# Multiplying Mixed Numbers – Methods & Examples

A mixed number is a number that contains a whole number and a fraction, for instance 2 ½ is a mixed number.

## How to Multiply Mixed Numbers?

Mixed numbers can be multiplied by first converting them to improper fractions. For example, 2 ½ can be converted to 5/2 before the multiplication process. Below are the general rules for multiplying mixed numbers:

• Convert the mixed numbers to improper fractions first.
• Multiply the numerators from each fraction to each other and place the product at the top.
• Multiply the denominators of each fraction by each other (the numbers on the bottom). The product is the denominator of the new fraction.
• Simplify or reduce the final answer to the lowest terms possible.

## Multiplying Mixed Fractions and Mixed Numbers

One method of multiplying mixed fractions is to convert them to improper fractions.

Example 1

3 1/8 x 2 2/3

Solution

• Convert each fraction to an improper fraction,

3 1/8 = {(3 x 8) +}/ 8 = 25/8
2 2/3 = {(2 x 3) + 2}/3 = 8/3

• Multiply the numerator and denominators,

25/8 x 8/3 = ( 25 x 8)/(8 x 3)

• In this case, common factors are at the top and bottom, therefore, simplify by cancellations,

= 25/3

• Convert the final answer to mixed fractions,

25/3 = 8 1/3

Example 2

1 4/5 x 5 3/8

Solution

• First change the mixed numbers to improper fractions

1 4/5 = (1 x 5 + 4)/5 = 9/5

5 3/8 = (8 x 5 +3)/8 = 43/8

• Multiply the fractions

9/5 x 43/8 = 387/40

• You either the answer as an improper fraction or convert it to a mixed number

387/40 = 9 27/40

### Area Model Method

Multiplication of mixed numbers can also be done using another method called area model. This method is illustrated below:

Example 3

2 2/5 x 3 1/4

Solution

• Draw a model that has a region for both whole number and fraction number
 X 2 2/5 3 ¼
• Multiply each row with each column
 X 2 2/5 3 2 x 3 =6 3 x 2/5 = 6/5 ¼ 1/4 x 2 = 1/2 1/4 x 2/5 = 2/20 = 1/10
• Add all the products in the table.

6 + 1/2 + 6/5 + 1/10

The L.C.M. of 2, 5 and 10 =10

Therefore, 1/2 + 6/5 + 1/10 = 5/10 + 12/10 + 1/10

• Add the numerators alone while maintaining the denominator

(5 + 12 + 1)/10

= 18/10 = 1 8/10

• Now add 1 8/10 + 6

= 7 8/10

• Simplify the fraction to its lowest terms.

= 7 4/5

### Practice Questions

1. A woman distributed a fraction of a pineapple among her $6$ daughters. If each person got $\dfrac{1}{9}$ of the pineapple. What is the total fraction of the pineapple that the woman distributed?

2. Edwin and Ann bought $15$ kg of sweets at their wedding and distributed $\dfrac{3}{4}$ of it among the visitors. How many sweets did they distribute?

3. My weight was $60$ kg before I lost $\dfrac{1}{10}$ of the weight in the past $3$ months. How much weight did I lose?

4. Jason had $\$3140$in his bank account. He spent$\dfrac{2}{5}$of it to buy essentials from the grocery. How much money did he spend? 5. Stella had$15$liters of milk in a container. If she consumed$\dfrac{3}{4}$of the milk. How many liters of milk were consumed? 6. A boy walks$3 \dfrac{1}{2}$kilometers daily. What is the total distance covered in one week? 7. Ahmed read$\dfrac{2}{3}$of his storybook having$420$pages. If Mike read$\dfrac{3}{4}$of the same storybook, find out who read many pages and how many were they? 8. A rectangular school garden is$6 \dfrac{4}{5}$meters long and$1\dfrac{3}{8}$meters wide. Which of the following shows the area of the garden? 9. It takes$\dfrac{5}{6}$yards of wool to manufacture a dress. How many yards of wool is needed to make$8$similar dresses? 10. A bike ride rode for$4 \dfrac{3}{7}$kilometers on Friday. He rode$8\$ times more distance on Saturday than he did on Friday. How many kilometers were covered on Saturday?