 # 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 Question

1. 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.
2. 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?
3. My weight was 60 kg before I lost 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 2/5 of it to buy food stuffs. How much money did he spent?
5. Stella had 15 liters of milk in a container. If she consumed 3/4 of the milk. How many liters of milk were consumed?
6. A boy walks 3 1/2 kilometers daily. What is the total distance covered in one week?
7. 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?
8. A rectangular school garden is 6 4/5 meters long and 1 3/8 meters wide. Calculate the area of the garden.
9. It takes 5/6 yards of wool to manufacture a dress. How many yards of wool are need to make 8 similar dresses?
10. 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.
11. 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?