Subtracting Fractions - Varsity Tutors

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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 equalityRemember 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

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Video explanation of this concept

concept. Use space or enter to play video.concept thumbnailBeginner

Start here! Easy to understand

BeginnerIntermediateAdvanced

Beginner Explanation

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

Practice Problems

Test your understanding with practice problems

1

Quick Quiz

Single Choice QuizBeginner

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

A$\frac{2}{8}$B$\frac{1}{8}$C$\frac{3}{8}$D$\frac{4}{8}$Check AnswerPlease select an answer for all 1 questions before checking your answers. 1 question remaining.2

Real-World Problem

Question ExerciseIntermediate

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?Show AnswerClick to reveal the detailed solution for this question exercise.3

Thinking Challenge

Thinking ExerciseIntermediate

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?

Show AnswerClick to reveal the detailed explanation for this thinking exercise.4

Challenge Quiz

Single Choice QuizAdvanced

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

A$\frac{7}{18}$B$\frac{1}{18}$C$\frac{5}{18}$D$\frac{11}{18}$Check AnswerPlease select an answer for all 1 questions before checking your answers. 1 question remaining.

Recap

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Review key concepts and takeaways

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