Lesson 8: Ratio Reasoning: Convert Customary Units

Property

To convert units, you can create an equivalent ratio by multiplying the numerator and denominator of a known conversion rate by the same number.

Examples

• To convert 7 feet to inches, use the rate $\frac{12 \text{ in}}{1 \text{ ft}}$. Find an equivalent rate for 7 feet:

So, 7 feet is equal to 84 inches.

• To convert 4 yards to feet, use the rate $\frac{3 \text{ ft}}{1 \text{ yd}}$. Find an equivalent rate for 4 yards:

So, 4 yards is equal to 12 feet.

Explanation

You can convert from a larger unit to a smaller unit by using ratio reasoning. First, write the known conversion rate as a fraction, such as 12 inches per 1 foot. Then, multiply both the numerator and the denominator by the number of units you are converting. This creates an equivalent ratio that shows the converted measurement.

Property

To convert customary units of capacity, set up a proportion using a known conversion rate. Find the equivalent rate by multiplying or dividing. Common conversions include: $8 \text{ fl oz} = 1 \text{ c}$, $2 \text{ c} = 1 \text{ pt}$, $2 \text{ pt} = 1 \text{ qt}$, and $4 \text{ qt} = 1 \text{ gal}$.

Examples

• How many quarts are in 5 gallons?

The rate is $\frac{4 \text{ qt}}{1 \text{ gal}}$. To find the equivalent rate for 5 gallons, multiply the numerator and denominator by 5:

There are 20 quarts in 5 gallons.

• How many cups are in 8 pints?

The rate is $\frac{2 \text{ c}}{1 \text{ pt}}$. To find the equivalent rate for 8 pints, multiply the numerator and denominator by 8:

There are 16 cups in 8 pints.

Explanation

You can convert customary units of capacity, such as gallons, quarts, pints, and cups, by using ratio reasoning. Start by writing the known conversion as a rate. Then, find an equivalent rate by multiplying or dividing both the numerator and denominator by the same number. This process helps you determine the equivalent measurement in the desired unit.

Property

The standard customary units of weight can be expressed as ratios:

These ratios are used to set up equivalent rates for conversion.

Examples

• To convert 5 pounds to ounces, find an equivalent rate:

So, 5 pounds is equal to 80 ounces.

• To convert 3 tons to pounds, find an equivalent rate:

So, 3 tons is equal to 6,000 pounds.

Explanation

To convert customary units of weight, you can use ratio reasoning. Start by writing the known conversion as a rate, such as $\frac{1 \text{ lb}}{16 \text{ oz}}$. To find an equivalent measure, multiply the numerator and denominator by the same number to create an equivalent rate. This method allows you to convert between ounces, pounds, and tons by scaling the base conversion rate up or down.