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Mastering Fractions: Multiplying and Dividing Fractions for KS3 Success

31/05/2025 / Tutorials

Mastering Fractions: Multiplying and Dividing Fractions for KS3 Success

Introduction

Imagine you’re doubling a recipe and need to multiply 2/3 of a cup of flour by 2, or splitting a pizza equally among 3 friends by dividing a fraction of it. Multiplying and dividing fractions are everyday skills that every KS3 student needs to master. In this tutorial, we’ll break down these processes step-by-step, giving students the confidence to tackle fractions with ease.

Understanding Multiplying Fractions

Multiplying fractions is often simpler than adding or subtracting them. There’s no need for common denominators. Just multiply the numerators (top numbers) together and the denominators (bottom numbers) together, then simplify the result.

Step-by-Step Example

Example 1: Multiply 2/3 by 4/5

  1. Multiply the numerators: 2 × 4 = 8.
  2. Multiply the denominators: 3 × 5 = 15.
  3. The product is 8/15.

No need to simplify since 8/15 is already in its simplest form.

Understanding Dividing Fractions

Dividing fractions involves a simple trick: multiply by the reciprocal. The reciprocal of a fraction is created by swapping its numerator and denominator.

Step-by-Step Example

Example 2: Divide 3/4 by 2/5

  1. Find the reciprocal of 2/5, which is 5/2.
  2. Change the division into multiplication: 3/4 × 5/2.
  3. Multiply the numerators: 3 × 5 = 15.
  4. Multiply the denominators: 4 × 2 = 8.
  5. The result is 15/8, or 1 7/8 as a mixed number.

More Worked Examples

Example 3: Multiply 5/6 by 2/3

  1. 5 × 2 = 10.
  2. 6 × 3 = 18.
  3. 10/18 simplifies to 5/9.

Example 4: Divide 7/8 by 1/2

  1. Reciprocal of 1/2 is 2/1.
  2. 7/8 × 2/1 = 14/8.
  3. 14/8 simplifies to 7/4, or 1 3/4 as a mixed number.

Why Multiplying and Dividing Fractions Matters

These skills are crucial not only for exams but also for real-world problem solving. Recipes, measurements, and even financial calculations often require multiplying and dividing fractions. Mastery in these areas also strengthens a student’s readiness for more advanced maths topics like algebra and ratios.

Practice Makes Perfect

Try these practice problems:

  1. 3/5 × 7/8
  2. 4/9 ÷ 2/3
  3. 5/12 × 3/10
  4. 9/16 ÷ 3/4
  5. 7/11 × 2/5

Answers

  1. 21/40
  2. 4/9 × 3/2 = 12/18 = 2/3
  3. 15/120 = 1/8
  4. 9/16 × 4/3 = 36/48 = 3/4
  5. 14/55

Building Strong Foundations

Multiplying and dividing fractions are essential skills for any KS3 student aiming for success in maths. Becoming confident with these operations prepares students for higher-level problem solving and real-world applications.

At Principal Tutors, we support students every step of the way. Our tutors are fully UK-qualified school teachers with real classroom experience. With our Tutor-Match service, we carefully match each student to a tutor who best suits their learning style and academic goals.

If you are looking for more comprehensive support in KS3 Maths, be sure to explore our KS3 Maths services designed to help students achieve their best.

Take the Next Step

Could your child use a boost in confidence with fractions or other maths topics? Principal Tutors is here to help. Contact us today and discover how our expert tutors can help your child excel in maths.

Visit Principal Tutors to book a consultation — because every child deserves to thrive in maths!

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