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Mastering Fractions: Adding and Subtracting Fractions for KS3 Success

31/05/2025 / Tutorials

Mastering Fractions: Adding and Subtracting Fractions for KS3 Success

Introduction

Imagine you’re baking a cake and need to add 1/3 of a cup of sugar and 1/6 of a cup of brown sugar. How do you know how much sugar you have in total? Understanding how to add and subtract fractions is essential not just for maths class but for real-life scenarios too. This tutorial will guide KS3 students through the process step-by-step, building confidence and clarity along the way.

Understanding the Basics

Before you can add or subtract fractions, you must understand that fractions must have the same denominator (the bottom number) to be combined. The denominator tells you the size of the pieces, and they must be the same size to add or subtract properly—like stacking blocks of the same shape and size.

Finding a Common Denominator

When two fractions have different denominators, find a common denominator, usually the least common multiple (LCM) of the two denominators.

Step-by-Step Example

Example 1: Add 1/3 and 1/6

  1. The denominators are 3 and 6. The LCM of 3 and 6 is 6.
  2. Rewrite 1/3 as 2/6 (because 1 × 2 = 2 and 3 × 2 = 6).
  3. Now you have 2/6 + 1/6.
  4. Since the denominators are the same, add the numerators: 2 + 1 = 3.
  5. 3/6 simplifies to 1/2.

Thus, 1/3 + 1/6 = 1/2.

Subtraction Example

Example 2: Subtract 5/8 – 1/4

  1. The denominators are 8 and 4. The LCM of 4 and 8 is 8.
  2. Rewrite 1/4 as 2/8.
  3. Now you have 5/8 – 2/8.
  4. Subtract the numerators: 5 – 2 = 3.
  5. The answer is 3/8.

More Worked Examples

Example 3: Add 2/5 + 3/10

  1. The LCM of 5 and 10 is 10.
  2. Rewrite 2/5 as 4/10.
  3. Now add: 4/10 + 3/10 = 7/10.

Example 4: Subtract 7/12 – 1/3

  1. The LCM of 12 and 3 is 12.
  2. Rewrite 1/3 as 4/12.
  3. Subtract: 7/12 – 4/12 = 3/12.
  4. Simplify 3/12 to 1/4.

Why Adding and Subtracting Fractions Matters

Mastering these operations lays the foundation for working with more advanced maths topics such as algebra, ratios, and even real-world tasks like measuring quantities or comparing data. With practice, these skills become second nature and open the door to deeper mathematical understanding.

Practice Makes Perfect

Try these on your own:

  1. 2/3 + 1/6
  2. 3/4 – 2/8
  3. 5/12 + 1/3
  4. 7/10 – 2/5
  5. 4/9 + 2/3

Answers

  1. 2/3 + 1/6 = 5/6
  2. 3/4 – 2/8 = 1/2
  3. 5/12 + 1/3 = 9/12 = 3/4
  4. 7/10 – 2/5 = 3/10
  5. 4/9 + 2/3 = 10/9 = 1 1/9

Building Strong Foundations

Adding and subtracting fractions is a key skill that all KS3 maths students must master. Developing fluency with fractions enhances a student’s ability to tackle more complex mathematical problems with confidence and ease.

At Principal Tutors, we are committed to helping students gain a deeper understanding of maths. Our tutors are fully UK-qualified school teachers who bring their classroom expertise to one-on-one tuition. With our unique Tutor-Match service, we ensure that each student is paired with a tutor who suits their individual needs and learning style.

If you are looking for more comprehensive support in KS3 Maths, be sure to check out our dedicated KS3 Maths tutoring page.

Take the Next Step

If your child could use a helping hand with fractions or any area of KS3 Maths, Principal Tutors is here to help. Contact us today and see how our expert tutors can boost your child’s confidence and performance in maths.

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

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