# Ratios and Rates

## Ratio

Compares two numbers using division. EX) 2/5

To write a ratio as a fraction simply put the first number in the numerator and the second in the denominator. Simplify if necessary.

Ex - 8 to 16

8/16 = 1/2

Ex - 3 to 5

3/5

## Rate

A ratio of two numbers with different units. EX) 180 miles/ 2 hours, 4 inches/ 2 years.

To write a rate as a fraction in simplest form...

Example - 16 dogs to 12 cats

1.Write as fraction

• 16 dogs / 12 cats

2. Simplify, in this case divide numerator and denominator by

• 4 dogs / 3 cats

Example - 45 males and 60 females

1. Write as fraction

• 45 males / 60 females

2. Simplify, in this case divide numerator and denominator by 15

• 3 males / 4 females

## Unit Rate

A rate with a denominator of one. EX) 30 miles/1 hour 43 words/1 minute \$3.46/1 pound

When finding a unit rate your final answer should always have a denominator of one.

Example - 2.5 miles in 5 minutes

1. Write as fraction

• 2.5 miles / 5 min

2. Divide numerator and denominator by denominator so that the denominator is 1 in this case we divide by 5.

• 0.5 miles / 1 minute

Example - 342 words in 6 minutes

1. Write as fraction

• 342 words / 6 minutes

2. Divide numerator and denominator by denominator so that denominator is 1, in this case we divide by 6.

• 57 words / 1 minute