Ratios and Rates Involving Fractions

• Complex fractions are fractions that have fractions within them. They are either in the numerator, the denominator, or both.

• Divide complex fractions by multiplying (keep, change, change)

Dividing Fractions Review

• When dividing fractions, they do NOT need to have a common denominator.

• To divide two fractions, change the operation to multiply and take the reciprocal of the second fraction (flip the second fraction). Keep-Change-Change.

2

5

9

2

2

52

9

Change Operation.

Flip 2nd Fraction.

Complex Unit Rates• Suppose a boat travels 30 miles in 2

hoursoHow do you write this rate?

Suppose a boat travels 12 miles in 2/3 of an houroHow do you write this as a rate?

oHow do you write this as a division problem?

oDetermine the unit rate: 18mph

mphhours

miles15

2

30

3

212 18

2

3

1

12

hours

miles

3/2

12

• Suppose a boat travels 8 ¾ miles in 5/8 of an hour.oHow do you write this as a rate?

oHow do you write this as a division problem?

oDetermine the unit rate:

hours

miles

8543

8

8

5

4

38

145

8

4

35

14 mph

Try the Following

1.Snowfall of 12 ¾ inches in 4 ½ hours. How many inches per hour does it snow?

2. Ian drove 30 miles in ½ hours. How many miles did he drive in 1 hour.

3. Use 5 ½ quarts of water for every 2 lbs of chicken. What is the unit rate? (Hint: Quarts per pound)

2 ¾ quarts per lb

2 5/6 inches per hour

60 mph

4. Mrs. Robare is making costumes for the school play.

Each costume requires ¾ yards of fabric. She bought 6 yards of fabric. How many costumes can Mrs. Robare make?

8 costumes

Who is Faster?During their last workout, Izzy ran 2 ¼ miles in 15 minutes and her friend Julia ran 3 ¾ miles in 25 minutes. Each girl thought she was the faster runner. Based on their last run, which girl is correct?

Find the unit rate for each runner:

Izzy 15 ÷ 2 ¼ =

Julia25 ÷ 3 ¾ =

6 or 6.67 They both ran the same speed, so neither girl is faster. 6

oUse the recipe to make fruit punch. Is the amount of sugar used proportional to the amount of mix used? Explain.

Yes, each ratio reduces to ½

Cups of Sugar ½ 1 1 ½ 2

Envelopes of Mix

1 2 3 4

1. Mary is making pillows for her Life Skills class. She bought yards of

fabric. Her total cost was

$16. What was the cost per yard?

2. Doug entered a canoe race. He rowed miles in hour.

What is his average speed?

3. Mrs. Robare is making costumes for the school play. Each costume

requires ¾ yards of fabric. She bought 6 yards of fabric. How many costumes can Mrs. Robare make?

4. A lawn company advertises that they can spread 7,500 square feet of grass seed in hours. Find the number of square feet of grass seed that can be spread in an hour.

TRY the FOLLOWINGWrite each rate. Then determine the unit rate and write in both fraction and word form

$5 or $5.82 per yard

3000 ft per hour7mph

8 costumes

4

32

2

12

2

13

2

1

Tahira and Brendan going running at the track. Tahira runs 3 ½ miles in a half an hour and Brendan runs 4 miles in 3/5 of an hour. Who runs at a faster pace (miles per hour)?

Show your work!

A

B

Tahira

Brendan

Practice Worksheet!