LESSON 61 Adding Three or More Name...

$Page 1: LESSON 61 Adding Three or More Name Fractionsmrstrammell.weebly.com/uploads/9/1/9/3/9193986/crs1...Count the number of parts. 2 1 __ 4 = 9 __ 4 Use fraction manipulatives for help.$
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Adding Three or More Fractions (page 320)

• To add three or more fractions, apply the S. O. S. method:

1. Shape—Write the problem in the correct shape. Rename fractions to have common denominators. (Find the LCM. Use the times table for help.)

2. Operate—Add or subtract.

3. Simplify—Reduce or convert.

Practice Set (page 321)

a. b. c.

1 __

2 = __

3 __

4 = __

+ 1 __

8 = __

=

1

__ 2

= __

1

__ 3

= __

+ 1

__ 6

= __

=

1 1

__ 2

= __

1 1

__ 3

= __

+ 1 1 __

4 = __

=

d. e. f.

1 __

2 = __

2 __

3 = __

+ 5 __

6 = __

=

1

__ 2

= __

3

__ 4

= __

+ 7

__ 8

= __

=

1 1 __

4 = __

1 1 __

8 = __

+ 1 1

__ 2 = __

=

g. perimeter

5 __

8 = __

3 __

8 = __

+ 1 __

2 = __

=

h. Word problem for a.: John ate 1 _ 2 of a . Sam ate 3 _ 4 and Becky

ate 1 _ 8 of another . All together how many did they eat?

Saxon Math Course 1 L61-241 Adaptations Lesson 61

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1. 20

___ 6 = 2. (2 × ) +

1 __

2 fathom =

fathom = ? ft

3. average

3 ) _______

2 7 6 9

4.

5 1 __

2 = __

– 1 2 __

3 = __

5.

5 1 __

3 = __

– 2 1 __

2 = __

6.

1 1 __

2 = __

2 1 __

3 = __

+ 3 1 __

4 = __

7.

3 3 __

4 = __

+ 3 1

__ 3

= __

8. a. 2 __

3

3 __

5 b. 4 2 √

_____ 144

___ 15

___ 15

9. 5 __

6 × 6 2 = 10.

3 __

8 ∙

2 __

3 =

Written Practice (page 321)

b. a.

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11. 3 __

8 ÷

2 __

3

__ × __ =

12. (4 – 0.4) ÷ 4 =

.– 0.4 )

_____

13. 4 – (0.4 ÷ 4) =

) _____

.– .

14.

49.638.7

15. $642.23

$861.17

Round $642.23 to and

$861.17 to .

Then .

16. a. The diameter is t the radius.

17. 100, 10, 1, 18. perimeter in.

each side

area

19. dime

quarter

__ = 20. 15m = 3 ∙ 10 2

Written Practice (continued) (page 322)

4 cm

.

a.

b.

m =

.

.

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21. 1 ___

10 =

n ____

100 22.

2 __

3 × __ = ___

15

23. time now

Count forward hours.

Count forward minutes.

24. area

each side

perimeter

25. 26. Round $4.95 to and $2.79 to .

Add to get $ . Multiply 7% times $

to get ¢. Add again.

27. shift

$37.00

28.

29. area of each face 30. surface area of 6 faces


n =

a.

b.

c.

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Teacher Notes:• Review Hint #33, “Improper

Fractions.”

• Refer students to “Mixed Numbers and Improper Fractions” on page 12 in the Student Reference Guide.”

Writing Mixed Numbers as Improper Fractions (page 324)

• To change mixed numbers to improper fractions, do one of the following:

Count the number of parts.

2 1 __

4 =

9 __

4

Use fraction manipulatives for help.

Try this shortcut:

1. Multiply the denominator times the whole number: 4 × 2 = 8

2. Add the numerator: 8 + 1 = 9

3. Keep the original denominator: 9

__ 4

Example: 2 1 _ 4 Multiply; then add. (4 × 2) + 1 9 __

4


Write each mixed number as an improper fraction.

a. 2 4

__ 5 = b. 3

1 __

2 = c. 1

3 __

4 =

d. 6 1 __

4 = e. 1

5 __

6 = f. 3

3 ___

10 =

g. 2 1 __

3 = h. 12

1 __

2 = i. 3

1 __

6 =

j. Write 1 1 _ 2 and 3 1 _ 3 as improper fractions. Then multiply the improper fractions. What is the product?

1 1 __

2 3

1 __

3

___ ×

___ =

+

×


+

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1. a. 1 = __ 4

b. 1 __

4 = __

8

2. (5 × )+ 2 1

__ 2

in. = ft = ? in.

3. not prime

A 11 B 21 C 31 D 41

4. 1 1 __

3 1

1 __

2

___ ×

___ =

5. part 20%

partwhole 100%

6. average

$36.2541.50

$43.75

7. Double both.

15 2 1

__ 2

÷ =

8. m – 4 3 __

8 = 3

1 __

4

4 3

__ 8

= ___

3 1

__ 4

= ___

9. n + 3 ___

10 =

3 __

5

3

__ 5 = ___

3 ___

10 = ___

10. 6d = 0.456

a.

b.

÷ = m =

d =n =

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11. 0.04w = 1.5 12.

13.

5 __

6 = ___

– 1

__ 2

= ___

14. 1 __

2 ∙

4 __

5 =

15. 2 __

3 ÷

1 __

2

___ ×

___ =

16. 1 – (0.2 – 0.03) =

0.2 0.03

1. .

17. (0.14)(0.16) =

0.14 0.16

18. cm

mm

1 ___

10

2.5 ___

?

19. • List the factors of the smaller number, 18.

• Cross off the factors that are NOT factors of the

larger number, 24.

• Circle the greatest factor.

, , , , ,

20. a. red

total

___ =

b. The probability of

drawing not

is .

1

__ 2 =

___

3

__ 4 =

___

+ 5

__ 8 =

___

w =

Use work area.Use work area.

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21. perimeter

each side

area

22. 14° 0° –6°

23. C = πd 24. baseball football

25. baseball

total

___ = 26. . A majority of 100 people is at least

. sport was the favorite

of or more people.

27. football percent 28. 40% =

is

of

___ ___

29. 30. median

8.99.09.19.2

9.2


Favorite Sportof 100 People

Baseball40

Other16

Football22

Basketball22

==

Use work area.

∙ ∙

a.

b.

1 1 _ 2 in.

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Subtracting Mixed Numbers with Regrouping, Part 2 (page 329)

• To subtract mixed numbers with regrouping:

1. Rename the fraction to have common denominators.

2. If needed, borrow from the whole number. Combine the borrowed fraction with the given fraction.

3. Subtract.

4. Reduce to lowest terms, if needed.

Example: Rename Borrow Combine

5 1 __

2 = 5

3 __

6

– 1 2 __

3 = 1

4 __

6

4 9 __

6

– 1 4

__ 6

3 5

__ 6


a. b. c.

5 1 __

2 = __

– 3 1 __

3 = __

4 1

__ 4

= __

– 2 1

__ 3

= __

6 1 __

2 = __

– 1 3

__ 4

= __

d. e. f.

7 2 __

3 = __

– 3 5 __

6 = __

6 1 __

6 = __

– 1 1

__ 2

= __

4 1 __

3 = __

– 1 1

__ 2

= __

g. h. i.

4 5

__ 6 = __

– 1 1 __

3 = __

6 1 __

2 = __

– 3 5

__ 6

= __

8 2 __

3 = __

– 5 3

__ 4

= __

j. John had 5 1 _ 2 pizzas. His friends ate of them. How many pizzas were left?

Answer:


5 3 __

6 +

6 __

6 =

4

=

= =

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1. ( + ) – ( × ) = 2. Mt. Whitney 14,494 ftsea level 0 ftDeath Valley –282 ft

3.

39° 11°

Fahrenheit or Centigrade?

4. 4 2 __

3 =

5. Find the tens place.

$678.25 $6 .00

is more than 5, so I rounded .

6. time now

Count forward hours.

Count forward minutes.

7. (30 × 15) ÷ (30 – 15) = 8. 5 __

8

2 __

3

9. w – 3 2 __

3 = 1

1 __

2

3 2 __

3 = __

1 1 __

2 = __

10.

6 __

8 = __

– 3

__ 4

= __


==

w =

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19. 10th prime number 20. perimeter

11.

6 1 __

4 = __

– 5 5 __

8 = __

12. 3 __

4 ×

2 __

5 =

13. 3 __

4 ÷

2 __

5

___ ×

___ =

14. (1 – 0.4)(1 + 0.4) =

1.0– 0.4

1.0+ 0.4

15. 60% =

is

of

___ ___

16. 0.4 ÷ 8 =

) ______

.

17. 8 ÷ 0.4 =

) _____

18. 0.2, 0.4, 0.6, 0.8, , ...


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21. A triangular prism has how many

a. faces? b. edges? c. vertices?

22. 2 1 __

2 1

1 __

5

___ ×

___ =

23. 24. ( × ) + 1

__ 2 ton =

ton = ? lb

25. 0.2 26. Round each answer to the nearest centimeter. Use 3.14 for π.

27. 30% =

is

of

__ __

28. 11.5 mi + d = 26.2 mi

26.2+ 11.5

29.

$15.49+ $

+ 0.07

30.

1 __

2 = ___

3

__ 4

= ___


a.

b.

d =

c. b. a.

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Teacher Notes:• Introduce Hint #52, “Classifying

Quadrilaterals.”• Refer students to “Classifying

Quadrilaterals” and “Quadrilaterals” on pages 16 and 18 in the Student Reference Guide.


Classifying Quadrilaterals(page 333)

• A quadrilateral is any polygon with four sides.

• The chart shows different types of special quadrilaterals and their names.

• Looking at the chart, you can see that:

A quadrilateral is a special kind of polygon.

A parallelogram is a special kind of quadrilateral.

A rectangle is a special kind of parallelogram.

A square is a special kind of rectangle.

A square is also a special kind of rhombus.


a. What is a quadrilateral? A quadrilateral is a polygon with sides.

b. Describe the difference between a parallelogram and a trapezoid. A parallelogram has pairs of

parallel sides; a trapezoid has only pair of parallel sides.

c. Draw a rhombus that is a square.

d. Draw a rhombus that is not a square.

e. True or false: Some rectangles are squares.

f. True or false: All squares are rectangles.

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1. ( + ) ÷ ( – ) = 2. Shakespeare died

1616 1564 born

3. yd

ft

1

__ __ ? 4. A square is a four-sided p , so it

is a q . The four sides of a square are

the same l , and the four angles are

the s size, so a square is

“r .”

5. sides

inches

___ 36

1 __

? 6.

1 __

4 =

? ____

100

7. 8 × 8

______ 8 + 8

= 8.

5 2

__ 3

= __

+ 3 3 __

4 = __

9.

1 __

2 = __

2 __

3 = __

+ 1 __

4 = __

10.

9 ___

10 = __

– 1

__ 2

= __


Use work area.

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19. 12th prime number 20. area sq. cm

a. each side

b. perimeter

11.

6 1 __

2 = __

– 2 7

__ 8

= __

12. 2 × 0.4 2 + 0.4

13.

0.35× 04.8

14. over, over, up

1 ÷ 0.4 =

) _____

15. over, over, up

) _____

4.80

16. rounded

0.38 0.33

17. area 18. See the Student Reference Guide.


a. b.

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21. How many faces? Use a cube.

Draw a pattern of 6 squares to show a cut apart box.

22. a. area of each face

b. total surface area

23. mc

cm

1 __

2.5 ___

? 24. 1

1 __

2 2

1 __

2

___ ×

___ =

25. • List two factors of the given number. • Continue to factor until each factor is a prime

number.• Write the prime factors in order.

9 = ∙

10 = ∙

12 = ∙ ∙

26. Write 75% as an unreduced fraction and as a decimal number.

27. Cancel the matching factors.

2 ∙ 2 ∙ 2 ∙ 3 ∙ 3

_____________ 2 ∙ 2 ∙ 3 ∙ 5 ∙ 5

=

28. 16.6 mi + d = 26.2 mi

26.2 16.6

29. a. Tuesday’s high °C 0° Tuesday’s low °C

b. highest °C 0° lowest °C


==

==

30. The daily low temperature probably about 5 degrees.

The two lines seem to be following each other closely.

Use work area.

Use work area.

a.

b.

d =

Use work area.

a.

b.

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• A prime number has exactly two factors—no more, no less. These factors are one and the prime number.

• A composite number has more than two factors.

• Prime factorization is writing a composite number as a product of its prime factors.

• To find the prime factorization of a number using the factor tree method:

1. List two factors of the given number.2. Continue to factor until each factor is a

prime number. (Circle the prime factors.)3. Write the prime factors in order.

• Another way to do prime factorization is Division by Primes.

1. Write the number in a division box.2. Divide by the smallest prime number that is

a factor. Divide that answer by the smallest prime number that is a factor.

3. Repeat until the quotient is 1.

4. The divisors are the prime factors of the number. Write them in order.

Teacher Notes:• Introduce Hint #53, “Prime

Factorization Using Division by Primes,” and Hint #54, “Finding Square Roots Using Prime Factorization.”

• Review “Prime Numbers” on page 9 in the Student Reference Guide.


Prime Factorization Division by Primes Factor Trees (page 337)


a. Which of these numbers are composite numbers? 19, 20, 21, 22, 23

b. Write the prime factorization of each composite number in problem a.

20 = · ·

21 = ·

22 = ·

c. Use a factor tree to find the prime factorization of 36.

36 = · · ·

d. Use division by primes to find the prime e. Write 125 as a product offactorization of 48. prime factors.

48 = ∙ ∙ ∙ ∙ 125 = · ·

Composite Number(Prime factorization)

Prime Number(Factors)

60 = 2 · 2 · 3 · 5 Remember: 1 is not a prime number.

Division by Primes

420 = 2 ∙ 2 ∙ 3 ∙ 5 ∙ 7

17 )

__ 7

5 ) ___

35 3 )

_____ 105

2 ) _____

210 2 )

_____ 420

) _____

) _____

) _____

) _____

) _____

48

, ,

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f. Write the prime factorization of 10, 100, 1000, and 10,000. What pattern do you notice?

The number of 2s and 5s increases by as the power of 10 i .


9.

1 ___

12 = __

1

__ 6 = __

+ 1 __

2 = __

10. 15 3

__ 4

– m = 2 1

__ 8

15 3 __

4 = __

2 1 __

8 = __

1. fifty-seven million, five hundred six thousand square miles

2. 3. madetotal

___

4. 5. composite

A 21 B 31 C 41

6. 2 2 __

3 ×

3 __

8

___ ×

___ =

7. not red

total

___ = 8.

8 1 __

2 = __

1 1 __

3 = __

+ 2 1

__ 6 = __


000,10 = 2 · 5100 = 2 · 2 · 5 · 5

1000 = ∙ ∙ ∙ ∙ ∙

10,000 = ∙ ∙ ∙ ∙ ∙ ∙ ∙

( × ) + 1

__ 2

ft = ft = ? in.

m =

∙ ∙

Practice Set (continued) (page 340)

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11. 4 ___

25 =

n ____

100 12. 12w = 0.0144

13. 3 __

8 × 1 __

3 = y 14.

1

__ 2

= __

– 1

__ 3

= __

2

__ 3

= __

– 1

__ 2

= __

15. 1 – (0.2 + 0.48)

0.2+ 0.48

.– .

16. erasers

$rasers

1 _____

0.50 __

?

plus tax

Half a dollar each for 2 dozen.8% is 8¢ per dollar.

17. dollars

quarters

1 __ __

? 18.

19.

) ___

) ___

) ___

50

20. Name this shape. How many vertices does it have?


n = w =

y =

a.

b.

c.

vertices ∙ ∙

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21. 3 4 __

7 = 22. area sq. in.

a. each side

b. perimeter

23. 16% = 24. millimeters

25. Use a meterstick to estimate. 26.

) _____

) _____

) _____

) _____

375

) ______

) ______

) ______

) ______

) ______

) ______

1000

375 = · · ·

1000 = · · · · ·

27. Reduce.

3 ∙ 5 ∙ 5 ∙ 5

________________ 2 ∙ 2 ∙ 2 ∙ 5 ∙ 5 ∙ 5

=

28. The diameter is ft.

π is a little more than ,

and times

is .

29. is

of

___ ___ 30. A rectangle is a f -sided polygon

with four right a . Since every

square is four-sided with four r

angles, every square is a r .

15 ft


a.

b.

Use work area.

Use work area.

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Multiplying Mixed Numbers (page 342)

• To multiply mixed numbers:

1. First, change the mixed numbers to improper (“top heavy”) fractions.

2. Then multiply.

3. Simplify (reduce) as necessary.

2 1 __

2 × 1

2 __

3

Change mixed numbers to improper fractions first.

5 __

2 ×

5 __

3 =

25 ___

6

25 ___

6 = 4

1 __

6

Multiply. Then simplify.


a. 1 1

__ 2 ×

2 __

3 b. 1

2 __

3 ×

3 __

4 c. 1

1 __

2 × 1

2 __

3

___ ×

___ =

___ ×

___ =

___ ×

___ =

d. 1 2 __

3 × 3 e. 2

1 __

2 × 2

2 __

3 f. 3 × 1

3 __

4

___ ×

___ =

___ ×

___ =

___ ×

___ =

g. 3 1

__ 3 × 1

2 __

3 h. 2

3 __

4 × 2 i. 2 × 3

1 __

2

___ ×

___ =

___ ×

___ =

___ ×

___ =

j. Check the reasonableness of the products in e. and h. by sketching rectangles on the grids below.( See the bottom of page 343 for an example.)

k. The strip of grass was 2 1 _ 2 ft wide and 6 2 _ 3 ft long. What was the area that needed to be mowed?

Answer:

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1. is

of

__ ?

__ 2. boys

students

girls

3. ydft

1 __

? ___

33

ydlb

1 ____

155 __

?

4. 1 1

__ 2 × 2

2 __

3

___ ×

___ =

5. 2 2 __

3 × 2

___ ×

___ =

6. average of 5 numbers

200

7. 100 + 75

_________ 100 – 75

= 8.

1 1

__ 5

= __

+ 3 1

__ 2

= __

9.

1 ___

3 = __

1 ___

6 = __

+ 1 ___

12 = __

10.

35 1

__ 4 = __

– 12 1 __

2 = __


a.

b.

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19. shift

0.075

20. sidesmeters

1 ___

0.8 __

?

11. 4 __

5 ×

1 __

2 = 12.

4 __

5 ÷

1 __

2

___ ×

___ =

13. 0.25 ÷ 5 =

) ______

14. 5 ÷ 0.25 =

) ______

15. × 0 0

17. 30

5

18. items$

_____ 0.75

6 __

?


16. 1 __

2 +

1 __

2 is equal to which of the following?

A 1 __

2 –

1 __

2 = B

1 __

2 ×

1 __

2 = C

1 __

2 ÷

1 __

2 =

∙ ∙

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21. 20

___ = 22. 12° 0° –8°

23. range 24. mean

25. How much does the

weigh than the ?

Answer:

26.

) ______

) ______

) ______

) ______

) ______

) ______

400

27. area

each side

28. shift

kglb

1 __

100 ____

?

29. Reduce.

5 ∙ 5 ∙ 5 ∙ 7

________________ 2 ∙ 2 ∙ 2 ∙ 5 ∙ 5 ∙ 5

=

30. Which of these polygons is not a regular polygon?

The sides of a regular polygon are equal in length.


==

A B C D

Use work area. ∙ ∙ ∙ ∙ ∙

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Using Prime Factorization to Reduce Fractions (page 346)

• To reduce fractions using prime factorization:

1. Write the prime factorization of the numerator and denominator.

375

_____ 1000

= 3 ∙ 5 ∙ 5 ∙ 5

_________________ 2 ∙ 2 ∙ 2 ∙ 5 ∙ 5 ∙ 5

2. Then reduce the common factors and multiply the remaining factors.

3 ∙ 5 ∙ 5 ∙ 5

________________ 2 ∙ 2 ∙ 2 ∙ 5 ∙ 5 ∙ 5

= 3 __

8

5 ) __

5 5 )

___ 25

5 ) _____

125 2 )

_____ 250

2 ) _____

500 2 )

______ 1000

5 ) __

5 5 )

___ 25

5 ) _____

125 3 )

_____ 375


Write the prime factorization of the numerator and denominator of each fraction and reduce each fraction.

a. 875

_____ 1000

= ∙ ∙ ∙ ________________

∙ ∙ ∙ ∙ ∙ = b.

48 ____

400 =

∙ ∙ ∙ ∙_________________ ∙ ∙ ∙ ∙ ∙

=

) _____

) _____

) _____

) _____

875

) ______

) ______

) ______

) ______

) ______

) ______

1000

) ___

) ___

) ___

) ___

) ___

48

) _____

) _____

) _____

) _____

) _____

) _____

400

c. 125

____ 500

= ∙ ∙ _____________

∙ ∙ ∙ ∙ = d.

36 ___

81 =

∙ ∙ ∙ __________ ∙ ∙ ∙

=

) _____

) _____

) _____

125

) _____

) _____

) _____

) _____

) _____

500

) ___

) ___

) ___

) ___

36

) ___

) ___

) ___

) ___

81

Teacher Note:• Review Hint #29, “Prime

Factorization Using the Factor Tree,” and Hint #53, “Prime Factorization Using Division by Primes.”

1 1 1

1 1 1

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1. ( 2 + 1

__ 2

+ 3 __

4 ) × $2 =

2 =

1 __

2 = __

3 __

4 = __

2.

6080+ 5280

3. 100 × each

$1.50 $0.05

÷ =

4. 6 cm + k = 11 cm

11+ 6

5. 8g = 9.6 6. 7 ___

10 – w =

1 __

2

7 ___

10 = ___

1 __

2 = ___

7. 3 __

5 =

n ____

100 8. average of 4 sides

172

There are many combinations of 4 lengths, so we (can, cannot) be certain.

9. $100.00 – ($46.75 + $9.68) =

$46.75+ $49.68

$100.00– $ .

10. (2 × 0.3)(0.2 × 0.3)

.– .


g =

n =

w =

k =

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11.

41 __

4 = __

– 27 __

8 = __

12. 2 2 __

3 × √

__ 9

___ ∙

___ =

13.

31

__ 3 = __

+ 23 __

4 = __

14. 1 1 __

3 × 2

1 __

4

___ ∙

___ =

15. 1.44 ÷ 60 =

) ______

16. $6.00 ÷ $0.15 =

) ______

17. ) ________

$5. 0 0 18. area

each side

perimeter

19. 625

_____ 1000

= ∙ ∙ ∙ ________________

∙ ∙ ∙ ∙ ∙ =

) _____

) _____

) _____

) _____

625

) ______

) ______

) ______

) ______

) ______

) ______

1000

20. area


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21. black

______ keys

___ = 22. Connect the correct corners to make a rectangular prism.

23. 1 1 __

2

___ × = 1

24. km

___ mk

1 __

2.5 ___

?

25. 0.1 26. Round to the nearest inch.

27. See the Student Reference Guide. 28. Write 51% as a fraction and as a decimal number.

29. probability of a prime number with one toss 30. See the Student Reference Guide.


6 in.

Use work area.

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Dividing Mixed Numbers (page 349)

• To divide mixed numbers:

1. First, change mixed numbers to improper (“top heavy”) fractions.

2. Copy the first fraction.

3. Change the ÷ sign to ×.

4. “Flip” the second fraction.

5. Cancel if you can.

6. Multiply across.

7. Simplify (reduce or convert) as necessary.

Example: 2 1 __

2 ÷ 1

3 __

4

5 __

2 ÷

7 __

4

5 __

2 ×

4 __

7 =

10 ___

7 = 1

3 __

7


a. 1 3

__ 5 ÷ 4 b.

1 __

4 of 1

3 __

5 c. 2

2 __

5 ÷ 3 d.

1 __

3 of 2

2 __

5

___ ×

___ =

___ ×

___ =

___ ×

___ =

___ ×

___ =

e. Dividing by 4 is the same as multiplying by 1 _ 4 because f. 1 2

__ 3 ÷ 2

1 __

2

both d the whole amount into fourths.

___ ×

___ =

g. 2 1 __

2 ÷ 1

2 __

3 h. 1

1 __

2 ÷ 1

1 __

2 i. 7 ÷ 1

3 __

4 j. 2

1 __

4 ÷

___ ×

___ =

___ ×

___ =

___ ×

___ =

___ ×

___ =

2

1

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1. ( + ) – ( × ) = 2. (2 × ) + =

3. (4 × ) + = 4. 1 1

__ 2 ÷ 2

2 __

3

___ ×

___ =

5. 1 1

__ 3 ÷ 4

___ ×

___ =

6. average in 6 games

108

7. 24

____ 200

= ∙ ∙ ∙ _____________

∙ ∙ ∙ ∙ =

) ___

) ___

) ___

) ___

24

) _____

) _____

) _____

) _____

) _____

200

8. m – 5 3 __

8 = 1

3 ___

16

53 __

8 = __

1 3 ___

16 = __

9. 3 3 __

5 + 2

7 ___

10 = n

3 3 __

5 = __

2 7 ___

10 = __

10. 25d = 0.375


min = ? s

ft = ? in.

m =

d =n =

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19. 641657344912

20. Divide bothby 8.

11. 3 __

4 =

w ____

100 12.

51

__ 8 = __

– 1 1 __

2 = __

13. 3 1 __

3 × 1

1 __

2

___ ×

___ =

14. 3 1

__ 3

÷ 1 1

__ 2

___ ×

___ =

15. area 16. (3.2 + 1) – (0.6 × 7) =

3.2 + 10.6 × 7 –

17. 12.5 ÷ 0.4 =

) ________

18. 3.2 × 10

A 32 ÷ 10 B 320 ÷ 10 C 0.32 ÷ 10


{88024

____ =

w =

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21. perimeter m

a. each side

b. area

22. $18,000× $18,000

23. 24. Polygons have s sides.

Since a c is curved, it

is not a p .

25. Compare:

1 __

3 × 4

1 __

2 4

1 __

2 ÷ 3

___ ×

___ =

___ ×

___ =

26.

27. obtuse 28. Write 3% as a fraction and as a decimal number.

29. See the Student Reference Guide.

r p

30. 6:20 a.m. 5:20 p.m. hr

5:20 p.m. 5:45 p.m. min


a. b.

Use work area.

∠

Use work area.

1,000,000

__________ 1,000,000

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• Complementary angles are two angles that total 90°.

• Supplementary angles are two angles that total 180°.

Teacher Note:• Refer students to “Angle Pairs” on

page 27 in the Student Reference Guide.


Lengths of Segments Complementary and Supplementary Angles (page 353)

• We know that points and vertices can have letter names.

• Lines and segments have letter names too.

• This line is line AB or line BA.

• There are three segments in this figure: ____

WX , ___

XY , and

____ WY . The length of

____ WX plus the length of

___ XY

equals the length of ____

WY .

WX + XY = WY WY – WX = XY


a. In this figure the length of ___

AC is 60 mm, and the length of

___ BC is 26 mm. Find

the length of ___

AB .

b. The complement of a 60° angle is an angle that measures how many degrees?

c. The supplement of a 60° angle is an angle that measures how many degrees?

d. If two angles are supplementary, can they both be acute? Why or why not?

(Yes / No) S angles total °. Acute angles are l than °.

Two angles less than ° cannot total 180°.

B A

DC

105°75°

105° 75°

∠PQR and ∠RQS are complementary angles because together they equal 90°.

∠A and ∠B are complementary angles because together they equal 90°.

∠A is the complement of ∠B. ∠B is the complement of ∠A.

30°

60°

A

B C

‹

___ › AB or

‹

___ › BA

∠1 and ∠2 are supplementary because together they equal 180°.

∠A and ∠B are supplementary because together they equal 180°.

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1. Draw a pair of parallel lines perpendicular to these lines. What kind of quadrilateraldid you make?

2. 1

__ 2

÷ ___

___ ×

___ =

3. 136° 0° –129°

4. 1 bill = 6 in.

bills = 1 ft

ft

____ bills

___ ? _____

1000

5. 45

___ 72

= ∙ ∙ _____________

∙ ∙ ∙ ∙ =

) ___

) ___

) ___

45

) ___

) ___

) ___

) ___

) ___

72

6. parallel to ___

RS

7. days

$ays

______ 27.50

1 __

$ 8.

1 × 2 × 3 × 4 × 5 _________________

1 + 2 + 3 + 4 + 5 =

9.

31 __

2 = __

2 3 __

4 = __

+ 15 __

8 = __

10. m + 1 3

__ 4 = 5

3 __

8

53 __

8 = __

13 __

4 = __


==

Practice Set (continued) (page 355)

e. In this figure, name two angles that appear to be supplementary.

∠ and ∠

f. Name two angles that appear to be complementary.

∠ and ∠

m =

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19. 20. eight-sided polygon

11. 3 __

4 – f =

1 __

3

3 __

4 = __

+ 1 __

3 = __

12. 2 __

5 w = 1

13. 8 ___

25 =

n ____

100 14. 1

2 __

3 ÷ 2

___ ×

___ =

15. 2 2

__ 3 × 1

1 __

5

___ ×

___ =

16. 2.4

_____ 0.08

=

) _______

17. 18. If a counting number is divisible by a

c number other than itself

or 1, then the number is c .


250

25

w =f =

n =

a.

b.

∙ ∙ ∙

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21. +

boysgirlsclass

a. girls

_____ class

___

b. boy

____ girl

___

22. Doubleboth.

23. reciprocal

2 1 __

2

24. kg

gk

1

__ 2.25

_____ ?

25.

cm

mm

1 ___

10 __

?

26.

27. Complete the cylinder.

See the Student Reference Guide.

28. least to greatest

0.1, 1, –1, 0

29. Shade 1 _ 4 of the circle.

What percent is that?

30.

×

{41 __

2

11

__ 2

___ =

number of cubes in bottom layer number of layerstotal cubes


a.

b.

Use work area. , , ,

WY =

L E S S O N

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Teacher Note:• Review Hint #40, “Canceling

Fractions.”


Reducing Fractions Before Multiplying (page 358)

• Reducing before multiplying is also known as canceling.

• Canceling may be done to the terms of multiplied fractions only.

• Canceling may be done in a diagonal direction.

• Canceling may be done in both directions.

• You cannot cancel horizontally.

10

___ 9

× 6 __

5 =

4 __

3 = 1

1 __

3

Long Way Shortcut

3 __

5 ×

2 __

3 =

6 ___

15 reduces to

2 __

5

3 __

5 ×

2 __

3 =

2 __

5


Cancel before multiplying.

a. 3 __

4 ∙

4 __

5 = b.

2 __

3 ∙

3 __

4 = c.

8 __

9 ∙

9 ___

10 =

Write in fraction form. Then cancel before multiplying.

d. 2 1

__ 4 × 4 e. 1

1 __

2 × 2

2 __

3 f. 3

1 __

3 × 2

1 __

4

9 __

4 ×

4 __

1 =

___ ×

___ =

___ ×

___ =

Rewrite each division problem as a multiplication problem. Then cancel before multiplying.

g. 2 __

5 ÷

2 __

3 h.

8 __

9 ÷

2 __

3 i.

9 ___

10 ÷ 1

1 __

5

2 __

5 ×

3 __

2 =

___ ×

___ =

___ ×

___ =

2

3

2

1

1

1

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1. seven million, two hundred-thousand dollars 2. 1 __

2 ÷ __

___ ×

___ =

3. 12 1 __

2 × 2 =

2 1

__ 2 × 2 =

4. 5 __

6 ∙

4 __

5 =

5. 5 __

6 ÷

5 __

2

___ ×

___ =

6. 9 ___

10 ∙

5 __

6 =

7. 8. √____

100 + 10 2 =

9.

3 2 __

3 = __

+ 4 5 __

6 = __

10.

7 1

__ 8 = __

– 2 1 __

2 = __


_____

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11.

4.37..

12. 0.46 ÷ 5 =

) _________

13. 60 ÷ 0.8

) _________

14. average

15. 1.5 ÷ 0.06 Shift.

A 15 ÷ 6 B 150 ÷ 6 C 150 ÷ 60

16. LmL

1 __

3.8 ___

?

17. 2 __

3 + n = 1

1

2 __

3

18. 2

__ 3

m = 1

19. f – 3 __

4 =

5 __

6

5 __

6 = __

3 __

4 = __

20.


m =n =

f =

a.

b.

c.

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21. 1 2 __

3 × 1

1 __

5

___ ×

___ =

22. 8

__ 9

÷ 2 2

__ 3

___ ×

___ =

23. 24. Monday =

+ 3

25. How much did John’s pulse increase from

to ?

Answer: beats per minute

26. 72

____ 300

= ∙ ∙ ∙ ∙ _____________ ∙ ∙ ∙ ∙

=

) ___

) ___

) ___

) ___

) ___

72

) _____

) _____

) _____

) _____

) _____

300

27. perimeter 28. area

29. 30.


2.5 cm

1.5 cm

SaturdayTuesday

Tuesda

Use work area.

and

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