Complex Fractions
Ratios
Rates
Unit Rates
Converting Unit Rates
100
What is a complex fraction?

A fraction that has a fraction numerator, denominator or both. 

100

A local community theater group is putting on a musical.  Here is the exact breakdown of the groups involved:

What is the Ratio of actors to backstage crew? (simplified ratios only)

  • Lead Actors: 6 people
  • Ensemble Dancers: 18 people
  • Backstage Crew: 24 people
  • Live Orchestra Musicians: 12 people

1:3

100

Write as a rate: 120 miles in 3 hours.

40 mph

100

What is a unit rate?

A rate with a denominator of 1. 

100

72 mph to miles per minute

1.2 miles / 1 minute

200

3/4/1/2

1 1/2

200

A local community theater group is putting on a musical.  Here is the exact breakdown of the groups involved:

What is the ratio of Dancers to musicians? (simplified ratios only)

  • Lead Actors: 6 people
  • Ensemble Dancers: 18 people
  • Backstage Crew: 24 people
  • Live Orchestra Musicians: 12 people

3:2

200

A train goes 270 miles in 6 hours. What is the rate in miles/hour?

45 mph

200

$36 for a 9lb turkey. 

$4 /lb

200

5 feet per second to inches per second

60 inches / 1 second

300

2/3/5/6

4/5

300

A local community theater group is putting on a musical.  Here is the exact breakdown of the groups involved:

What is the ratio of Backstage crew to Dancers and Musicians? (Simplified ratios only)

  • Lead Actors: 6 people
  • Ensemble Dancers: 18 people
  • Backstage Crew: 24 people
  • Live Orchestra Musicians: 12 people

4:5

300

7 1/2 pages of a book in 9 minutes, is how many pages per minute?

0.833 pages per minute

300

Sam typed 440 words in 8 minutes. 

55 words per minute. 

300

150 inches per minute to feet per minute 

12.5 feet / 1 minute

400

7/8/2

7/16

400

A local community theater group is putting on a musical.  Here is the exact breakdown of the groups involved:

What is the ratio of Backstage Crew to the entire cast and crew? (Simplified ratios only)

  • Lead Actors: 6 people
  • Ensemble Dancers: 18 people
  • Backstage Crew: 24 people
  • Live Orchestra Musicians: 12 people

2:5

400

A runner jogs 6 miles in 45 minutes. What is the rate in miles per minute?

0.133 miles per minute

400

60 miles in 1 1/2 hours. 

40 mph

400

A car travels 60 miles per hour. Convert this rate to feet per second.

88 feet / 1 second

500

5/2/5

12 1/2

500

A local community theater group is putting on a musical.  Here is the exact breakdown of the groups involved:

What is the ratio of Actors to Dancers to the entire cast and crew? (Simplified ratios only)

  • Lead Actors: 6 people
  • Ensemble Dancers: 18 people
  • Backstage Crew: 24 people
  • Live Orchestra Musicians: 12 people

1:3:10

500

What is the definition of a rate?

A comparison of 2 quantities with different units

500

A 12-ounce box of cereal costs $4.20, while a 15-ounce box costs $4.80. This is the unit rate per ounce of the cheaper option.

15 oz box is $0.32

500

: A train travels 90 miles per hour. Convert its speed to feet per second.

132 feet per second