Notes-Ratios and Proportions Lesson 11: Ratios of Fractions and Their Unit Rates
Name _________________________Date _______________Period _____
Example 1: 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?
Izzy
Time
(minutes)
Time
(hours)
Distance
(miles)
15
30
45
60
75
¼
½
¾
1
1¼
2¼
4½
6¾
9
11 ¼
75
100
Julia
Time
(minutes)
Time
(hours)
25
Distance
(miles)
3¾
=
50
=
=
7½
= 1
11 ¼
= 1
15
Who appears to be the faster runner? Julia’s table shows her running 15 total miles, so she may
appear to be the faster runner.
Who is the faster runner? Neither is faster, they are running at the same speed.
Use the distance formula to further investigate.
d = rt
distance = rate • time
Izzy
d = rt
Julia
d = rt
2¼=r•¼
3¾=r•
r=9
r=9
9 miles per hour (mph)
9 miles per hour (mph)
Notes-Ratios and Proportions Lesson 11: Ratios of Fractions and Their Unit Rates
Use the clocks below to make a visual representation of the girls distance covered over 1 hour.
Izzy
Julia
Conclusion: Who is the faster runner? Explain.
The girls run at the same speed of 9 mph.
Exercise 1:
A turtle walks 7/8 of a mile in 50 minutes. What is the unit rate expressed in miles per hour?
=
• 60 =
÷ 50
A turtle walks 1 1/20 miles per hour.
•
=1
Notes-Ratios and Proportions Lesson 11: Ratios of Fractions and Their Unit Rates
Exercise 2:
Sally is making purple paint by mixing red and blue paint together. The table shows the
different amounts used.
Red Pain
(quarts)
Blue Paint
(quarts)
1
½
2
½
3¾
2
6¼
4
4
6
1.2
1.8
2
3
a.) What is the blue quarts per red quart unit rate? Label your answer.
2
½ ÷ 1½ =
÷
=
•
=
=
1
b.) Is the amount of blue paint proportional to the amount of red paint? Justify.
Yes. All the unit rates are 1 2/3 quarts blue per quart of red paint.
c.) Describe, in words, what the unit rate means in the context of this problem.
The unit rate of 1 2/3 means that for every 1 quart of red paint used to make a certain shade
of purple paint, 1 2/3 quarts of blue must be used.
Lesson Summary:
A fraction whose numerator or denominator is itself a fraction is called a complex fraction.
To reduce a complex fraction, divided the numerator by the denominator, using the division of
fractions rules.
Review: a unit rate is a rate, containing an x per 1 comparison.