# Word problem involving multiplication or division with mixed numbers

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