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:

1. How to perform basic arithmetic operations.
2. 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