**Finding unit rates:**

A rate is a comparison of two quantities that have different units, such as miles and hours. Ratios and rates can be expressed as fractions. A rate or ratio with a denominator of 1 unit is called a unit rate.

(60 miles ÷ 2) / (2 hours ÷ 2) = 30 miles / 1 hour

This means 30 miles per hour.

When one or both of the quantities being compared in the rate is a fraction, the rate is expressed as a complex fraction.

15 miles / (1/2 hour)

This means 15 miles per 1/2 hour.

**Example 1 : **

While remodeling her kitchen, Angela is repainting. She estimates that she paints 55 square feet every half-hour. How many square feet does Angela paint per hour ?

**Solution : **

**Step 1 : **

Determine the units of the rate.

The rate is area in square feet per time in hours.

**Step 2 : **

Find Angela’s rate of painting in area painted per time.

Area painted : 55 sq ft and Time : 1/2 hour

Area painted / Time = (55 square ft) / (1/2 hour)

The fraction represents area in square feet per time in hours.

**Step 3 : **

Find Angela’s unit rate of painting in square feet per hour.

Rewrite the fraction as division :

(55 square ft) / (1/2 hour) = 55 ÷ 1/2

Multiply by the reciprocal :

= 55 x 2/1

= 110 square feet / 1 hour

(The unit rate has a denominator of 1)

Angela paints 110 square feet per hour.

**Example 2 : **

Paige mows 1/6 acre in 1/4 hour. How many acres does Paige mow per hour?

**Solution : **

**Step 1 : **

Determine the units of the rate.

The rate is area in acre per time in hours.

**Step 2 : **

Find Paige's rate of mowing in area mowed per time.

Area mowed : 1/6 acre and Time : 1/4 hour

Area mowed / Time = (1/6 acre) / (1/4 hour)

The fraction represents area in acre per time in hours.

**Step 3 : **

Find Paige’s unit rate of mowing in acre per hour.

Rewrite the fraction as division :

(1/6 acre) / (1/4 hour) = 1/6 ÷ 1/4

Multiply by the reciprocal :

= (1/6) x 4/1

= (4/6) / 1

= 2/3 acre / 1 hour

(The unit rate has a denominator of 1)

Paige mows 2/3 of an acre per hour.

**Example 3 : **

Greta uses 3 ounces of pasta for every 3/4 cup of sauce. How much pasta does she use per cup of sauce ?

**Solution : **

**Step 1 : **

Determine the units of the rate. The rate is in ounces per cup.

**Step 2 : **

**Find Greta's rate of using pasta in ounces per cup of sauce. **

Pasta used : 3 ounces and Sauce : 3/4 cups

Pasta used / Sauce = 3 ounces / (3/4 cups)

The fraction represents pasta in ounces per 3/4 cup of sauce.

**Step 3 : **

Rewrite the fraction as division :

3 ounces / (3/4 cups) = 3 ÷ 3/4

Multiply by the reciprocal :

= 3 x 4/3

= 4 / 1

= 4 ounces / 1 cup

(The unit rate has a denominator of 1)

Greta uses 4 ounces of pasta for every 1 cup of sauce.

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