Unit 4 – Number Patterns and Fractions Lesson 8 – Dividing Fractions

1

Blue – Divide Fractions and Mixed Numbers 1. Sara's weight is 1

2of Luke’s weight, whose weight is 3

4 of Dan’s weight, whose weight

is 78

of Ed’s weight. If Sara weighs 105 pounds, how much does Ed weigh?

2. Claire said to Anna, “I will give you half of my remaining money after I give 7

8 of it to

my favorite charity.” If Claire gave $43,750 to her favorite charity, how much money will Anna receive?

3. A meter is defined as the distance light travels in 1299,792,460

of a second. How many

meters does light travel in 14

of a second?

MULTIPLYING AND DIVIDING RATIONAL ALGEBRAIC EXPRESSIONS

Objective Given 2 rational expressions, multiply or divide them, and then simplify the answer.

Examples:

Multiply: 38

• 49

Combine the numerators with a multiplication sign between them (do the same with the denominators) Cancel any common factors of the numerator and denominator

(In this example, the 4 & 8 have a common factor of 2, and the 3 & 9 have a common factor of 3)

Divide: 6x2÷9x3

To divide, simply “flip” the second fraction (find the reciprocal in math terms) and multiply as above. Notice that you can cancel the variables in exactly the same fashion as numbers; just factor out the GCF.

Unit 4 – Number Patterns and Fractions Lesson 8 – Dividing Fractions

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4. 1065 8

yxy xi

5. 5a7b

÷25a21b

6. 20 4249 10

p ps si

7. 30m13t

÷15t52m

8. 26 42

35 18ab ab abi

9. 2 3 4

5 2

3 125 10p c p cc c

÷

10. 5 6 84 10 12r r ts s ti i

11. a. ab÷1b b. a

b÷ b c. b÷ a

b d. b÷ b

a

e. a2÷a3 f. a

2÷3a g. 2

a÷3a h. 2

a÷a3

i. a÷ 1a j. 2÷ 1

x k. 1

x÷ 5 l. 1

b÷ b

m. 1c÷3 n. 6÷ 1

m o. a

b÷ab p. 2a

3÷ a

q. 3a4÷a2

2 r. t

8÷t2

12 s. a

b÷abc

t. 2a2

b÷a6

Task: Practice multiplying and dividing fractions with variables. Find the value of the variable in each question to make each equation true.

12. p • 56=23

13. a ÷ 34=13

14. 78n = 1

4

15. m ÷34= 102

3

Unit 4 – Number Patterns and Fractions Lesson 8 – Dividing Fractions

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Solutions

1. 320 pounds Sara's weight: 105 pounds Luke's weight is twice as much as Sara's weight: 210 pounds

Luke's weight of 210 pounds is 3/4 of Dan's weight. If 3/4 is 210 pounds, then 1/4 must be 210 ÷ 3 = 70 pounds. If 1/4 = 70 then 4/4 (or all) must equal 280 pounds Dan's weight: 280 pounds

Dan's weight of 280 pounds is 7/8 of Ed's weight. If 7/8 is 280 pounds, then 1/8 must be 280 ÷ 7 = 40 pounds. If 1/8 = 40 pounds, then 8/8 = 8 x 40 = 320 pounds. Ed's weight: 320 pounds

2. $3,125 If 7/8 of Claire’s money is $43,750, then 1/8 of her money must be $43,750 ÷ 7 = $6250. If 1/8 is equal to $6250, then 8/8 (or all) of Claire’s money must be equal to $6250 x 8 = $50,000 $50,000 - $43,750 = $6250 remaining Half of $6250 = $3125

3. 74,948,115 meters 1/4 ÷ 1/299,792,460 = 74,948,115 HELPFUL STRATEGY: It is often very difficult to figure out what numbers to multiply or divide when problems contain fractions. If you substitute “easy” whole numbers into the problem and solve, it makes the steps to solving the problem much easier to see. Change numbers to 2 and 10 to help the brain understand the problem: If light travels a meter in 2 seconds, how far does it travel in 10 seconds? Here it is easy to see that you would divide 10 by 2 = 5 meters. Thus you can see you have to divide the amount of time by the

4. 32

5. 35

6. 2

2

127ps

7. 2

28mt

8. 25a

9. 12p2c

10. 2

22rs

Unit 4 – Number Patterns and Fractions Lesson 8 – Dividing Fractions

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11. a. a b. ab2

c. b2

a d. a

e. 32 f. a

2

6 g. 2

3 h. 6

a2

i. a2 j. 2x k. 15x

l. 1b2

m. 13c

n. 6m o. 1 p. 23

q. 32a

r. 32t

s. cb2

t. 12ab

12. p = 45

13. a = 14

14. n = 27

15. x = 8

Unit 4 – Number Patterns and Fractions Lesson 8 – Dividing Fractions

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Bibliography Information Teachers attempted to cite the sources for the problems included in this problem set. In some cases, sources may not have been known.

Problems Bibliography Information

1-3 Zaccaro, Edward. Challenge Math (Second Edition): Hickory Grove Press, 2005.