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# 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}

** **

### Practice Question

- A woman distributed a fraction of a pineapple among her 6 daughters. If each person got 1/9 of the pineapple. Calculate the total fraction of the pineapple that the woman distributed.
- Edwin and Ann bought 15 kg of sweets on their wedding and distributed 3/4 of it among the visitors. How much sweets did they distribute?
- My weight was 60 kg before I lost 1/10 of the weight in the past 3 months. How much weight did I lose?
- Jason had $ 3140 in his bank account. He spent 2/5 of it to buy food stuffs. How much money did he spent?
- Stella had 15 liters of milk in a container. If she consumed 3/4 of the milk. How many liters of milk were consumed?
- A boy walks 3
^{1}/_{2 }kilometers daily. What is the total distance covered in one week? - Ahmed read 2/3 of his story book having 420 pages. If Mike read 3/4 of the same story book, find who read many pages and how many were they?
- A rectangular school garden is 6 4/5 meters long and 1 3/8 meters wide. Calculate the area of the garden.
- It takes 5/6 yards of wool to manufacture a dress. How many yards of wool are need to make 8 similar dresses?
- A bike ride rode for 4
^{3}/_{7 }kilometers on Friday. If he rode 8 times on Saturday than he did on Friday. How many kilometers were covered on Saturday? Write the final as a mixed fraction. - A tailor needs enough fabric to make three and a half hats. If it requires one and two sevenths to make one hat, how much fabric is required to make three and a half hats?