# Word problem involving multiplication or division with mixed numbers

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In this lesson, we solve word problems involving multiplication or division with mixed numbers.

While multiplying, or dividing mixed numbers and other fractions, we use the rules we have learnt in previous lessons.

Diana needed $1\frac{2}{3}$ of a mug of water for 1 plant. If she had seven plants how many mugs of water would she need?

### Solution

Step 1:

Water needed for 1 plant $= 1\frac{2}{3} = \frac{\left ( 1 \times 3 + 2 \right )}{3} = \frac{5}{3}$ mugs

Number of plants $= 7$

Step 2:

Water needed for 7 plants $= 7 \times 1\frac{2}{3}$

$= 7 \times \frac{5}{3} = \frac{35}{3} = 11\frac{2}{3}$ mugs

Sandra's hair was originally $5\frac{1}{4}$ inches long. She asked her hair dresser to cut three-sevenths of it off. How many inches did she have cut off?

### Solution

Step 1:

Length of Sandra’s hair $= 5\frac{1}{4} = \frac{\left ( 5 \times 4 + 1 \right )}{4} = \frac{21}{4}$ inches

Length to be cut off $= \frac{3}{7}$ of the hair length

Step 2:

Length of cut off hair in inches $= \frac{3}{7} \times 5\frac{1}{4}$

$= \frac{3}{7} \times \frac{21}{4} = \frac{9}{4} = 2\frac{1}{4}$ inches

A store had $3\frac{1}{3}$ cartons of candies. How many days would it take to sell the candies if each day they sold one-sixth of a carton?

### Solution

Step 1:

Number of cartons of candies $= 3\frac{1}{3} = \frac{\left ( 3 \times 3 + 1 \right )}{3} = \frac{10}{3}$ inches

Number of cartons sold per day $= \frac{1}{6}$

Step 2:

Number of days in which all cartons will be sold $= 3\frac{1}{3} \div \frac{1}{6} = \frac{10}{3} \div \frac{1}{6}$

$= \frac{10}{3} \times \frac{6}{1} = 20$ days

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