Question

Which rate does not belong with the other three?Explain

8 pounds for every 2 feet
12 pounds peer 3 feet
20 pounds per 4 feet
24 pounds for every 6 feet

Answer 1

The rate "20 pounds per 4 feet", doesn't belong with the other three because you get "5 pounds per foot" for the unit rate and for the other three, you get "4 pound per foot" for the unit rate.

Explanation:

Unit rate = How much of something per 1 unit of something else

We write this as a ratio with a denominator of one

In this case, we are using "pound per foot"

1. "8 pounds for every 2 feet"

You can find the unit rate by dividing the first term of the ratio by the second term

`\mathrm{( 8\:pounds )/( 2\:feet )}`

Simplify

`\mathrm{4\:pounds}`

Unit rate = 4 pounds per foot

2. "12 pounds per 3 feet"

First, write the rate as a fraction

`\mathrm{( 12\:pounds )/( 3\:feet )}`

Next, divide the numerator and denominator by 3

`\mathrm{( 12\:pounds / 3 )/( 3\:feet / 3 )}`

Lastly, simplify and turn the denominator equal to 1

`\mathrm{( 4\:pounds )/( 1\:foot )}`

Unit rate = 4 pounds per foot

3. "20 pounds per 4 feet"

First, write the rate as a fraction

`\mathrm{( 20\:pounds )/( 4\:feet )}`

Next, divide the numerator and denominator by 4

`\mathrm{( 20\:pounds / 4 )/( 4\:feet / 4 )}`

Lastly, simplify and turn the denominator equal to 1

`\mathrm{( 5\:pounds )/( 1\:foot )}`

Unit rate = 5 pounds per foot

4. "24 pounds for every 6 feet"

You can find the unit rate by dividing the first term of the ratio by the second term

`\mathrm{( 24\:pounds )/( 6\:feet )}`

Simplify

`\mathrm{4\:pounds}`

Unit rate = 4 pounds per foot

The rate that doesn't belong is "20 pounds per 4 feet"