Lesson 2: Ratios and Rates with Fractions

Ratios and Rates with Fractions

Student Summary

There are 12 inches in 1 foot, so we can say that for every 1 foot, there are 12 inches, or the ratio of feet to inches is $1:12$ . We can find the unit rates by dividing the numbers in the ratio:

$1\div 12 = \frac{1}{12}$ ,
so there is $\frac{1}{12}$ foot per inch.

$12 \div 1 = 12$ ,
so there are 12 inches per foot.

When the numbers in a ratio are fractions, we calculate the unit rates the same way: by dividing the numbers. For example, if someone runs $\frac34$ mile in $\frac{11}{2}$ minutes, the ratio of minutes to miles is $\frac{11}{2}:\frac34$ .

$\frac{11}{2} \div \frac34 = \frac{22}{3}$ , so the person’s
pace is $\frac{22}{3}$ minutes per mile.

$\frac34 \div \frac{11}{2} = \frac{3}{22}$ , so the person’s
speed is $\frac{3}{22}$ mile per minute.

Visual / Anchor Chart

Standards

Building On

6.NS.1

6.NS.A.1

6.RP.3

6.RP.A.3

7.G.1

7.G.A.1

Addressing

7.RP.1

7.RP.A.1

7.RP.1

7.RP.A.1

Building Toward

7.RP.1

7.RP.A.1

7.RP.A