Unit 1 · Topic 2

Adding & Subtracting Fractions

Overview

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

Topic 2 of 4~46 min
Unit overview

The lesson

This lesson teaches Adding & Subtracting Fractions. 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.

When you study same denominator, slow down and write one example in your notebook without looking at the screen. That active step is what turns reading into learning.

Different denominators

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

LCM answers questions like: "When will both buses arrive at the same time again?" or "What is the smallest batch size that works for two different recipes?"

If two denominators are different, the LCM of those denominators is often the least common denominator you need for adding fractions.

  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

Adding & Subtracting Fractions shows up constantly in same bottom number? Add the tops. Different? Find a common denominator first. It also connects to what you will see on homework, quizzes, and the next unit in this grade.

Teachers often move fast in class. This page is here so you can pause, re-read, and practice until the idea feels familiar, not just until you have memorized a rule for one day.

Common mistakes to avoid

Rushing to the answer without writing steps. Middle-school math rewards clear work, and you catch errors earlier when steps are visible.

Mixing up similar ideas from the same topic. If two terms feel alike, make a two-column note: what is the same, what is different, and one example of each.

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 walkthrough

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

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.

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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