Unit Rates

Learn to find and use unit rates in real-world situations

What is a Rate?

A rate is a ratio that compares two different units.

Examples:

A unit rate is a rate where the second quantity is 1 unit.

Examples:

Divide the first quantity by the second quantity:

$\text{Unit Rate} = \frac{\text{First Quantity}}{\text{Second Quantity}}$

Example: $\$ 12$ for 4 pounds $\frac{12}{4} = 3 \text{ dollars per pound}$

Unit rates help us:

A car travels 150 miles in 3 hours. What is the unit rate (speed)?

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Solution:

Divide distance by time: $\frac{150 \text{ miles}}{3 \text{ hours}} = 50 \text{ miles per hour}$

Answer: 50 miles per hour (or 50 mph)

Store A sells 6 apples for $\$ 4.50 $. Store B sells 8 apples for$ $5.60$. Which store has the better price per apple?

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Solution:

Store A: $\frac{\$4.50}{6} = \$0.75 \text{ per apple}$

Store B: $\frac{\$5.60}{8} = \$0.70 \text{ per apple}$

Compare: $\$ 0.70 < $0.75$

Answer: Store B has the better price ( $\$ 0.70$ per apple)

Jamie can type 240 words in 6 minutes. At this rate, how many words can Jamie type in 25 minutes?

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Solution:

Step 1: Find the unit rate $\frac{240 \text{ words}}{6 \text{ minutes}} = 40 \text{ words per minute}$

Step 2: Multiply by 25 minutes $40 \times 25 = 1,000 \text{ words}$

Answer: Jamie can type 1,000 words in 25 minutes

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