Unit 1 · Topic 2

Adding & Subtracting Fractions

Overview

Same bottom number? Add the tops. Different? Find a common denominator first.

Topic 2 of 4~14 min
Next: Multiplying & Dividing FractionsAll units
Unit overview

The lesson

Read each section in order, work through every example on paper, then use the practice problems and quick check at the bottom.

Same denominator

When the bottom numbers (denominators) already match, just add or subtract the top numbers (numerators) and keep the denominator the same. For example, 2/7 + 3/7 = 5/7.

Different denominators

When the bottoms are different, you first rewrite both fractions with a common denominator - usually the LCM of the two denominators.

  1. 1Find a common denominator (the LCM of the bottom numbers).
  2. 2Rewrite each fraction with that denominator.
  3. 3Add or subtract the numerators; keep the denominator.
  4. 4Simplify the answer if you can.
Worked example

1/3 + 1/4

  1. 1A common denominator is 12.
  2. 21/3 = 4/12 and 1/4 = 3/12.
  3. 34/12 + 3/12 = 7/12.

Why this matters

Same bottom number? Add the tops. Different? Find a common denominator first.

These ideas show up on homework, quizzes, and the next unit in this grade. Getting comfortable here saves time later when the problems stack more steps together.

Common mistakes to avoid

Adding numerators and denominators separately (2/3 + 1/4 is not 3/7). Match denominators first, or use a clear model.

Forgetting to simplify the final answer when a smaller equivalent fraction is possible.

Key ideas from this lesson

  1. Same denominator
  2. Different denominators
  3. Find a common denominator (the LCM of the bottom numbers).
  4. Rewrite each fraction with that denominator.
  5. Add or subtract the numerators; keep the denominator.
  6. Simplify the answer if you can.

Video walkthroughs

Math Antics

Adding & Subtracting Fractions

Find common denominators, then add or subtract.

Watch on YouTube
Virtual Nerd

Adding Fractions (another take)

Same and different denominators, side by side.

Watch on YouTube
Math Antics

Simplifying Fractions

Reduce fractions to lowest terms using the greatest common factor.

Watch on YouTube
Khan Academy

Fractions in Lowest Terms

Write equivalent fractions in simplest form step by step.

Watch on YouTube

Practice

For each problem: write your work in the box, type your answer, and check it. If you are stuck, reveal the solution one step at a time. Do not skip straight to the final answer.

Exercise 1

Try it yourself

What is 3/8 + 1/8?

Step-by-step solution

  1. 1The denominators already match.
  2. 2Add the numerators: 3 + 1 = 4.
  3. 3Keep the denominator: 4/8, which simplifies to 1/2.

Exercise 2

Try it yourself

What is 5/6 − 1/3?

Step-by-step solution

  1. 11/3 = 2/6.
  2. 25/6 − 2/6 = 3/6.
  3. 3Simplify: 3/6 = 1/2.

Exercise 3

Try it yourself

What is 2/5 + 1/4?

Step-by-step solution

  1. 1Rewrite: 2/5 = 8/20 and 1/4 = 5/20.
  2. 28/20 + 5/20 = 13/20.
  3. 313/20 is already in simplest form.

Exercise 4

Try it yourself

Mia had 7/8 of a pizza. She ate 1/6 of a pizza. How much pizza is left?

Step-by-step solution

  1. 1Subtract: 7/8 − 1/6. Common denominator is 24.
  2. 27/8 = 21/24 and 1/6 = 4/24.
  3. 321/24 − 4/24 = 17/24 of a pizza left.

Exercise 5

Try it yourself

What is 2 1/3 − 1 5/6?

Step-by-step solution

  1. 12 1/3 = 7/3 and 1 5/6 = 11/6.
  2. 2Common denominator 6: 7/3 = 14/6.
  3. 314/6 − 11/6 = 3/6 = 1/2.

Re-read the lesson section if you get stuck, then try again without peeking at the solution.

Math Worksheets 4 Kids

Fractions practice

Open resource

Quick check

Answer all questions. Retake the quiz until you feel confident before moving on.

Adding & Subtracting Fractions

Question 1 of 5

Easy

What is 2/7 + 3/7?

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