- Home
- >
- Multiplying Mixed Numbers – Methods & Examples

JUMP TO TOPIC

# 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

- Add the fractions

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}