Dividing Mixed Numbers

How do you divide mixed numbers?

dividing mixed numbers

See the examples below to be more clear.

Example:\frac{1}{3} \div\frac{5}{9}

Step 1: To convert 2\frac{1}{3} to improper fraction, multiply the whole number, 2 by the denominator, 3, which means 2 × 3 = 6

Add numerator to the above product, so 6 + 1 = 7

2 \frac{1}{3} to improper fraction is \frac{7}{3}   .

Similarly, 2\frac{5}{9} to improper fraction involve the following steps:

(2 × 9) + 5 = 18 + 5 = 23

2 \frac{5}{9}  to improper fraction is \frac{23}{9}  .

Step 2: In terms of improper fractions, the given problem is \frac{7}{3} \div \frac{23}{9}

Step 3: Take the reciprocal of the second fraction and convert division symbol to multiplication symbol.

\frac{7}{3}  \div   \frac{23}{9}   = \frac{7}{3}\times\frac{9}{23}

Step 4: Reduce to lowest terms and leave the answer as it is or write it as a mixed fraction.

\frac{7}{3}\times\frac{9}{23}  = 7\times\frac{3}{23}  = \frac{21}{23}

Example 2: David made 1\frac{1}{2} quart of pineapple shake. If each glass can hold \frac{1}{6}  of a quart, then how many glasses can David fill?

 

Solution: To find the number of glasses David can fill, divide the amount of shake David has made with the amount each glass can hold.

So, number of glasses David can fill =1\frac{1}{2} ÷ \frac{1}{6} = \frac{3}{2} ÷ \frac{1}{6}\frac{3}{2} × 6 = 3 × 3 = 9 (Answer)

CHECK POINT 

  1. 1\frac{5}{6}\div\frac{7}{10}
  2. 5\frac{2}{3} \div 1\frac{1}{6}
  3. Jessica roasted almonds 4\frac{2}{5} pounds and then puts \frac{1}{5} pound almonds to each bag. How many bags of almonds can Jessica fill?
  1. 1\frac{1}{6} \div2\frac{1}{2}
  2. A bakery shop uses \frac{1}{12} of a bag of sugar for each batch of donuts. If the shop used \frac{1}{3} bag of sugar on Tuesday, how many batches of donuts did the shop made on Tuesday?

 

Answer key
  1. 2\frac{13}{21}
  2. 4\frac{6}{7}
  3. 22 bags
  4. \frac{7}{15}
  5. 4 batches

Download/Solve a Worksheet for Dividing Mixed Numbers