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Subtracting Fractions

Master subtracting fractions with interactive lessons and practice problems! Designed for students like you!

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Subtracting Fractions

Study Guide

Key Definition

A fraction is a portion of a quantity out of the whole. It consists of a $\frac{\text{numerator}}{\text{denominator}}$.

Important Notes

When subtracting fractions, you need a common denominator.
For like denominators, subtract the numerators: $\frac{a}{c} - \frac{b}{c} = \frac{a-b}{c}$.
For unlike denominators, find the least common denominator.
Convert mixed numbers to improper fractions before subtracting.
Simplify the result, if possible.

Mathematical Notation

$\frac{a}{b}$ represents a fraction

$-$ represents subtraction

$=$ represents equality

Remember to use proper notation when solving problems

Why It Works

Subtracting fractions is about finding a common denominator to ensure you're comparing equivalent quantities: $\frac{a}{b} - \frac{c}{d}$ becomes $\frac{ad}{bd} - \frac{bc}{bd} = \frac{ad-bc}{bd}$.

Remember

Always simplify fractions to their simplest form: $\frac{4}{8} = \frac{1}{2}$.

Quick Reference

Subtract Like Denominators:$\frac{a}{c} - \frac{b}{c} = \frac{a-b}{c}$

Subtract Unlike Denominators:Find the LCD (call it L): $\frac{a}{b} - \frac{c}{d} = \frac{a\left(\tfrac{L}{b}\right) - c\left(\tfrac{L}{d}\right)}{L}$

Understanding Subtracting Fractions

Choose your learning level

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Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

When subtracting fractions with the same denominator, subtract the numerators: $\frac{3}{4} - \frac{1}{4} = \frac{2}{4} = \frac{1}{2}$.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

What is $\frac{5}{8} - \frac{3}{8}$?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

You have $\frac{3}{4}$ of a pizza left and you eat another $\frac{1}{3}$ of the whole pizza. How much pizza is left?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

If $\frac{7}{10}$ of a tank is full and you remove $\frac{1}{5}$ of its content, how much is left?

Challenge Quiz

Single Choice Quiz

Advanced

Calculate $\frac{5}{6} - \frac{2}{9}$.

Recap

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Review key concepts and takeaways