Lesson
Title: Division and Multiplication of Fractions.
Objective:
At the end of this lesson, you will be able to solve division and multiplication of fractions.
What you should know:
- How to perform basic arithmetic operations.
- How to change mixed fractions to improper fractions.
Introduction:
In solving the division of fractions, the fraction after the division sign is flipped upside down and the division sign is changed to the multiplication sign.
e.g a /b ÷ c /d => a /b x d /c
To solve the multiplication of fractions, multiply all the numerators and the denominators.
e.g a /b x c/d = a*c/b*d
If both signs are present in an expression to be solved, solve the division first then the multiplication.
Presentation/ Steps:
Given (i) 1/3 ÷ 2 /5 (ii) 2 /5 x 1/5 (iii) 21/4 x 7/5 ÷ 2/5
Step 1: 1/3 ÷ 2/5 , flip the fraction after the division sign upside down and change the sign to multiplication,
1/3 x 5/2 = 1*5/3*2 => 5/6.
Step 2: 2/5 x 1/5 , multiply the numerators and the denominators,
2*1/5*5 = 2/25
Step 3: 21/4 x 7/5 ÷ 2/5 , flip the fraction 2/5 which is after the division sign, and change the sign to multiplication,
21/4 x 7/4 x 5/2 , change the mixed fraction 21/4 to improper fraction, 9/4 x 7/4 x 5/2, multiply all the numerators and denominators,
(9 * 7 * 5)/(4 * 4 * 2) = 315/32. You can leave your answer in this form or a mixed fraction = 927/32.
Summary / Conclusion:
=> It is important you know how to convert mixed fractions to improper fractions and understand arithmetic precedence- BODMAS.
=> The above lesson is one of the approaches for performing division and multiplication of fractions.
Exercise:
Solve, 11/2 ÷ 11/3 x 33/5