Math teachers edition

8/9/2019 Math teachers edition

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Chapter 1 24 Course 1

C o p yr i gh t © Gl en c o e / M c Gr a w-Hi l l , a d i vi s i on of T h eM c Gr a w-Hi l l C om p ani e s ,I n c .

1-1

Find 5.2 × 6.13.

Estimate: 5 × 6 or 30

5.2 one decimal place

× 6.13 two decimal places

156

52

+312

31.876 three decimal places

The product is 31.876. Compared to the estimate, the product is reasonable.

Find 2.3 × 0.02.

Estimate: 2 × 0.02 or 0.04

2.3 one decimal places

× 0.02 two decimal place

0.046 Annex a zero to make three decimal places.

The product is 0.046. Compared to the estimate, the product is reasonable.

Exercises

Multiply.

1. 7.2 × 2.1 2. 4.3 × 8.5 3. 2.64 × 1.4

4. 14.23 × 8.21 5. 5.01 × 11.6 6. 9.001 × 4.2

7. 3.24 × 0.008 8. 0.012 × 2.9 9. 0.9 × 11.2

When you multiply a decimal by a decimal, multiply the numbers as if you were multiplying all whole

numbers. To decide where to place the decimal point, fi nd the sum of the number of decimal places ineach factor. The product has the same number of decimal places.

Reteach

Multiply DecimalsE

Example 1

Example 2


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C o p y r i g h t © G l e n c o e / M c G r a w - H

i l l , a d i v i s i o n o f T h e M c G r a w - H

i l l C o m

p a n i e s , I n c .

1-1 Skills Practice

Multiply Decimals

Multiply.

1. 0.3 × 0.5 2. 1.2 × 2.1

3. 2.5 × 6.7 4. 0.4 × 8.3

5. 2.3 × 1.21 6. 0.6 × 0.91

7. 6.5 × 0.04 8. 8.54 × 3.27

9. 5.02 × 1.07 10. 0.003 × 2.9

11. 0.93 × 6.8 12. 7.1 × 0.004

13. 3.007 × 6.1 14. 2.52 × 0.15

15. 2.6 × 5.46 16. 16.25 × 1.3

17. 3.5 × 24.09 18. 0.025 × 17.1

19. 11.04 × 6.18 20. 14.83 × 16.7

21. 27.1 × 10.15 22. 41.2 × 10.34

E


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1-2


Find 10.14÷ 5.2.

Estimate: 10 ÷ 5 = 2

Multiply by 10 tomake a whole number.

1.95 Place the decimal point.5.2 10.14 52 101.40 Divide as with whole numbers. - 520 0

Multiply by thesame number, 10.

4940 - 4680

260 Annex a zero to continue. - 260 0

10.14 divided by 5.2 is 1.95. Compare the quotient with the estimate.Check 1.95 × 5.2= 10.14

Find 4.09÷ 0.02.

204.5 Place the decimal point.0.02

4.09 2

409.0 Divide. - 4

Multiply each by 100. 00

- 0 09

- 8 10 Write a zero in the dividend - 10 and continue to divide. 0

4.09 divided by 0.02 is 204.5.

Check 204.5 × 0.02 = 4.09

Exercises

Divide.

1. 9.8 ÷ 1.4 2. 4.41 ÷ 2.1 3. 16.848 ÷ 0.72

4. 8.652÷ 1.2 5. 0.5÷ 0.001 6. 9.594 ÷ 0.06

When you divide a decimal by a decimal, multiply both the divisor and the dividend by the same powerof ten. Then divide as with whole numbers.

Reteach

Divide Decimals by DecimalsE

Example 1

Example 2


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Skills Practice

Divide Decimals by Decimals

Divide.

1. 4.86 ÷ 0.2 2. 2.52 ÷ 0.7

3. 14.4 ÷ 1.2 4. 17.1 ÷ 3.8

5. 3.96 ÷ 1.32 6. 628.2 ÷ 34.9

7. 0.105÷ 0.5 8. 1.296÷ 0.16

9. 3.825÷ 2.5 10. 8.253 ÷ 0.5

11. 0.9944 ÷ 0.8 12. 1.638 ÷ 0.35

13. 13.59 ÷ 0.75 14. 4.4208 ÷ 1.8

15. 16.16 ÷ 0.2 16. 158.1÷ 5.1

17. 247.5÷ 3.3 18. 0.132÷ 1.1

E


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2-2

D

Reteach

Multiply Mixed Numbers

To multiply mixed numbers, write the mixed numbers as improper fractions, and then multiply as withfractions.

Find 1

4 × 1 2

3 . Estimate Use compatible numbers 1

2

× 2 = 1

1

4 × 1 2

3 =

1 4

× 5

3 Write 1 2

3 as

5

3 .

= 1 × 5

4 × 3 Multiply.

= 5

12 Simplify. Compare to the estimate.

Find 11

3

× 21

4

.

1 1

3 × 2 1

4 = 4

3 ×

9

4 Convert mixed numbers to improper fractions.

= 4 3 ×

9

4 Divide the numerator and denominator by their common factors, 3 and 4.

= 3

1

or 3 Simplify.

Exercises

Multiply. Write in simplest form.

1.1

3

× 11

3

2. 11

5

×

3

4

3.2

3

× 13

5

4.2

3

× 31

2

5. 2

9

× 1 1

6

6. 2 4

9

× 4 11

7. 2 1

2

× 1 1

3

8. 1 1

4

× 33

5

9. 8 1

5

× 1 1

4

10. 13

8

× 2 1

2

11. 4 2

3

× 1 1

8

12. 1 1

9

× 3 2

5

13. Find the product of

1

5

and 3

1

3

.

14. Simplify 4 2

3

× 1 1

4

.

Example 1

Example 2

1

/ / 1

3

/ / 1


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2-2

Multiply. Write in simplest form.

1. 1 3 × 1 1

4 2. 2 1

2 × 3

5

3. 3

4

×

3 1

3

4. 6 1

5

×

1

2

5. 5

7

×

4 1

5

6. 4

7

× 3 1

9

7. 4 1

6

× 9 10

8. 8

9

×

5 1

7

9. 5 7 × 4 3

8 10. 2 4

9 × 6

11

11. 2 5

8 × 1

6

12. 2

5 × 1 2

5

13. 1 3

5

× 3 2

3

14. 1 3

8

× 2 2

7

15. 3 1

3

× 2 1

4

16. 3 3

4

× 2 4

5

17. 5 3 4 × 1 1

11 18. 2 5

8 × 2 5

7

19. 2 2

9 × 4 4

5

20. 5 3

8 × 2 2

7

21. 6 2

3

× 5 2 11

22. 6 2

5

×

5 5

9

23. 8 8

9

×

3 1 10

24. 9 3

5

×

8 7

8

25. Find the product of 2 3 ×

5 1 6 .

26. Simplify 4 1 2 × 6 2

3

.

D

Skills Practice

Multiply Mixed Numbers


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2-3

Find 1 2

3 ÷ 3

4 .

1 2

3 ÷

3

4 =

5

3 ÷

3

4 Write the mixed number as an improper fraction.

= 5

3 × 4

3 Multiply by the reciprocal.

= 20 9

or 2 2

9 Simplify.

Find 2 2

3

÷ 1 1

5

. Estimate: 3 ÷ 1 = 3

2 2

3 ÷ 1 1

5 = 8

3 ÷ 6

5 Write mixed numbers as improper fractions.

= 8

3 × 5

6 Multiply by the reciprocal, 5

6 .

= 8× 5

3 × 6 Divide 8 and 6 by the GCF, 2.

= 20

9

or 2 2

9 Simplify. Compare to the estimate.

Exercises

Divide. Write in simplest form.

1. 2 1

2 ÷ 4

5

2. 9 ÷ 1 1 9

3. 5 ÷ 13

7

4. 2 1

3 ÷

7

9

5. 5 2 5 ÷

9

10 6. 2 1

4 ÷ 2

7 7. 2 1

2 ÷ 3 1

3 8. 7 1

2 ÷ 1 2

3

9. 1 2

3 ÷ 1 1

4

10. 4 4

5 ÷ 2

6

7

11. 5 1 10

÷ 18

9

12. 2 3

8 ÷ 2 1

4

13. Simplify 6 ÷ 43

5

.

14. Simplify 4 2

3 ÷ 1

3

4

.

To divide mixed numbers, express each mixed number as an improper fraction. Then divide as withfractions.

E

Reteach

Divide Mixed Numbers

Example 1

Example 2

4

3


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Skills Practice

Divide Mixed Numbers

Divide. Write in simplest form.

1. 2 5

6 ÷ 6 4

5

2. 4 6

7 ÷ 3 2

5

3. 31 2

3 ÷ 7

3

5

4. 3 ÷ 1 1 3

5. 6 ÷ 2 2 5

6. 1 3

4 ÷ 3

4

7. 2 ÷ 4 2 7

8. 7 ÷ 3 1 9

9. 6 2

3 ÷ 4

5

10. 1

2

9 ÷

5

6

11. 6÷

1

7

20

12.

7

10 ÷

2

5

8

13. 3 5

6 ÷ 1 1

3

14. 1 7

9 ÷ 4

9

15. 5 ÷ 8 3 4

16. 2 2

9 ÷ 1 1

3

17. 3 1

5 ÷ 1

7

9

18. 6 ÷ 3 1

3

19. 3 2

3 ÷ 2 2

3

20. 4 1

4 ÷ 2

5

8

21. 4 1

3 ÷ 3 1

3

22. 4 2 3 ÷ 2 2

9 23. 6 3

5 ÷ 2 3

5 24. 5 5

8 ÷ 3 3

4

25. Simplify 10 3

4 ÷ 6 1

2

.

26. Simplify 9 4

9 ÷ 4

9

.

2-3E


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A

Reteach

Ratio Tables

A ratio table organizes data into columns that are filled with pairs of numbers that have the sameratio, or are equivalent. Equivalent ratios express the same relationship between two quantities.

Example 1 BAKING You need 1 cup of rolled oats to make 24 oatmeal cookies.Use the ratio table below to find how many oatmeal cookies you can make with5 cups of rolled oats.

Cups of Oats 1 5

Oatmeal Cookies 24

Find a pattern and extend it.

Cups of Oats 1 2 3 4 5

Oatmeal Cookies 24 48 72 96 120

So, 120 oatmeal cookies can be made with 5 cups of rolled oats.

Example 2 SHOPPING A department storehas socks on sale for 4 pairs for $10. Use the

ratio table at the right to find the cost of6 pairs of socks.

There is no whole number by which you canmultiply 4 to get 6. Instead, scale back to 2 andthen forward to 6.

So, the cost of 6 pairs of socks would be $15.

Exercises

For Exercises 1–2, use the ratio tables given to solve each problem.

1. EXERCISE Keewan bikes 6 miles in30 minutes. At this rate, how longwould it take him to bike 18 miles?

2. HOBBIES Christine is making fleeceblankets. 6 yards of fleece will make2 blankets. How many blankets can she

make with 9 yards of fleece?

Pairs of Socks 4 6

Cost in Dollars 10

Distance Biked (mi) 6 18

Time (min) 30

Yards of Fleece 6 9

Number of Blankets 2

Pairs of Socks 2 4 6

Cost in Dollars 5 10 15

Multiplying or dividing two related quanitities by the same number is called scaling. You maysometimes need to scale back and then scale forward or vice versa to find an equivalent ratio.

+ 1 + 1 + 1 + 1

+ 24 + 24+ 24+ 24

÷ 2

× 3

÷ 2

× 3


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4-2

A

Skills Practice

Ratio Tables

Use the ratio table given to solve each problem.

1. BAKING A recipe for 1 apple pie calls for 6 cups of sliced apples. Howmany cups of sliced apples are needed to make 4 apple pies?

Number of Pies 1 4

Cups of Sliced Apples 6

2. BASEBALL CARDS Justin bought 40 packs of baseball cards for a discountedprice of $64. If he sells 10 packs of baseball cards to a friend at cost,how much should he charge?

Number of Baseball

Card Packs10 40

Cost in Dollars 64

3. SOUP A recipe that yields 12 cups of soup calls for 28 ounces of beef

broth. How many ounces of beef broth do you need to make 18 cups ofthe soup?

Number of Cups 12 18

Ounces of Beef Broth 28

4. ANIMALS At a dog shelter, a 24-pound bag of dog food will feed 36 dogsa day. How many dogs would you expect to feed with a 16-pound bagof dog food?

Pounds of Dog Food 16 24

Number of Dogs Fed 36

5. AUTOMOBILES Mr. Fink’s economy car can travel 420 miles on a 12-gallontank of gas. Determine how many miles he can travel on 8 gallons.

Miles 420

Gallons 12 8


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4-2

A

For Exercises 1– 3, use the ratio tables given to solve each problem.

1. CAMPING To disinfect 1 quart of stream

water to make it drinkable, you need toadd 2 tablets of iodine. How manytablets do you need to disinfect4 quarts?

2. BOOKS A book store bought 160 Number of Copies 160 2

Cost in Dollars 4,000copies of a book from the publisherfor $4,000. If the store gives away 2 books,how much money will it lose?

3. BIRDS An ostrich can run at a rate ofDistance Run (mi) 50 15

Time (min) 60

50 miles in 60 minutes. At this rate,

how long would it take an ostrich torun 15 miles?

4. SALARY Luz earns $400 for 40 hoursof work. Use a ratio table to determinehow much she earns for 6 hours of work.

5. DISTANCE If 10 miles is about 16 kilometers and the distance between two towns is 45miles, use a ratio table to find the distance between the towns in kilometers. Explainyour reasoning.

RECIPES For Exercises 6–8, use the following information.

A soup that serves 16 people calls for 2 cans of chopped clams, 4 cups of chicken broth, 6cups of milk, and 4 cups of cubed potatoes.

6. Create a ratio table to represent this

situation.

7. How much of each ingredient wouldyou need to make an identical recipe

that serves 8 people? 32 people?

8. How much of each ingredient would you need to make an identical recipe that serves 24

people? Explain your reasoning.

Homework Practice

Ratio Tables

Get ConnectedGet Connected For more examples, go to glencoe.com.

Number of Tablets 2

Number of Quarts 1 4


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6-1


Find the value of 48 ÷ (3 + 3) - 22.

48 ÷ (3 + 3) - 22 = 48 ÷ 6 - 22 Simplify the expression inside the parentheses.= 48 ÷ 6 - 4 Find 22.= 8 - 4 Divide 48 by 6.= 4 Subtract 4 from 8.

Write and solve an expression to find the total cost of plantingflowers in the garden.

Item Cost per Item Number of Items Needed

Pack of flowers $4 5

Bag of dirt $3 1

Bottle of fertilizer $4 1

Words cost of 5 flower packs plus cost of dirt plus cost of fertilizer

Expression 5 × $4 + $3 + $4

5 × $4 + $3 + $4 = $20 + $3 + $4=

$23+

$4= $27

The total cost of planting flowers in the garden is $27.

Exercises

Find the value of each expression.

1. 7 + 2 × 3 2. 12 ÷ 3 + 5 3. 16 - (4 + 5)

4. 8 × 8 ÷ 4 5. 10 + 14 ÷ 2 6. 3 × 3 + 2 × 4

7. 25 ÷ 5 + 6 × (12 - 4) 8. 80 - 8 × 32 9. 11 × (9 - 22)

10. GARDENING Refer to Example 2 above. Suppose that the gardener did not buy enough

flowers and goes back to the store to purchase four more packs. She also purchases ashovel for $16. Write an expression that shows the total amount she spent to plantflowers in her garden.

Order of Operations

1. Simplify the expressions inside grouping symbols, like parentheses.2. Find the value of all powers.

3. Multiply and divide in order from left to right.4. Add and subtract in order from left to right.

Reteach

Numerical ExpressionsA

Example 1

Example 2


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Skills Practice

Numerical Expressions

Find the value of each expression.

1. 7 - 6 + 5 2. 31 + 19 - 8

3. 64 - 8 + 21 4. 17 + 34 - 2

5. 28 + (89 - 67) 6. (8 + 1) × 12 - 13

7. 63 ÷ 9 + 8 8. 5 × 6 - (9 - 4)

9. 13 × 4 - 72 ÷ 8 10. 16 ÷ 2 + 8 × 3

11. 30 ÷ (21 - 6) × 4 12. 6 × 7 ÷ (6 + 8)

13. 88 - 16 × 5 + 2 - 3 14. (2 + 6) ÷ 2 + 4 × 3

15. 43 - 24 ÷ 8 16. 100 ÷ 52 × 43

A


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6-1B


Evaluate 35 + x if x = 6.

35 + x = 35 + 6 Replace x with 6.= 41 Add 35 and 6.

Evaluate y + x if x = 21 and y = 35.

y + x = 35 + 21 Replace x with 21 and y with 35.= 56 Add 35 and 21.

Evaluate 4n + 3 if n = 2.

4n + 3 = 4 · 2 + 3 Replace n with 2.= 8 + 3 Find the product of 4 and 2.= 11 Add 8 and 3.

Evaluate 4n - 2 if n = 5.

4n - 2 = 4 · 5 - 2 Replace n with 5.= 20 - 2 Find the product of 4 and 5.= 18 Subtract 2 from 20.

Exercises

Evaluate each expression if y = 4.

1. 3 + y 2. y + 8 3. 4 · y

4. 9 y 5. 15 y 6. 300 y

7. y2 8. y2 + 18 9. y2 + 3 · 7

Evaluate each expression if m = 3 and k = 10.

10. 16 + m 11. 4k 12. m · k

13. m + k 14. 7m + k 15. 6k + m

16. 3k - 4m 17. 2mk 18. 5k - 6m

19. 20m ÷ k 20. m3 + 2k 2 21. k 2 ÷ (2 + m)

Example 1

Example 2

Example 3

Example 4

Reteach

Algebra: Variables and Expressions

• A variable is a symbol, usually a letter, used to represent a number.

• In addition to the symbol×, the other ways to show multiplication are 2·3, 5t , and st .• Algebraic expressions contain at least one variable and at least one operation.


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6-1B


Complete the table.

Algebraic Expressions Variables Numbers Operations

1. 5d + 2c

2. 5w - 4 y + 2s

3. xy ÷ 4 + 3m - 6

Evaluate each expression if a = 3 and b = 4.

4. 10 + b 5. 2a + 8 6. 4b - 5a

7. a · b 8. 7a · 9b 9. 8a - 9

10. b · 22 11. a 2 + 1 12. 18 ÷ 2a

13. a 2 · b 2 14. ab ÷ 3 15. 15a - 4b

16. ab + 7 · 11 17. 36 ÷ 6a 18. 7a + 8b · 2

Evaluate each expression if x = 7, y = 15, and z = 8.

19. x + y + z 20. x + 2 z 21. xz + 3 y

22. 4 x - 3 z 23. 4 x - 17 24. 6 z - 5 z

25. 9 y ÷ (2 x + 1) 26. 14 + 2 z 27. z ÷ 2

28. xz 29. y - x 30. 13 y - zx ÷ 4

31. xz - 2 y + 8 32. 2 xz 33. 3 y · 40 x - 1,000

Skills Practice

Algebra: Variables and Expressions


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6-2C


Reteach

The Distributive Property

Find 6 × 38 mentally using the Distributive Property.

6 × 38 = 6(30 + 8) Write 38 as 30 + 8.

= 6(30) + 6(8) Distributive Property

= 180 + 48 Multiply mentally.

= 228 Add.

So, 6 × 38 = 228.

Use the Distributive Property to rewrite 4( x + 3).

4( x + 3) = 4( x) + 4(3) Distributive Property

= 4 x + 12 Multiply.

So, 4( x + 3) can be rewritten as 4 x + 12.

Exercises

Find each product mentally. Show the steps you used.

1. 4 × 82 2. 9 × 26

3. 12 × 44 4. 8 × 5.7

Use the Distributive Property to rewrite each algebraic expression.

5. 5( y + 4) 6. (7 + r)3 7. 12( x + 5)

8. (b + 2)9 9. 4(4 + a) 10. 9(7 + v)

• To multiply a sum by a number, multiply each addend by the number outside the parentheses.

• a(b + c) = ab + ac

• (b + c)a = ba + ca

Example 1

Example 2


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6-2C


Find each product mentally. Show the steps you used.

1. 3 × 78 2. 7 × 74

3. 8 × 92 4. 6 × 57

5. 11 × 42 6. 12 × 27

7. 6 × 5.2 8. 4 × 9.4

Use the Distributive Property to rewrite each algebraic expression.

9. 7( y + 2) 10. (8 + r)4 11. 8( x + 9)

12. (b + 5)12 13. 4(2 + a) 14. 7(6 + v)

15. (b - 5)15 16. 3(5 - v) 17. 6(11 - s)

Skills Practice

The Distributive Property


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Reteach

Algebra: Properties

6-2

Determine whether 6 + (4 + 3) and (6 + 4) + 3 are equivalent.

The numbers are grouped differently. They are equivalent by the Associative Property. So,6 + (4 + 3) = (6 + 4) + 3.

The formula for the perimeter of a triangle is P = a + b + c.Find the perimeter of a triangle where a = 12, b = 5, and c = 8.

P = a + b + c Write the formula. P = 12 + 5 + 8 Replace a with 12, b with 5, and c with 8. P = 12 + 8 + 5 Commutative Property P = 25 units

Exercises

Determine whether the two expressions are equivalent. If so, tellwhat property is applied. If not, explain why.

1. 9 · 1 and 9 2. 7 · 3 and 3 · 7

3. 6 - (3 - 2) and (6 - 3) - 2 4. (10 · 2) · 5 and 10 · (2 · 5)

5. The formula for the volume of a rectangular prism is V = ℓwh, where ℓ is

the length, w is the width, and h is the height. Find the volume of a

rectangular prism, in cubic units, if the length is 8 units, the width is

11 units, and the height is 10 units. Use the Commutative Property.

Example 1

Example 2

Property Symbols Numbers

Commutative a + b = b + aa · b = b · a

5 + 3 = 3 + 55 · 3 = 3 · 5

Associative (a + b) + c = a + (b + c)

(a · b) · c = a · (b · c)

(2 + 3) + 4 = 2 + (3 + 4)

(2 · 3) · 4 = 2 · (3 · 4)

Identity a + 0 = a

a · 1 = a5 + 0 = 55 · 1 = 5

Use the properties to make mental math easier.


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A


Determine whether the two expressions are equivalent. If so, tell

what property is applied. If not, explain why.

1. 2 · (3 · 7) and (2 · 3) · 7 2. 6 + 3 and 3 + 6

3. 26 - (9 - 7) and (26 - 9) - 7 4. 18 · 1 and 18

5. 7 · 2 and 2 · 7 6. 6 - (4 - 1) and (6 - 4) - 1

7. 7 + 0 and 7 8. 0 + 12 and 0

9. 625 + 281 and 281 + 625 10. (12 · 18) · 5 and 12 · (18 · 5)

11. 2 + (8 + 2) and (2 + 8) + 2 12. 40 ÷ 10 and 10 ÷ 40

Use one or more properties to rewrite each expression as an

expression that does not use parentheses.

13. ( p · 1) · 6 14. (a + 5) + 23

15. 7 · ( y · 3) 16. (b + 4) + 17

17. 6 + ( x + 50) 18. ( y · 200) · 2

6-2Skills Practice

Algebra: Properties


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7-1


You can solve an equation by using inverse operations, which undo operations. To solve an additionequation, you would use subtraction.

Reteach

Solve and Write Addition EquationsD

Solve x + 2 = 7.

Method 1: Use models.

x + 2 7=

=

x + 2- 2 7 - 2=

=

So, the solution is 5.

Method 2: Use symbols.

x + 2 = 7 Write the equation. −2 −2 Subtract 2 from each side to undo the

addition of 2 on the left.

x = 5 Simplify.

Check

x + 2 = 7 Write the equation.

5+

2

7Replace x with 5.

7 = 7 The sentence is true.

Subtraction Property of Equality If you subtract the same number from each side of an equation, thetwo sides remain equal.

Example 1

While at an aquarium, Alec saw sharks swimming together. Henoticed the 8-foot blacktip shark and a spinner shark togetherwere the length of the 14-foot hammerhead shark. What was thelength of the spinner shark?

Example 2

Words Blacktip length and spinner length is hammerhead length.

Variable Let s represent the spinner length.

Model

14 feet

8 feet s feet

Equation 8 + s = 14

8 + s = 14 Write the equation.− 8 − 8 Subtract 8 from both sides.

s = 6 14 – 8 = 6

So, the length of the spinner shark is 6 feet.

Exercises

Solve each equation. Check your solution.

1. a + 1 = 7 2. 3 + b = 8 3. c + 3 = 10

4. 9 = x + 4 5. 10 = x + 6 6. 11 = 2 + j


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7-1F

Reteach

Solve and Write Subtraction Equations

Solve x −

4 = 10.


Model the equation.

x

10 4

Solve the equation.

By looking at the bar diagram, you can seethat you will have to add to find x.

10 + 4 = 14

The solution is 14.


x − 4 = 10 Write the equation.

+4 +4 Add 4 to each side.

x = 14 Simplify.

Check

x − 4 = 10 Write the original equation.

14 − 4 10 Replace x with 14.


An average Sandhill crane is 37 inches tall. This is 22 inches lessthan the average Whooping crane’s height. How tall is the averageWhooping crane?

Words Whooping crane’s height minus 22 is Sandhill crane’s height.

Variable Let w represent the Whooping crane’s height.

Model w

37 in. 22 in.

Equation w − 22 = 37

w − 22 = 37 Write the equation.

+ 22 + 22 Add 22 to both sides.

w = 59 Simplify.

An average Whooping crane has a height of 59 inches.

Exercises


1. a − 2 = 3 2. b − 1 = 7 3. c − 4 = 4

4. 5 = v − 8 5. 4 = t − 6 6. 9 = m − 3

Example 1

Example 2

Addition and subtraction are inverse operations. Therefore, you can solve a subtraction equation byadding.

Addition Property of Equality If you add the same number to each side of an equation, the two sides

remain equal.


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NAME ________________________________________ DATE _____________ PERIOD _____




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7-2 Reteach

Solve and Write Multiplication Equations

The number by which a variable is multiplied is called the coefficient. For example, in the expression

5 x , the coefficient of x is 5. Because multiplication and division undo each other, use division to solvea multiplication equation.

Solve 2 x = 6.

A category 5 hurricane can have a storm surge of 20 feet. This isabout 5 times greater than the storm surge of a category 1hurricane. What is the storm surge of a category 1 hurricane?

5c = 20 Write the equation.

5c

5 =

20

5

Divide both sides by 5.

c = 4 Simplify.

The storm surge of a category 1 hurricane is about 4 feet.

Exercises


1. 5a = 25 2. 7c = 49 3. 3u = 27

4. 24 = 6d 5. 18 = 3 z 6. 56 = 7v

Example 1


=

=

2x 6=

x = 3

The solution is 3.


2 x = 6 Write the equation.

2 x

2 =

6

2

Divide each side by 2 to undo

the multiplication on the left.

x = 3 Simplify.

Check 2 x = 6 Write the original equation.

2(3) 6 Replace x with 3.


Example 2

Words 5 times category 1 surge is category 5 surge.

Variable Let c = category 1 storm surge.

Equation 5c = 20

B

Model the equation.

Divide the countersequally into two groups.


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7-2

D

Reteach

Solve and Write Division Equations

Use multiplication to solve division equations.

Solve x

4

= 6.

The Yungs are making 6 payments of $200 on their new televisionset. What was the cost of the television set?

Words: Total cost divided by 6 is $200.

c

6 = 200 Write the equation.

c

6

(6) = 200(6) Multiply both sides by 6.

c = 1,200 Simplify.

The total cost of the television was $1,200.

Exercises


1. a

2 = 4 2. c

3 = 6

3. g

5 = 10 4. 6 = d

4

5. 9 = t 3

6. 11 = w 6

Example 1


Model the equation.

There are four equal groups of 6. Multiply.6 × 4 = 24

The solution is 24.


x

4 = 6 Write the equation.

x

4

(4) = 6(4)Multiply each side by 4 to

undo the division on the left.

x = 24 Simplify.

Check x

4 = 6 Write the original equation.

24

4 6 Replace x with 24.


6

Example 2


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


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NAME ________________________________________ DATE _____________ PERIOD _____



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8-1D

Reteach

Function Rules

Use words and symbols to describe the value of each term as afunction of its position. Then find the value of the tenth term in thesequence.

Position 1 2 3 4 n

Value of Term 4 8 12 16

Study the relationship between each position and Position Value of term

1 × 4 = 4

2 × 4 = 8

3 × 4 = 12

4 × 4 = 16

n × 4 = 4n

the value of its term.

Notice that the value of each term is 4 times its

position number. So, the value of the term in positionn is 4n.

To find the value of the tenth term, replace n with 10in the algebraic expression 4n. Since 4 × 10 = 40,the value of the tenth term in the sequence is 40.

Exercises

Use words and symbols to describe the value of each term as afunction of its position. Then find the value of the tenth term in the

sequence.

1. Position 3 4 5 6 n






A sequence is a list of numbers in a specifi c order. Each number in the sequence is called a term. Anarithmetic sequence is a sequence in which each term is found by adding the same number to the

previous term.

Example


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NAME ________________________________________ DATE _____________ PERIOD _____



8-1D

Skills Practice

Function Rules

Use words and symbols to describe the value of each term as afunction of its position. Then find the value of the tenth term in the

sequence.

1.Position 5 6 7 8 n








Find a rule for each function table.

5. Input ( x) Output ( y)

5 0

6 1

7 2

8 3

x


2 14

4 16

6 18

8 20

x

7.Input ( x) Output ( y)

4 0

5 1

6 2

7 3

x


1 11

2 22

3 33

4 44

x


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NAME ________________________________________ DATE _____________ PERIOD _____



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9-1


Find the area of the trapezoid.

A = 1 2

h(b1 + b

2) Area of a trapezoid

A = 1 2 (4)(3 + 6) Replace h with 4, b

1 with 3, and b

2 with 6.

A = 1 2 (4)(9) Add 3 and 6.

A = 18 Simplify.

The area of the trapezoid is 18 square centimeters.

Exercises

Find the area of each figure. Round to the nearest tenth if necessary.

1.

7 in.

5 in.

14 in. 2. 8 cm

13.5 cm

18 cm

3.

7 in.

12 in.

26 in.

4.

0.8 m

0.4 m

0.9 m

A trapezoid has two bases, b1 and b

2. The height of a trapezoid is the

distance between the two bases. The area A of a trapezoid equals half

the product of the height h and the sum of the bases b1 and b

2.

A = 1 2 h(b

1 + b

2)

b 1

b 2

h

Example

4 cm

3 cm

6 cm

Reteach

Area of TrapezoidsD


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NAME ________________________________________ DATE _____________ PERIOD _____


9-1


Skills Practice

Area of Trapezoids

Find the area of each figure. Round to the nearest tenth if necessary.

1.

10 cm

9 cm

12 cm 2.

3 ft

2 ft

1.5 ft

3. 12 mm

18 mm

10 mm

4.

4 ft

3 ft

6.5 ft

5.

7 cm

9.2 cm

2 cm

6.

24 mm

20.7 mm

8 mm

7.

12 ft

20.1 ft

25 ft

8.

5.6 in.

6.9 in.

3.2 in.

9.

7.5 cm

12.2 cm

4.5 cm 10. 14 mm

3.8 mm

15.3 mm

11. trapezoid: bases 22.8 mm and 19.7 mm, height 36 mm

12. trapezoid: bases 5 ft and 3.5 ft, height 7 ft

13. DESKS What is the area of the top of the desk shown at right?

36 in.

18 in.

24 in.

D


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Answers for Activities (Please complete on your own first then

check your answers)—You must show work on the activities to get

full-credit!!!!

Activity 1:P. 24

1) 15.122) 36.553) 3.6964) 116.82835) 58.1166) 37.80427) 0.025928) 0.03489) 10.08P. 25

1) 0.152) 2.523) 16.754) 3.325) 2.7836) 0.5467) 0.268) 27.92589) 5.371410) 0.008711) 6.32412) 0.028413) 18.342714) 0.37815) 14.19616) 21.12517) 84.31518) 0.427519) 68.227220) 247.66121) 275.06522) 426.008

Activity 2:

P. 42

1) 72) 2.13) 23.44) 7.215) 5006) 159.9P. 43

1) 24.32) 3.63) 124) 4.55) 36) 187) 0.218) 8.19) 1.5310) 16.50611) 1.24312) 4.6813) 18.1214) 2.45615) 80.816) 3117) 7518) 0.12

Activity 3:P. 36

1)

2)

3)

4) 2

5)

6)

7)

8)

9) 10

10)

11)

12)

13)

14)

P. 37

1)

2)

3)

4)

5) 3

6)

7)

8)

9)

10)

11)

12)

13)

14)

15)

16)

17)

18)

19)

20)

21)

22)

23)

24)

25)

26) 30

Activity 4:P. 55

1)

2)


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full-credit!!!!

3)

4) 3

5) 66)

7)

8)

9)

10)

11)

12)

13)

14)

P. 56

1)

2) 1

3)

4)

5)

6)

7)

8)

9)

10)

11)

12)

13)14) 4

15)

16)

17)

18)

19)

20)

21)

22)

23)

24)

25)

26)

Activity 5:

P. 25

1) 90 min2) 3 blanketsP. 26

1) 24 cups2) $163) 42 oz4) 24 dogs5) 280 mi

Activity 6A:

P. 121) 132) 93) 74) 165) 176) 177) 538) 89) 5510) (4+5)x4+3+4+16

P. 131) 62) 423) 774) 495) 506) 957) 15

8) 259) 4310) 3211) 812) 313) 714) 1615) 6116) 256

Activity 6B:P. 18

1) 72) 123) 164) 365) 606) 12007) 168) 349) 3710) 1911) 4012) 3013) 1314) 3115) 6316) 1817) 6018) 3219) 620) 22721) 20P. 19

4) 145) 14

6) 17) 128) 7569) 1510) 8811) 1012) 313) 144


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full-credit!!!!

14) 415) 2916) 8917) 218) 8519) 3020) 2321) 10122) 423) 1124) 825) 926) 3027) 428) 5629) 830) 18131) 3432) 11233) 11,600

Activity 7A:P. 40

1) 3282) 2343) 5284) 45.65) 5y+206) 21+3r7) 12x+608) 9b+189) 16+4a10) 63+9vP. 41

1) 2342)518

3) 7364) 3425) 4626) 3247) 31.28) 37.69) 7y+1410) 32+4r

11) 8x+7212) 12b+6013) 8+4a14) 42+7v15) 15b-7516) 15-3v17) 66-6s

Activity 7B:P. 33

1) yes, Identity Property2) Yes; CommutativeProperty3) No; expressions notequal4) yes; AssociativeProperty5) V=8·10·11=880 cubicunitsP. 34

1) yes; AssociativeProperty2) yes; CommutativeProperty3) No; expressions arenot equal4) yes; Identity Property5) yes; CommutativeProperty6) No; expressions arenot equal7) yes; Identity Property8) No; expressions arenot equal9) yes; CommutativeProperty

10) yes; AssociateProperty11) yes; AssociativeProperty12) No; expressions arenot equal13) p·6 14) a+28

15) 21y16) b+2117) x+5618) 4000y

Activity 8A:P. 22

1) 62) 53) 74) 55) 46) 9

Activity 8B:P. 28

1) 52) 83) 84) 135) 106) 12

Activity 8C:P. 35

1) 52) 73) 94) 45) 66) 8

Activity 8D:P. 41

1) 82) 18

3) 504) 245) 276) 66


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full-credit!!!!

Activity 9:P. 23

1) subtract 2; n - 2; 82) multiply by 5; 5n; 503) add 7; n + 7; 17P. 24

1) subtract 3; n – 3; 72) multiply by 6; 6n; 603) add 9; n + 9; 194) multiply by 5; 5n; 505) n – 56) n + 127) n – 48) 11n

Activity 10:P. 25

1) 52.5 in² 2) 175.5 cm² 3) 198 in² 4) 0.5 m² P. 26

1) 105 cm² 2) 4.5 ft² 3) 150 mm² 4) 19 ft² 5) 39.2 cm² 6) 331.2 mm² 7) 270.6 ft² 8) 30.4 in² 9) 73.2 cm² 10) 136.2 mm² 11) 765 mm² 12) 29.8 ft² 13) 648 in²

Math teachers edition

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