7th grade intensive math - slots...

7th Grade

Intensive Math

McGraw-Hill Supplemental Resources

Student Edition

October 2014 – January 2015

Course 2 • Chapter 3 Integers 47

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Example 1Find 5(-2).

5(-2) = -10 The integers have different signs. The product is negative.

Example 2Find -3(7).

-3(7) = -21 The integers have different signs. The product is negative.

Example 3Find -6(-9).

-6(-9) = 54 The integers have the same sign. The product is positive.

Example 4Find (-7)2.

(-7)2 = (-7)(-7) There are 2 factors of -7.

= 49 The product is positive.

Example 5Find -2(-3)(4).

-2(-3)(4)= 6(4) Multiply -2 and -3.

= 24 Multiply 6 and 4.

ExercisesMultiply.

1. -5(8) 2. -3(-7) 3. 10(-8)

4. -8(3) 5. -12(-12) 6. (-8)2

7. -5(7) 8. 3(-2) 9. -6(-3)

10. 5(-4)(5) 11. -4(-4) 12. 2(-3)(5)

13. -2(-3) 14. 9(-4) 15. (-3)(-4)

16. -3(-3)(5) 17. -2(5)2 18. (-3)(-4)(5)

Lesson 4 ReteachMultiply Integers

The product of two integers with different signs is negative.

The product of two integers with the same sign is positive.

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Course 2 • Chapter 3 Integers

NAME __________________________________________ DATE ____________ PERIOD _______

Lesson 4 Extra Practice

Multiply Integers

Multiply.

1. 5(2) 10 2. 6(4) 24 3. 4(21) 84

4. 11(5) 55 5. 6(5) 30 6. 50(0) 0

7. 5(5) 25 8. 4(8) 32 9. (6)2 36

10. (2)2 4 11. (4)3 64 12. (5)3 125

Evaluate each expression if a = 5, b = 2, c = 3, and d = 4.

13. 2d 8 14. 6a 30 15. 3ab 30

16. 12d 48 17. 4b2 16 18. a2 25

19. 5cd 60 20. 13ab 130 21. 3c 9

Course 2 • Chapter 3 Integers 49

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.Lesson 5 ReteachDivide Integers

The quotient of two integers with different signs is negative.

The quotient of two integers with the same sign is positive.

Example 1Find 30 ÷ (-5).

30 ÷ (-5) The integers have different signs.

30 ÷ (-5) = -6 The quotient is negative.

Example 2Find -100 ÷ (-5).

-100 ÷ (-5) The integers have the same sign.

-100 ÷ (-5) = 20 The quotient is positive.

ExercisesDivide.

1. -12 ÷ 4 2. -14 ÷ (-7)

3. 18 −

-2 4. -6 ÷ (-3)

5. -10 ÷ 10 6. -80 −

-20

7. 350 ÷ (-25) 8. -420 ÷ (-3)

9. 540 −

45 10. -256 −

16

ALGEBRA Evaluate each expression if d = -24, e = -4, and f = 8.

11. 12 ÷ e 12. 40 ÷ f

13. d ÷ 6 14. d ÷ e

15. f ÷ e 16. e2 ÷ f

17. -d − e 18. ef ÷ 2

19. f + 8

−

-4 20. d - e −

5

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Course 2 • Chapter 3 Integers

NAME __________________________________________ DATE ____________ PERIOD _______


Divide Integers

Divide.

1. 4 (2) 2 2. 16 (8) 2 3. 14 (2) 7

4. 328 4 5. 18 (3) 6 6. 18 3 6

7. 8 (8) 1 8. 0 (1) 0 9. 25 5 5

10. 147

2 11. 32 8 4 12. 56 (8) 7

13. 81 9 9 14. 42 (7) 6 15. 121 (11) 11 Evaluate each expression if a = 2, b = 7, x = 8, and y = 4.

16. 64 x 8 17. 16y 4 18. x 2 4

19. a2 1 20. ax y 4 21.

bxy 14

22. 2y 1 8 23. xay 1 24. y a 2

25. x2 y 16 26. ab1 14 27.

xya 16

NAME _____________________________________________ DATE __________________ PERIOD _________

Course 2 • Chapter 4 Rational Numbers 51

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.Lesson 1 ReteachTerminating and Repeating Decimals

To write a fraction as a decimal, divide the numerator by the denominator. Division ends when the remainder is zero.

You can use bar notation to indicate that a number pattern repeats indefi nitely. A bar is written over the digits that repeat.

Example 1Write 3 −−

20 as a decimal.

0.1520 � �� 3.00 Divide 3 by 20. 20 100 100 0 The remainder is 0.

So, 3 −− 20

= 0.15.

Example 3Write -0.32 as a fraction in simplest form.

-0.32 = - 32 −−− 100

The 2 is in the hundredths place.

= - 8 −− 25

Simplify.

ExercisesWrite each fraction or mixed number as a decimal. Use bar notation if the decimal is a repeating decimal.

1. 8 −− 10

2. - 3 − 5 3. 7 −−

11

4. 4 7 − 8 5. - 13 −−

15 6. 3 47 −−

99

Write each decimal as a fraction in simplest form.

7. -0.14 8. 0.3 9. 0.94

Example 2Write 5 −

9 as a decimal.

0.555... 9 � �� 5.000 45 50 The remainder after each step is 5. 45 50 45 5

You can use bar notation 0. −

5 to indicatethat 5 repeats forever. So, 5 −

9 = 0.

−

5 .

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Course 2 • Chapter 4 Rational Numbers

NAME __________________________________________ DATE ____________ PERIOD _______


Terminating and Repeating Decimals

Write each fraction or mixed number as a decimal. Use bar notation if needed.

1. 1620 0.8 2.

30120 0.25 3. 1

78 1.875

4. 16 5. 5

1140 0.275 6. 5

1350 5.26

7. 55

300 8. 112 1.5 9.

59

10. 234 2.75 11.

911 12. 4

19

Write each decimal as a fraction or mixed number in simplest form.

13. 0.26 1350 14. 0.75

34 15. 0.4

25

16. 0.1 110 17. 4.48 4

1225 18. 9.8 9

45

19. 0.91 91100 20. 11.15 11

320 21. 4.3 4

310

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.Lesson 6 ReteachMultiply Fractions

To multiply fractions, multiply the numerators and multiply the denominators.

5 −

6 × 3 −

5 = 5 × 3 −−−−

6 × 5 = 15 −−

30 = 1 −

2

To multiply mixed numbers, rename each mixed number as an improper fraction. Then multiply the fractions.

2 2 −

3 × 1 1 −

4 = 8 −

3 × 5 −

4 = 40 −−

12 = 3 1 −

3

Example 1

Find 2 −

3 × 4 −

5 . Write in simplest form.

2 −

3 × 4 −

5 = 2 × 4 −−−−

3 × 5 ← Multiply the numerators.

← Multiply the denominators.

= 8 −−

15 Simplify.

Example 2

Find 1 −

3 × 2 1 −


1 −

3 × 2 1 −

2 = 1 −

3 × 5 −

2 Rename 2 1

−

2 as an improper fraction, 5

−

2 .

= 1 × 5 −−−−

3 × 2 Multiply.

= 5 −

6 Simplify.

ExercisesMultiply. Write in simplest form.

1. 2 −

3 × 2 −

3 2. 1 −

2 × 7 −

8 3. - 1 −

3 × 3 −

5

4. 5 −

9 × 4 5. 1 2 −

3 ×

(

- 3 −

5 )

6. 3 3 −

4 × 1 1 −

6

7. 3 −

4 × 1 2 −

3 8. -3 1 −

3 ×

(

-2 1 −

2 )

9. 4 1 −

5 × 1 −

7

10. 7 −

5 × 8 11. -2 1 −

3 × 4 −

6 12. 1 −−

8 × 2 3 −

4

45

23

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Multiply Fractions

Multiply. Write in simplest form.

1. 23

35

25 2.

16

25

115 3.

49

37

421

4. 512

611

522 5.

38

89

13 6.

25

58

14

7. 715

321

115 8.

56

1516

2532 9.

23

313

213

10. 49

16

227 11. 3

19

13 12. 5

67 4

27

13. 35 15 9 14. 3

12 4

13 15

16 15._

45 2

34 2

15

16. 618 5

17 31

12 17. 2

23 2

14 6 18.

78 16 14

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.Lesson 8 ReteachDivide Fractions

To divide by a fraction, multiply by its multiplicative inverse or reciprocal. To divide by a mixed number, rename the mixed number as an improper fraction.

Example Find 3 1 −

3 ÷ 2 −


3 1 −

3 ÷ 2 −

9 = 10 −−

3 ÷ 2 −

9 Rename 3 1

−

3 as an improper fraction.

= 10 −−

3 · 9 −

2 Multiply by the reciprocal of 2

−

9 , which is 9

−

2 .

= 10 −−

3 · 9 −

2 Divide out common factors.

= 15 Multiply.

ExercisesDivide. Write in simplest form.

1. 2 −

3 ÷ 1 −

4 2. 2 −

5 ÷ 5 −

6 3. - 1 −

2 ÷ 1 −

5

4. 5 ÷ (

- 1 −

2 )

5. 5 −

8 ÷ 10 6. 7 1 −

3 ÷ 2

7. 5 −

6 ÷ 3 1 −

2 8. 36 ÷ 1 1 −

2 9. -2 1 −

2 ÷ (-10)

10. 5 2 −

5 ÷ 1 4 −

5 11. 6 2 −

3 ÷ 3 1 −

9 12. 4 1 −

4 ÷ 2 −

8

13. 4 6 −

7 ÷ 2 3 −

7 14. 12 ÷

(

-2 1 −

2 )

15. 4 1 −

6 ÷ 3 1 −

6

5

1

3

1

/ // /


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NAME __________________________________________ DATE ____________ PERIOD _______


Divide Fractions

Divide. Write in simplest form.

1. 23

32

49 2.

35

25 1

12 3.

710

38 1

1315

4. 59

25 1

718 5. 4

23 6 6.8

45 10

7. 9 59 16

15 8.

27 2

17 9.

114 7

198

10. 15 35 25 11.

914

34

67 12.

78 10

780

13. 16 34 21

13 14.

38 2

12

320 15._5

12 2

12 2

15

16. 314 5

12

1322 17. 12

56 2

16 5

1213 18. 7

12 3

12 2

17

Name: ______________________________ Period: ______ Date: _______________________

Multiplying and Dividing Decimals

Find each product.

1. -5.5 x (-4.87) 2. 1.7 x (-2.1)

3. 0.2 x (-1.6)

4. 1.7 x (-3.1)

5. -4.6 x (-7.2)

6. -5.928 x (-11.6)

7. -1.5 x (-7.1)

8. 7.8 x 5.1

9. -7.5 x (-8.3)

10. -4.04 x 3

11. 3.2 x 8.7

12. 8.1 x (-5.2)

Find each quotient.

13. 3.15 ÷ 0.05

14. 26.008 ÷ 0.4

15. -983.1 ÷ (-0.3)

16. 1.44 ÷ 0.16

17. 236.4 ÷ 0.0012

18. -10.08 ÷ 0.005

19. 2.253 ÷ 0.15

20. -1.161 ÷ 0.18

21. 2.25 ÷ (-0.009)

22. -234.72 ÷ 3.6

23. -4330.8 ÷ (-8.02)

24. 38.46 ÷ 0.8

Solve each problem. Check your solution.

25. Mrs. Johnson harvested 107 pounds of tomatoes from her garden. She sold them for $0.85 a

pound. How much did she receive from selling all the tomatoes?

26. Emma bought 2.5 yards of cording for the trim around the edge of a square pillow. How much

will she use for each side of the pillow?

27. Sean has a loan of $8804.46 including interest. He makes payments of $209.63 each month on

the simple interest loan. How many months will it take Sean to repay his loan?

28. Travis painted for 6.25 hours. He received $27 an hour for his work. How much was Travis paid

for doing this painting job?

Course 2 • Chapter 5 Expressions 69

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Example 1Evaluate 6x - 7 if x = 8.

6x - 7 = 6(8) - 7 Replace x with 8.

= 48 - 7 Use the order of operations.= 41 Subtract 7 from 48.

Example 2Evaluate 5m - 3n if m = 6 and n = 5.

5m - 3n = 5(6) - 3(5) Replace m with 6 and n with 5.

= 30 - 15 Use the order of operations.= 15 Subtract 15 from 30.

Example 3Evaluate ab ——

3 if a = 7 and b = 6.

ab −−

3 = (7)(6)

−−−−

3 Replace a with 7 and b with 6.

= 42 −−

3 The fraction bar is like a grouping symbol.

= 14 Divide.

Example 4Evaluate x3 + 4 if x = 3.

x3 + 4 = 33 + 4 Replace x with 3.= 27 + 4 Use the order of operations.= 31 Add 27 and 4.

ExercisesEvaluate each expression if a = 4, b = 2, and c = 7.

1. 3ac 2. 5b3 3. abc

4. 5 + 6c 5. ab −−

8 6. 2a - 3b

7. b4 −−

4 8. c - a 9. 20 - bc

10. 2bc 11. ac - 3b 12. 6a2

13. 7c 14. 6a - b 15. ab - c

To evaluate an algebraic expression you replace each variable with its numerical value, then use the order of operations to simplify.

Lesson 1 ReteachAlgebraic Expressions


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Course 2 • Chapter 5 Expressions

NAME __________________________________________ DATE ____________ PERIOD _______


Algebraic Expressions

Evaluate each expression if a = 3, b = 4, c = 12, and d = 1.

1. a + b 7 2. c d 11 3. a + b + c 19 4. b a 1 5. c ab 0 6. a + 2d 5 7. b + 2c 28 8. ab 12

9. a + 3b 15 10. 6a + c 30 11. cd 12 12. abc 144

13. 2(a + b) 14 14. 2cb 6 15. 144 abc 0 16. 2ab 24

17. b2 2 18. a 9 19. c 100 44 20. a + 3 30 2 2 3

21. 2b2 32 22. b3 + c 76 23. a2

d 9 24. 5a + 2d 47 2 2

25. 4d2

b 1 26. 15a 5 27. 3a 27 28. 10d 10 2 3

29. (2c + b)

b 7 30. (b2 + 2d)

a 6 31. (2c + ab)

c 3 32. (3.5c + 2)

11 4


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.Lesson 2 ReteachSequences

An arithmetic sequence is a list in which each term is found by adding the same number to the previous term. 1, 3, 5, 7, 9, …

+2 +2 +2 +2

Example 1Describe the relationship between terms in the arithmetic sequence 17, 23, 29, 35, … Then write the next three terms in the sequence.

17, 23, 29, 35, …. Each term is found by adding 6 to the previous term.

+6 +6 +6 35 + 6 = 41 41 + 6 = 47 47 + 6 = 53The next three terms are 41, 47, and 53.

Example 2MONEY Brian’s parents have decided to start giving him a monthly allowance for one year. Each month they will increase his allowance by $10. Suppose this pattern continues. What algebraic expression can be used to find Brian’s allowance after any given number of months? How much money will Brian receive for allowance for the 10th month?

Make a table to display the sequence.

Position Operation Value of Term

1 1 · 10 10

2 2 · 10 20

3 3 · 10 30

n n · 10 10n

Each term is 20 times its position number. So, the expression is 10n.How much money will Brian receive after 10 months?10n Write the expression.10(10) = 100 Replace n with 10

So, Brian will receive $100 after 10 months.

ExercisesDescribe the relationship between terms in the arithmetic sequences. Write the next three terms in the sequence.

1. 2, 4, 6, 8, … 2. 4, 7, 10, 13, … 3. 0.3, 0.6, 0.9, 1.2, …

4. 200, 212, 224, 236, … 5. 1.5, 2.0, 2.5, 3.0, … 6. 12, 19, 26, 33, …

7. SALES Mama’s bakery just opened and is currently selling only two types of pastry. Each month, Mama’s bakery will add two more types of pastry to their menu. Suppose this pattern continues. What algebraic expression can be used to find the number of pastries offered after any given number of months? How many pastries will be offered in one year?


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Sequences

Describe the relationship between the terms in each arithmetic sequence. Then write the next three terms in each sequence.

1. 5, 9, 13, 17, … 2. 3, 5, 7, 9, … 3. 10, 15, 20, 25, … 4 is added to the previous 2 is added to the previous 5 is added to the previous term; 21, 25, 29 term; 11, 13, 15 term; 30, 35, 40 4. 90, 93, 96, 99, … 5. 8, 14, 20, 26, … 6. 4.5, 5.4, 6.3, 7.2, … 3 is added to the previous 6 is added to the previous 0.9 is added to the previous term; 102, 105, 108 term; 32, 38, 44 term; 8.1, 9.0, 9.9 7. 0.3, 0.4, 0.5, … 8. 2.3, 3.4, 4.5, 5.6, … 9. 8.9, 9.1, 9.3, 9.5, … 0.1 is added to the previous 1.1 is added to the previous 0.2 is added to the previous term; 0.6, 0.7, 0.8 term; 6.7, 7.8, 8.9 term; 9.7, 9.9, 10.1 10. 3, 11, 19, 27, … 11. 350, 375, 400, 425, … 12. 620, 635, 650, 665, … 8 is added to the previous 25 is added to the previous 15 is added to the previous term; 35, 43, 51 term; 450, 475, 500 term; 680, 695, 710 13. 2, 7, 12, 17, … 14. 10, 17, 24, 31, … 15. 9, 90, 171, 252, … 5 is added to the previous 7 is added to the previous 81 is added to the previous term; 22, 27, 32 term; 38, 45, 52 term; 333, 414, 495 16. 2.6, 2.8, 3.0, 3.2, … 17. 4.1, 4.6, 5.1, 5.6, … 18. 6.6, 7.7, 8.8, 9.9, … 0.2 is added to the previous 0.5 is added to the previous 1.1 is added to the previous term; 3.4, 3.6, 3.8 term; 6.1, 6.6, 7.1 term; 11.0, 12.1, 13.2 19. 19.5, 21, 22.5, 24, … 20. 14.5, 14.8, 15.1, 15.4, … 21. 0.1, 0.4, 0.7, 1.0, … 1.5 is added to the previous 0.3 is added to the previous 0.3 is added to the previous term; 25.5, 27, 28.5 term; 15.7, 16.0, 16.3 term; 1.3, 1.6, 1.9


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Example 1Name the property shown by the statement u + v = v + u.The order in which the variables are being added changed. This is the Commutative Property of Addition.

Example 2State whether the following conjecture is true or false. If false, provide a counterexample.

Subtraction of integers is commutative.

Write two subtraction expressions using the Commutative Property.

17 - 9 � 9 - 17 State the conjecture.

8 ≠ - 8 Subtract.

We found a counterexample. That is, 17 - 9 ≠ 9 - 17. So, subtraction is not commutative. The conjecture is false.

Example 3Simplify the expression. Justify each step.

9 + (3x + 4)

9 + (3x + 4) = 9 + (4 + 3x) Commutative Property of Addition

= (9 + 4) + 3x Associative Property of Addition

= 13 + 3x Simplify.

ExercisesName the property shown by each statement.

1. 7 · 1 = 7 2. 4 + (3y + 2) = (4 + 3y) + 2

State whether the following conjectures are true or false. If false, provide a counterexample.

3. The product of two even numbers is odd.

4. The difference of two odd numbers is even.

5. Simplify 4 + (5x + 2) . Justify each step.

Lesson 3 ReteachProperties of Operations


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Properties of Operations

Name the property shown by each statement.

1. 1 • 4 = 4 Identity () 2. 6 + (b + 2) = (6 + b) + 2 Associative (+) 3. 9(6n) = (9 • 6)n Associative () 4. 8t • 0 = 0 • 8t Commutative () 5. 0(13n) = 0 Multiplicative (0) 6. 7 + t = t + 7 Commutative (+) Simplify each expression. Justify each step. 7. (12 + x) + 9 8. 31 + (15 + c) = (x + 12) + 9 Commutative (+) = (31 + 15) + c Associative (+) = x + (12 + 9) Associative (+) = 46 + c Simplify. = x + 21 Simplify. 9. (8 + d) + 19 10. 2 • (6 • m) = (d + 8) + 19 Commutative (+) = (2 • 6) • m Associative () = d + (8 + 19) Associative (+) = 12c Simplify. = d + 27 Simplify. 11. (5 • p) • 3 12. 9(4f) = (p • 5) • 3 Commutative () = (9 • 4) • f Associative () = p • (5 • 3) Associative () = 36f Simplify. = 15p Simplify.


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Distributive PropertyWords To multiply a sum or difference by a number, multiply each

term inside the parentheses by the number outside the parentheses.

Symbols a (b + c) = ab + ac a (b - c) = ab - ac

Examples 3 (2 + 5) = 3 · 2 + 3 · 5 6 (8 - 3) = 6 · 8 - 6 · 3

ExamplesUse the Distributive Property to evaluate each expression.

1 5 (x + 3) 5 (x + 3) = 5 · x + 5 · 3 Expand using the Distributive Property

= 5x + 15 Simplify.

2 (4x - y)9 (4x - y) 9 = [4x + (-y)]9 Rewrite 4x - y as 4x + (-y).

= (4x)9 + (-y)9 Expand using the Distributive Property.

= 36x + (-9y) Simplify.

= 36x - 9y Defi nition of subtraction.

Example 3MOVIES Alwyn is taking three of his friends to the movies. Tickets cost $8.90 per person. Find Alwyn’s total cost.

You can use the Distributive Property to find the total cost mentally.

4 ($9 - $0.10) = 4 ($9) - 4 ($0.10) Distributive Property

= $36 - $0.40 Multiply.

= $35.60 Subtract.

Alwyn will pay $35.60 for himself and three friends to go to the movies.

ExercisesUse the Distributive Property to evaluate or rewrite each expression.

1. 5 (w + 4) 2. (x - 5) (-2) 3. 7 (6x - 2y)

4. -6 (4 + 2m) 5. 8 (2n + 7) 6. (3v + 6w) 2

7. BOOKS Mariah bought 7 books costing $11.20 each. Find the total cost of the 7 books. Justify your answer by using the Distributive Property.

Lesson 4 ReteachThe Distributive Property


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The Distributive Property

Use the Distributive Property to evaluate each expression.

1. 2(4 + 5) 18 2. 4(5 + 3) 32 3. 3(7 6) 3 4. (2 + 5)9 63 5. (10 4)3 18 6. 6(1 + 3) 24 Use the Distributive Property to rewrite each expression.

7. 3(m + 4) 3m + 12 8. (y + 7)5 5y + 35 9. 6(x + 3) 6x 18 10. (p 4)5 5p 20 11. 3(s 9) 3s + 27 12. 5(x + y) 5x + 5y 13. b(c + 3d) bc + 3bd 14. (a b)(5) 5a + 5b 15. 6(v 3w) 6v + 18w 16. 5(x + 12) 5x + 60 17. (m 6)(4) 4m 24 18. 2(a b) 2a + 2b 19. (8 m)(3) 24 + 3m 20. 8(p 3q) 8p 24q 21. (2x + 3y)(4) 8x + 12y 22. 2(x + 3) 2x + 6 23. 3(a + 7) 3a + 21 24. 3(g 6) 3g 18 25. 2(a + 3) 2a 6 26. 1(x 6) x + 6 27. 4(a 5) 4a 20


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.Lesson 5 ReteachSimplify Algebraic Expressions

When a plus or minus sign separates an algebraic expression into parts, each part is called a term. The numerical factor of a term that contains a variable is called the coefficient of the variable. A term without a variable is called a constant. Like terms contain the same variables to the same powers, such as 3x2 and 2x2.

Example1 Identify the terms, like terms, coefficients, and constants in the

expression 7x - 5 + x - 3x.

7x - 5 + x - 3x = 7x +

(

-5) + x + (-3x) Defi nition of subtraction = 7x + (-5) + 1x + (-3x) Identity Property; x = 1x

The terms are 7x, -5, x, and -3x. The like terms are 7x, x, and -3x. The coefficients are 7, 1, and -3. The constant is -5.

An algebraic expression is in simplest form if it has no like terms and no parentheses.

ExamplesWrite each expression in simplest form.

2 5x + 3x

5x + 3x = (5 + 3) x or 8x Distributive Property; simplify.

3 -2m + 5 + 6m - 3

-2m and 6m are like terms. 5 and -3 are also like terms.

-2m + 5 + 6m - 3 = -2m + 5 + 6m + (-3) Defi nition of subtraction = -2m + 6m + 5 + (-3) Commutative Property =

(

-2 + 6) m + 5 + (-3) Distributive Property = 4m + 2 Simplify.

ExercisesIdentify the terms, like terms, coefficients, and constants in each expression.

1. - 4y - 3 + 2y 2. -5g + 3 + 2g - g 3. 5 + 3a - 4 - a

Write each expression in simplest form.

4. 3d + 6d 5. 2 + 5s - 4 6. 2z + 3 - 9z - 8


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Simplify Algebraic Expressions

Identify the terms, like terms, coefficients, and constants in each expression.

1. 8b + 7b 4 6b 2. 9 + 8z 3 + 5z 3. 11q 5 + 2q 7 terms: 8b, 7b, 4, 6b terms: 9, 8z, 3, 5z terms: 11q, 5, 2q, 7 like terms: 8b, 7b, 6b like terms: 8z and 5z, 9 and 3 like terms: 11q and 2q, coefficients: 8, 7, 6 coefficients: 8, 5 5 and 7 constant: 4 constants: 9, 3 coefficients: 11, 2 constants: 5, 7

4. a + 1 + 2a + 8a 5. 1 2c 3c + 100 6. 14j 6 + 8j 5 terms: a, 1, 2a, 8a terms: 1, 2c, 3c, 100 terms: 14j, 6, 8j, 5 like terms: a, 2a, 8a like terms: 1 and 100, like terms: 14j and 8j, coefficients: 1, 2, 8 2c and 3c 6 and 5 constant: 1 coefficients: 2, 3 coefficients: 14, 8 constants: 1, 100 constants: 6, 5 Write each expression in simplest form.

7. 3x + 2x 5x 8. 6x 3x 3x 9. 2a 5a 3a 10. 5x 6x x 11. 8a 3a 5a 12. a 4a 3a 13. 3a + 2a 6 5a 6 14. 6x + 2x 3 8x 3 15. 5a 3 + 2a 7a 3 16. 3x + 7 5x 2x + 7 17. x 3 + 5x 6x 3 18. 6x 3x 2 3x 2 19. a 2a + 5 a + 5 20. 6x 2 + 7x 13x 2 21. 5a 7a + 2 2a + 2 22. 4a + 2 7a 5 3a 3 23. 3a 2 + 5a 7 8a 9 24. 5x 3x + 2 5 2x 3


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.Lesson 6 ReteachAdd Linear Expressions

You can use models to add linear expressions.

Example 1Add (3x + 5) + (2x + 3).

Step 1 Model each expression.

3x + 5 2x + 3

xxx xx1 1 1

1 1

1 1

1

Step 2 Combine like tiles and write an expression for the combined tiles.

3x 2x

x xx xx1 1 1

1 1

1 1

1

+ + +5 3

So, (3x + 5) + (2x + 3) = 5x + 8.

Example 2Add (x - 2) + (- 2x + 4).

Step 1 Model each expression.

x - 2 (-2x) + 4

-1

-1

x -x -x1 1

1 1

Step 2 Combine like tiles and write an expression for the combined tiles.

x (-2x) (-2)

-1

-1

x -x-x1 1

1 1

+ + + 4

Step 3 Remove all zero pairs and write an expression for the remaining tiles.

(-x)

-xx -x-1

-1

1

1

1

1

+ 2

So, (x - 2) + (- 2x + 4) = - x + 2.

ExercisesAdd. Use models if needed.

1. (5x + 2) + (3x + 1) 2. (- 8x + 1) + (- 2x + 6)

3. (- 7x + 4) + (x - 5) 4. (- 6x + 1) + (4x - 1)


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Add Linear Expressions

Add. Use models if needed.

1. (3x + 5) + (4x 1) 7x + 4 2. (5x 3) + (2x + 1) 3x 2 3. (7x + 4) + (5x 12) 12x 8 4. (4x 10) + (5x 2) x 12 5. (7x 9) + (x 6) 6x 15 6. (3x + 9) + (14x 2) 11x + 7 7. (6x 7) + (3x 5) 9x 12 8. (7x 5) + (9x + 6) 2x + 1 9. (4x + 2) + (3x 1) 7x + 1 10. (3x + 5) + (2x 2) x + 3 11. 3(2x + 4) + (4x 2) 10x + 10 12. 4(3x + 1) + (6x + 3) 6x + 7 13. 2(4x 5) + (6x 4) 14x 14 14. (7x + 12) + (4)(2x + 3) 15x 15. (2x + 6) + 8(3x 7) 26x 50 16. 4(3x + 6) + (10x 15) 2x + 9


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.Lesson 7 ReteachSubtract Linear Expressions

When subtracting expressions, subtract like terms. You can use models or the additive inverse.

Example 1Find (- 3x - 2) - (4x).

Step 1 Model the expression - 3x - 2.

+

-1

-1

-x -x-x

(-3x) (-2)

Step 2 Since there are no positive x-tiles to remove, add four zero pairs of x-tiles. Remove four positive x-tiles.

xx xx -x-1

-1

-x -x-x -x -x-x

Zero pairs

So, (- 3x - 2) - (4x) = - 7x - 2.

Example 2Subtract (4x + 6) - (-7x + 1).

The additive inverse of - 7x + 1 is 7x - 1.

4x + 6 Arrange like terms in columns. + 7x - 1 Add. 11x + 5

So, (4x + 6) - (- 7x + 1) = 11x + 5.

ExercisesSubtract. Use models if needed.

1. (9x + 10) - (2x + 4)

2. (3x + 4) - (2x - 5)

3. (6x + 3) - (- x - 2)

4. (4x - 1) - (x + 3)

5. (3x - 1) - (2x - 6)


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Subtract Linear Expressions

Subtract. Use models if needed.

1. (6x + 2) (9x + 3) 3x 1 2. (4x + 7) (7x 8) 3x + 15 3. (6x 7) (2x + 5) 4x 12 4. (6x 8) (4x 7) 2x 1 5. (4x 8) (3x + 10) 7x 18 6. (9x 11) (x 5) 8x 16 7. (3x + 4) (x + 1) 2x + 3 8. (2x + 4) (x + 2) x + 2 9. (6x + 3) (4x 4) 2x + 7 10. (x + 4) (2x + 6) 3x 2 11. (3x 2) (x 2) 2x 12. (x 9) (2x 1) x 8


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.Lesson 8 ReteachFactor Linear Expressions

A linear expression is in factored form when it is expressed as the product of its factors.

Example 1Factor 5x + 10.

Use the GCF to factor the linear expression.

5x = 5 · x Write the prime factorization of 5x and 10.

10 = 5 · 2 Circle the common factors.

The GCF of 5x and 10 is 5. Write each term as a product of the GCF and its remaining factors.

5x + 10 = 5(x) + 5(2)

= 5(x + 2) Distributive Property

So, 5x + 10 = 5(x + 2).

Example 2Factor 3x + 8.

3x = 3 · x

8 = 2 · 2 · 2

There are no common factors, so 3x + 8 cannot be factored.

ExercisesFactor each expression. If the expression cannot be factored, write cannot be factored.

1. 15x + 10 2. 7x - 3

3. 6x + 9 4. 30x - 25

5. 13x + 14 6. 50x - 75

7. 24x - 18 8. 18x + 13

9. 16x - 12 10. 36x + 45


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Factor Linear Expressions

Find the GCF of each pair of monomials.

1. 28, 42x 14 2. 21a, 45 3 3. 16m, 56n 8 4. 42x, 56y 14 5. 20c, 28cd 4c 6. 5ab, 6b b 7. 7x, 14xy 7x 8. 14b, 56bc 14b 9. 21a, 63ab 21a Factor each expression. If the expression cannot be factored, write cannot be factored. Use algebra tiles if needed. 10. 12x + 3 3(4x + 1) 11. x 2 cannot be factored 12. 4x 3 cannot be factored 13. 3x + 9 3(x + 3) 14. 6x 12 6(x 2) 15. 2x 7 cannot be factored 16. 7x + 14 7(x + 2) 17. 12x 10 2(6x 5) 18. 3x + 36 3(x + 12) 19. 4x + 20 4(x + 5) 20. 15x + 7 cannot be factored 21. 10x + 18 2(5x + 9)

Course 2 • Chapter 6 Equations and Inequalities 91

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.

Example 1 Solve 15 = 0.5n. Check the solution.

15 = 0.5n Write the equation.

15 −− 0.5

= 0.5n −−− 0.5

Division Property of Equality

30 = n Simplify.

Example 2Solve 4 −

5 x = 8. Check your solution.

4 − 5 x = 8 Write the equation.

( 5 − 4 ) 4 −

5 x = ( 5 −

4 ) 8 Multiply each side by the reciprocal of 4 −

5 , 5 −

4 .

x = 10 Simplify.

The solution is 10.

ExercisesSolve each equation. Check your solution.

1. 4.9 = 0.7m 2. - 1 − 2 = - 6 −−

18 h 3. -2.8 = 4b

4. 3 − 5 x = 12 5. 16 = 10 −−

3 a 6. 9 = 0.3n

7. 15 −− 7 y = 3 8. 21 = 0.75a 9. 14 −−

3 = - 7 −

9 b

Lesson 3 ReteachSolve Equations with Rational Coefficents

Multiplicative inverses, or reciprocals, are two numbers whose product is 1. To solve an equation in which the coefficient is a fraction, multiply each side of the equation by the reciprocal of the coefficient.


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Course 2 • Chapter 6 Equations and Inequalities

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Solve Equations with Rational Coefficients

Solve each equation. Check your solution.

1. 0.5m = 3.5 7 2. 1.8 = 0.6x 3 3. 0.4y = 2 5 4. 1.86 = 6.2z 0.3 5. 1.67t = 10.02 6 6. 0.9x = 4.5 5

7. 113a = 2

32 or 1

12 8.

89x = 24 27 9.

38r = 36 96

10. 34t =

12

23

12 11. 16 =

14h 64 12.

18m = 12 96

13. 58n = 45 72 14. 10 =

110b 100 15.

17x = 7 49

16. 5 = 15y 25 17.

43m = 28 21 18.

23z = 20 30

19. 19c = 81 729 20.

49f = 16 36 21.

158 x = 225 120


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.

Example 1Solve 7v - 3 = 25. Check your solution.

7v - 3 = 25 Write the equation. +3 = +3 Undo the subtraction by adding 3 to each side.7v = 28 Simplify.

7v −− 7 = 28 −−

7 Undo the multiplication by dividing each side by 7.

v = 4 Simplify.

Check 7v - 3¬= 25 Write the original equation. 7(4) - 3¬� 25 Replace v with 4. 28 - 3¬� 25 Multiply. 25¬= 25 � The solution checks.

The solution is 4.

Example 2Solve -10 = 8 + 3x. Check your solution.

-10 = 8 + 3x Write the equation. -8 = -8 Undo the addition by subtracting 8 from each side.

-18 = 3x Simplify.

-18 −−− 3 = 3x −−

3 Undo the multiplication by dividing each side by 3.

-6 = x Simplify.

Check -10 = 8 + 3x Write the original equation. -10 � 8 + 3(-6) Replace x with -6. -10 � 8 + (-18) Multiply. -10 = -10 � The solution checks.

The solution is -6.

ExercisesSolve each equation. Check your solution.

1. 4y + 1 = 13 2. 6x + 2 = 26 3. -3 = 5k + 7 4. 2 −

3 n + 4 = -26

5. 7 = -3c - 2 6. -8p + 3 = -29 7. -5 = -5t - 5 8. -9r + 12 = -24

9. 11 + 7 − 9 n = 4 10. 35 = 7 + 4b 11. -15 + 4 −

5 p = 9 12. 49 = 16 + 3y

13. 2 = 4t - 14 14. -9x - 10 = 62 15. 30 = 12z - 18 16. 7 + 4g = 7

Lesson 4 ReteachSolve Two-Step Equations

To solve a two-step equation, undo the addition or subtraction fi rst. Then undo the multiplication or division.


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Solve Two-Step Equations


1. 3x + 6 = 6 0 2. 2r 7 = 1 3 3. 10 + 2d = 8 9 4. 2b + 4 = 8 6 5. 5w 12 = 3 3 6. 5t 4 = 6 2 7. 2q 6 = 4 5 8. 2g 3 = 9 3 9. 15 = 6y + 3 2 10. 3s 4 = 8 4 11. 18 7f = 4 2 12. 13 + 3p = 7 2 13. 14e + 14 = 28 1 14. 92 16b = 12 5 15. 9m 9 = 9 2 16. 32 + 2c = 1 15.5 17. 5t 14 = 14 0 18. 5x + 24 = 4 4 19. 5w 4 = 8 2.4 20. 4d 3 = 9 3 21. 2g 16 = 9 3.5 22. 4k + 13 = 20 1.75 23. 7 = 5 2x 1 24. 8z + 15 = 1 2


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Example 1Solve 6(x + 2) = 42. Check your solution.

6(x + 2) = 42 Write the equation.

6(x + 2) −−−−−

6 = 42 −−

6 Division Property of Equality

x + 2 = 7 Simplify.

-2 = -2 Subtraction Property of Equality x = 5 Simplify.

Check 6(x + 2) = 42 Write the original equation. 6(5 + 2) � 42 Replace x with 5. 6(7) � 42 Add. Multiply. 42 = 42 � The solution checks.

The solution is 5.


5 (x - 5) = 4. Check your solution.

4 − 5 (x - 5) = 4 Write the equation.

5 − 4 � 4 −

5 (x - 5) = 5 −

4 � 4 Multiplication Property of Equality

(x - 5) = 5 − 4 � 4 −

1 5 −

4 � 4 −

5 = 1; write 4 as 4 −

1 .

x - 5 = 5 Simplify. + 5 = +5 Addition Property of Equality

x = 10 Simplify.

Check 4 − 5 (x - 5) = 4 Write the original equation.

Replace x with 10. 4 −

5 (10 - 5) = 4 Subtract then multiply.

4 − 5 (5) = 4 � The solution checks.

The solution is 10.

ExercisesSolve each equation.

1. 7(x + 4) = 49 2. 2(x - 8) = -22 3. 10(x + 3) = -20 4. 25(x - 3) = 175

5. 3 − 4 (x - 12) = 3 6. 2 −

3 (x + 4) = 14 7. 7 −

9 (x + 5) = 21 8. 1 −

8 (x - 15) = 4

Lesson 5 ReteachMore Two-Step Equations

An equation in the form p(x + q) = r contains two factors, p and (x + q) and is considered a two-step equation.


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More Two-Step Equations


1. 2(x + 4) = 22 16 2. 3(x 4) = 18 10 3. (10 + x)2 = 30 25

4. (x 12)4 = 36 21 5. 12(x 4) = 8 12 6.

23(x + 7) = 6 2

7. 5(x 4) = 75 19 8. 2(x + 12) = 12 6 9. 24 = 6(x + 2) 2

10. 3(x 15) = 72 39 11. (18 + x)2 = 30 3 12. (11 + x) 34 = 27 25

13. 8(x + 12) = 64 4 14. 9(x 4) = 36 0 15. 4(x 9) = 32 1 16. 3(x 7) = 18 1 17. 5(x + 12) = 20 8 18. 6(x + 24) = 42 17


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ExamplesSolve each inequality.

1 x + 4 > 9 Write the inequality.

x + 4 - 4 > 9 - 4 Subtract 4 from each side.

x > 5 Simplify.

Any number greater than 5 will make the statement true. Therefore, the solution is x > 5.

2 -12 ≥ n - 9 Write the inequality.

-12 + 9 ≥ n - 9 + 9 Add 9 to each side.

-3 ≥ n Simplify.

The solution is -3 ≥ n or n ≤ -3.

3 Solve a + 1 −

3 < 1. Graph the solution set on a number line.

a + 1 − 3 < 1 Write the inequality.

a + 1 − 3 - 1 −

3 < 1 - 1 −

3 Subtract 1 −

3 from each side.

a < 2 − 3 Simplify.

ExercisesSolve each inequality.

1. t - 6 > 3 2. b + 9 ≤ 2

3. 8 < r - 9 4. -4 < p + 4

Solve each inequality. Graph the solution set on a number line.

5. s + 8 < 9 6. -3 ≤ d - 2

Lesson 6 ReteachSolve Inequalities by Addition or Subtraction

Solving an inequality means fi nding values for the variable that make the inequality true. You can use the Addition and Subtraction Properties of Inequality to help solve an inequality. When you add or subtract the same number from each side of an inequality, the inequality remains true.

21-1-2 021-1-2 0

30 1 2-1 23


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Solve Inequalities by Addition or Subtraction


1. y + 3 > 7 y > 4 2. c 9 < 5 c < 14

3. x + 4 9 x 5 4. y 3 < 15 y < 18

5. t 13 5 t 18 6. x + 3 < 10 x < 7

7. y 6 2 y 8 8. x 3 6 x 3

9. a + 3 5 a 2 10. c 2 11 c 13

11. a + 15 6 a 9 12. y + 3 18 y 15

13. y 6 17 y > 11 14. a + 5 21 a 16


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.Lesson 7 ReteachSolve Inequalities by Multiplication or Division

When you multiply or divide each side of an inequality by a positive number, the inequality remains true. However, when you multiply or divide each side of an inequality by a negative number, the direction of the inequality must be reversed for the inequality to remain true.

2120 22 24 25 261918 2317

-14-13-12-11-10 -9 -8 -7 -6 -5 -4432 5 6 7 8-2 -1 0 1

Example 1Solve t −−

-6 ≤ -4. Then graph the solution set on a number line.

t −− -6

≤ -4 Write the inequality.

t −− -6

(-6) ≥ -4(-6) Multiply each side by -6 and reverse the inequality symbol.

t ≥ 24 Simplify.

To graph the solution, place a closed circle at 24 and draw a line and arrow to the right.


5 x - 5 < 23.

4 − 5 x - 5 < 23 Write the inequality.

4 − 5 x - 5 + 5 < 23 + 5 Add 5 to each side.

4 − 5 x < 28 Simplify.

( 5 − 4 ) 4 −

5 x < ( 5 −

4 ) 28 Multiply each side by 5 −

4 .

x < 35 Simplify.

ExercisesSolve each inequality. Then graph the solution on a number line.

1. 3a > 12 2. 6 ≥ r −− -2

Solve each inequality. Check your solution.

3. -3.1c + 2 ≥ 2 4. 13 > - 2 − 3 y - 3

5. - h −− 5 - 6 < -10 6. 6a + 13 ≤ 31


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Solve Inequalities by Multiplication or Division


1. 5p 25 p 5 2. 4x < 12 x < 3

3. 15 3m m 5 4. d3 > 15 d > 45

5. 8 < r7 r > 56 6. 9g < 27 g < 3

7. 4p 24 p 6 8. 4 > k3 k > 12

9. z5 > 2 z < 10 10. 3x 9 x 3

11. 5x > 35 x < 7 12. a6

< 1 a > 6



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.Lesson 8 ReteachSolve Two-Step Inequalities

A two-step inequality is an inequality that contains two operations. To solve a two-step inequality, use inverse operations to undo each operation in reverse order of the order of operations.

Example 1Solve 4x - 2 ≤ 18. Graph the solution set on a number line.

4x - 2 ≤ 18 Write the inequality.

+ 2 +2 Addition Property of Inequality

4x ≤ 20 Simplify.

4x −− 4 ≤ 20 −−

4 Division Property of Inequality

x ≤ 5 Simplify.

The solution is x ≤ 5.

Graph the solution set.

Draw a closed dot at 5 with an arrow to the left.

Check 4x - 2 ≤ 18 Write the inequality.

4(3) - 2 18 Replace x with a number less than or equal to 5.

10 ≤ 18 This statement is true.

ExercisesSolve each inequality. Graph the solution set on a number line.

1. 3x - 4 < 17 2. -2 - x ≤ 3

3. 12 < 2x + 6 4. x − 2 - 3 ≤ –2

5. 7 > x - 2 6. 1 ≥ – x − 3 + 1

1 2 3 987654

9876543 10 11-2-3-4-5-6-7-8-9 -1

6543210-1 7 543210-1-2 6

111098765 12 13 3210-1-2-3-4 4


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Solve Two-Step Inequalities


1. 2x 3 > 11 x > 7 2. 6x + 5 23 x 3

3. 12 ≤ 3x 6 x 6 4. 3 < 4x + 1 x > 1

5. 8x + 4 ≤ 12 x 2 6. 5x 6 > 19 x < 5

7. x3 + 2 > 1 x > 9 8. 18 < 3x + 6 x < 8

9. 4 ≤ 6 + x3 x 6 10. 7 + 2x ≤ 5 x 6

11. 4x 5 > 7 x < 3 12. x5

+ 2 4 x 10


Course 2 • Chapter 7 Geometric Figures 105

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.Lesson 1 ReteachClassify Angles

exactly 90°

Right Angle

less than 90°

Acute Angle

between 90° and 180°

Obtuse Angle

exactly 180°

Straight Angle

ExampleName each angle below. Then classify the angle as acute, right, obtuse, or straight.

1.

1

2.

2

Use the vertex as the middle letter Use the vertex or the number only,and a point from each side, ∠ABC, ∠D or ∠2. The angle is less than∠CBA, or use the vertex or the 90˚, so it is an acute angle.number only, ∠B or ∠1. The angle is 90˚, so it is a right angle.

3. What is the value of x in the figure at the right? The angle labeled 5x˚ and the angle labeled 55˚ are vertical angles. Since vertical angles are congruent, the value of x is 11.

ExercisesName each angle. Then classify the angle as acute, right, obtuse, or straight.

1.

3

2. 3.

4. Find the value of x in the figure at the right. (3x - 4)°

146°34°

• An angle is formed by two rays that share a common endpoint called the vertex.

• An angle can be named in several ways. The symbol for angle is ∠.

• Angles are classifi ed according to their measures. Two angles that have the same measure are said to be congruent.

• Two angles are vertical if they are opposite angles formed by the intersection of two lines. Vertical angles are congruent.

• Two angles are adjacent if they share a common vertex, a common side, and do not overlap.

5x°125°

55°

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Classify Angles

Name each angle in four ways. Then classify each angle as acute, right, obtuse, or straight.

1.

2.

1, ABC, CBA, B; right 2, DEF, FED, E; obtuse

3.

3, LMN, NML, M; straight

4.

4, XYZ, ZYA, Y; acute

5.

5, KLM, MLK, L; acute

6.

6, RST, TSR, S; obtuse

Refer to the diagram at the right. Identify each angle pair as adjacent, vertical, or neither.

7. 1 and 2 adjacent 8. 2 and 5 neither 9. 1 and 3 vertical 10. 3 and 4 adjacent 11. 3 and 5 neither 12. 1 and 4 neither

Course 2 • Chapter 7 Geometric Figures


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.Lesson 2 ReteachComplementary and Supplementary Angles

• Two angles are complementary if the sum of their measures is 90°.

• Two angles are supplementary if the sum of their measures is 180°.

ExamplesIdentify each pair of angles as complementary, supplementary, or neither.

1. 150°30°

2. 16°

74°

30° + 150° = 180° 16° + 74° = 90°

The angles are supplementary. The angles are complementary.

Example 3ALGEBRA Find the value of x.

Since the two angles form a straight line, they are supplementary. The sum of their measures is 180°.

35°

5x°

5x + 35 = 180 Write the equation.

- 35 = -35 Subtract 35 from each side.

5x = 145 5 5 Divide each side by 5 x = 29 Simplify.

ExercisesIdentify each pair of angles as complementary, supplementary, or neither.

1.

43

2. 40°

50°

3.

120°

70°

ALGEBRA Find the value of x in each figure.

4. 36° 6x°

5.

56°4x°

6. 22°

2x°


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Complementary and Supplementary Angles

Identify each pair of angles as complementary, supplementary, or neither.

1.

2.

complementary supplementary

3.

4.

complementary neither

Find the measure of x in each figure.

5.

6.

70 20

7.

8.

40 20


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.Lesson 3 Reteach Triangles

Every triangle has at least two acute angles. One way you can classify a triangle is by using the third angle. Another way to classify triangles is by their sides. Sides with the same length are congruent segments.

Classify Triangles Using Angles

all acute angles 1 right angle 1 obtuse angleacute triangle right triangle obtuse triangle

Classify Triangles Using Sides

no congruent sides at least 2 congruent sides 3 congruent sidesscalene triangle isosceles triangle equilateral triangle

Example The figure shows a triangular pennant tied to a pole. Classify the marked triangle by its angles and by its sides.

The triangle has three acute angles and two sides the same length. So, it is an acute, isosceles triangle.

ExercisesDraw a triangle that satisfies each set of conditions. Then classify each triangle.

1. a triangle with three acute angles and three congruent sides

2. a triangle with one right angle and no congruent sides

20°


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Triangles

Classify each triangle by its angles and by its sides.

1.

2.

acute scalene right scalene

3.

4.

acute equilateral right scalene

Find the value of x.

5.

6.

50

135

7.

20

8.

45



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.Lesson 4 ReteachScale Drawings

A scale drawing represents something that is too large or too small to be drawn or built at actual size. Similarly, a scale model can be used to represent something that is too large or built too small for an actual-size model. The scale gives the relationship between the drawing/model measure and the actual measure.

ExampleOn this map, each grid unit represents 50 yards. Find the horizontal distance from Patrick’s Point to Agate Beach.

Patrick’s Point

N AgateBeach

Patrick'sPoint

Scale to Agate Beach

1 unit − 50 yards

= 8 units − x yards

1 × x = 50 × 8 Cross products

x = 400 Simplify.

It is 400 yards from Patrick’s Point to Agate Beach.

ExercisesFind the actual distance between each pair of cities. Round to the nearest tenth if necessary.

Cities Map Distance Scale Actual Distance

1. Los Angeles and San Diego, CA 6.35 cm 1 cm = 20 mi

2. Lexington and Louisville, KY 15.6 cm 1 cm = 5 mi

3. Des Moines and Cedar Rapids, IA 16.27 cm 2 cm = 15 mi

4. Miami and Jacksonville, FL 11.73 cm 1 −

2 cm = 20 mi

Find the length of each object on the scale drawing with the given scale. Then find the scale factor.

5. an automobile 16 feet long; 1 inch:6 inches

6. a pond 85 feet across; 1 inch = 4 feet

7. a parking lot 200 meters wide; 1 centimeter:25 meters

8. a flag 5 feet wide; 2 inches = 1 foot

mapactual

mapactual


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Scale Drawings

Use the scale drawing to find the actual length and width of each room. Then find the actual area of each room.

1. master bedroom 2. bedroom 2 15 ft by 12 ft; 180 ft2 12 ft by 12 ft; 144 ft2

3. kitchen and dining area 4. half bath 18 ft by 12 ft; 216 ft2 6 ft by 9 ft; 54 ft2

On a map, the scale is 1 inches = 50 miles. For each map distance, find the actual distance.

5. 5 inches 250 mi 6. 12 inches 600 mi 7. 238 inches 118

34 mi

8. 45 inch 40 mi 9. 2

56 inches 141

23 mi 10. 3.25 inches 162.5 mi

Master Bedroom

Master Bath Bedroom 2

Half Bath

Living Room

Kitchen and Dining Area

Key 1 cm = 3 ft

7th grade intensive math - slots...

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