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Chapter 4 · Ratios · page 20 of 68

Unit rates

levelPre-algebra
standard6.RP.A.2
practiceRatios and rates

A rate is a ratio of two different kinds of things, like miles and hours. A unit rate has 1 as the second amount: miles per one hour. "Per" means divide by.

How to use it

  1. Write the first amount over the second.
  2. Divide so the bottom is 1.
  3. Scaling a ratio: multiply both parts by the same number. Never add the same number to both.

Example

240 miles4 hours=60 miles per hour\frac{240 \text{ miles}}{4 \text{ hours}} = 60 \text{ miles per hour}
3:4=15:20 (both times 5)3 : 4 = 15 : 20 \text{ (both times 5)}
$60 in the ratio 2:3 is 24 and 36\$60 \text{ in the ratio } 2:3 \text{ is } 24 \text{ and } 36

Where it goes wrong

  • Dividing the wrong way round. Miles per hour is miles divided by hours.
  • Scaling by adding: 3:4 is not 4:5.
  • Sharing in a ratio: the parts are 2 + 3 = 5, so one part is 60 ÷ 5 = 12, not 60 ÷ 2.

Related

Ratios and simplest formProportions and cross multiplyingDividing fractions
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