Adding and Subtracting Fractions

Study Guide

Key Definition

A fraction represents a part of a whole. It consists of a numerator (the part) and a denominator (the whole). To add or subtract fractions with the same denominator, add or subtract the numerators. If fractions have different denominators, first find the least common denominator (LCD), rewrite each fraction with that denominator, then add or subtract the numerators.

Important Notes

Always make sure the fractions have the same denominator before adding or subtracting. If they don't match, find the least common denominator (LCD), rewrite the fractions with the LCD, then proceed.
Simplify your answer if possible.
Remember the denominator doesn't change when adding or subtracting fractions with the same denominator.

Mathematical Notation

$\frac{a}{b}$ represents a fraction where 'a' is the numerator and 'b' is the denominator

$\frac{2}{3} = \frac{4}{6}$ (rewriting with denominator 6)

We use the '/' symbol to denote division or fractions. To rewrite fractions with unlike denominators, multiply numerator and denominator by the necessary factor to achieve a common denominator.

Why It Works

Adding or subtracting fractions is just like adding or subtracting parts of a whole. The denominator tells us how many equal parts the whole is divided into, and the numerator tells us how many of those parts we have.

Remember

Always check if fractions have the same denominator before adding or subtracting. If not, rewrite them using the LCD.

Quick Reference

Adding Fractions:$\frac{a}{b} + \frac{c}{b} = \frac{a + c}{b}$

Subtracting Fractions:$\frac{a}{b} - \frac{c}{b} = \frac{a - c}{b}$

Adding Fractions with Unlike Denominators:$\frac{a}{b} + \frac{c}{d} = \frac{a \times \frac{LCD}{b} + c \times \frac{LCD}{d}}{LCD}$

Subtracting Fractions with Unlike Denominators:$\frac{a}{b} - \frac{c}{d} = \frac{a \times \frac{LCD}{b} - c \times \frac{LCD}{d}}{LCD}$

Understanding Adding and Subtracting Fractions

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Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

When you add or subtract fractions with the same denominator, simply add or subtract the numerators. If the denominators differ, find the least common denominator, rewrite the fractions, then add or subtract the numerators.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

What is $\frac{2}{8} + \frac{5}{8}$?

Real-World Problem

Question Exercise

Intermediate

Pizza Scenario

You and your friends ordered a large pizza that was cut into 8 slices. You ate 2 slices and your friend ate 3 slices. How much of the pizza is left?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

If you have $\frac{3}{4}$ of a pie and you eat $\frac{1}{4}$ of the pie, how much pie do you have left?

Quick Quiz

Single Choice Quiz

Beginner

What is $\frac{7}{10} - \frac{3}{10}$?

Recap

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Review key concepts and takeaways