value is a distance, and distance is never negative.

21. 10 and 210 22. 7

Puzzle

You must be a negative number.

Answer Key


Practice

1. 3 2. 24 3. 23 4. 0 5. 27 6. 2 7. 24 8. 25 9. 210 10. 5

11. 28 12. 1 13. 2188C 14. 240 points 15. 0 16. n

Puzzle

1 24 3

2 0 22

23 4 21

Answer Key


Practice:

First Try

1. C 2. A 3. D 4. B 5. 24 1 (27) 5 211 6. 1 1 (28) 5 27 7. 3 1 1 5 4 8. 27 1 2 5 25

Second Try

1. 5 1 6 5 11 2. 26 1 (23) 5 29 3. 2 1 (25) 5 23 4. 21 1 4 5 3 5. 25 1 (25) 5 210 6. 8 1 2 5 10 7. 7 1 (29) 5 22 8. 24 1 6 5 2 9. 26 10. 21 11. 24 12. 28 13. 22 14. 9 15. 11 16. 212 17. 11 18. 20,602 ft

19. Subtracting is the same as adding the opposite, and the opposite of a negative number is a positive num-ber. So, subtracting a negative number is the same as adding a positive number.

Puzzle

6

Answer Key

Section 1 Whole Numbers, Decimals, and Integers

Lesson 14 (pp. 27–28)

Practice:

First Try

1. 216 2. 230 3. 14 4. 60 5. 233 6. 8 7. 28 8. 26 9. 3 10. 14 11. 24 12. 29

Second Try 1. 15 2. 218 3. 254 4. 28 5. 1 6. 272 7. 3 8. 5 9. 6 10. 21 11. 22 12. 7 13. positive; negative; negative Puzzle a star; 3 cubes

6 6

66

6

6

66

6 6

6 6

0 0

66

0

6

66

6 6

6 6

Answer Key


Practice:

First Try

1. (25, 4) 2. (2, 2) 3. (0, 3) 4. (4, 24) 5. (22, 0) 6. (24, 23)

7.212

112345 2 3 4 5

4U

V

Y

ZX

5

3

2

1

1

2

3

4

5

W

Second Try

1. (4, 2) 2. (3, 22) 3. (23, 1) 4. (25, 24) 5. (1, 0) 6. (24, 4) 7. (1, 24) 8. (22, 22)

9. (2, 5) 10. (0, 23) 11. T 12. U 13. O 14. Q 15. P 16. S 17. N 18. W 19. R

20. M 21. II 22. IV 23. III

Puzzle

a star

Answer Key


Practice:

First Try

1. 9 2. 12 3. 4 4. 4 5. 18 6. 3 7. 3 8. 21 9. 6 10. 30 11. 39 12. 10

Second Try

1. 54 2. 2 3. 2 4. 8 5. 7 6. 40 7. 7 8. 19 9. 0 10. 2 11. 12 12. 17 13. 5

14. 0 15. 3 16. 15 17. 10 18. 1 19. 25 20. 5 21. 63 22. 2 23. 8 24. 14

25. n 1 8 5 15; n 5 7 26. 7n 5 42; n 5 6

27. n 1 9 5 55; n 5 46 28. n 2 16 5 13; n 5 29

Puzzle

zephyr

Answer Key


Practice:

First Try

1. 3 2. 4 3. 28 4. 36 5. 3 6. 30

Second Try

1. 2 2. 12 3. 32 4. 3 5. 40 6. 9 7. 24 8. 14 9. 6 10. 1 11. 3 12. 49 13. 14 14. 3 15. 1 16. 2t 1 7 5 25; Miriam can buy 9 ride tickets.

Puzzle

PUZZLE

Documents

Algebra Summer Math Packet