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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
X22/5
3  
¼  
  • Multiply each row with each column
X22/5
32 x 3 =63 x 2/5 = 6/5
¼1/4 x 2 = 1/21/4 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 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?


 

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