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

Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions.

6.RP.3

Use ratio and rate reasoning to solve real-world and mathematical problems.

7.G.1

Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

Addressing

7.RP.1

Compute unit rates associated with ratios of fractions.

Building Toward

7.RP.1

Compute unit rates associated with ratios of fractions.

7.RP.A

No additional information available.