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Rate Problems with Fractions

A rate is a ratio where we compare two different quantities, which are measured in different units.

Here we are going to discuss how we compare two fractions. We solve rate problems by equating two ratios and then solving them for the unknown variable. See the example below.

Example: Donna stitches \frac{5}{6} of a cushion cover in  \frac{3}{4} hour. If she stitches at the same speed, how many cushion covers would she be able to stitch in 4 hours?

Let us assume that Donna can stitch x cushion covers in 4 hours.

Then\frac{3}{4}:4=\frac{5}{6}:X

\frac{3}{4}\div4=\frac{5}{6}\divX

\frac{3}{4}\times\frac{1}{4}=\frac{5}{6}\times\frac{1}{X}=>\frac{3}{16}=\frac{5}{6X}

X=\frac{5\times16}{3\times6}=\frac{80}{18}=\frac{40}{9}

Example: If Joshua ate \frac{5}{2}   sandwiches in \frac{34}{5}minutes, then how many sandwiches did he ate per minute?

Let us assume that Joshua ate N sandwiches per minute.

Then \frac{5}{2}  : N = \frac{35}{4}  : 1

\frac{5}{2}÷ N = \frac{35}{4}   ÷ 1 =>\frac{5}{2}   × \frac{1}{N}  = \frac{35}{4}

\frac{1}{N}=\frac{7}{2}  =  N =\frac{2}{7}   sandwich

 

 

Check Point

  1. A chocolate cake recipe needs \frac{1}{4} cup cocoa powder for 1\frac{1}{4}  cup flour. If Nancy uses 3 cups of flour, then how many cups of cocoa powder would she need?
  2. If 5\frac{1}{2} miles of thread is used to stitch 6\frac{3}{4}  boxes of trousers, then how many miles of thread is needed to stitch 9 boxes of such trousers?
  3. If  \frac{3}{4} teaspoon of chocolate syrup is needed to make 1\frac{1}{4} cup of coffee mocha, then how many teaspoons of chocolate syrup would be needed to make  2\frac{1}{2}cups of coffee mocha?
  4. If 3\frac{1}{4} tablespoons of olive oil is needed to make 1\frac{3}{4}  cups of oats, then how many tablespoons of olive oil would be needed to make 3 cups of oats?
  5. Angel jogs 1\frac{3}{4} of a mile in \frac{3}{10}hr.   How much distance would she cover in 1 hour?
Answer key
  1. \frac{3}{5}cup
  2.  \frac{22}{3} = 7\frac{1}{3}  cups
  3.  1\frac{1}{2}teaspoon
  4.  5\frac{4}{7}tablespoons
  5. 5\frac{5}{7}miles

Download/Solve a Worksheet for Rate problems with Fractions