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Fraction Operations

Master fraction operations with interactive lessons and practice problems! Designed for students like you!

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Fraction Operations

Study Guide

Key Definition

To add or subtract fractions, find a common denominator, write each fraction with this denominator, then add or subtract the numerators. To multiply fractions, multiply the numerators together and the denominators together. To divide by a fraction, multiply by its reciprocal.

Important Notes

Always find the least common denominator when adding or subtracting fractions.
Multiplying fractions involves multiplying numerators and denominators.
When dividing by a fraction, multiply by its reciprocal.
Convert mixed numbers to improper fractions for calculations.
Simplify your answer whenever possible.

Mathematical Notation

$+$ represents addition

$-$ represents subtraction

$\times$ or $*$ represents multiplication

$\div$ or $/$ represents division

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

Remember to use proper notation when solving problems

Why It Works

Finding a common denominator allows you to add or subtract fractions by aligning them on the same scale. Multiplying fractions works because you are scaling the parts by the numerators and denominators respectively. Dividing fractions works by multiplying by the reciprocal, which determines how many times the divisor fits into the dividend.

Remember

Always simplify fractions and check your work by ensuring denominators are the same when adding or subtracting.

Quick Reference

Adding Fractions:$\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}$

Subtracting Fractions:$\frac{a}{b} - \frac{c}{d} = \frac{ad - bc}{bd}$

Multiplying Fractions:$\frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd}$

Dividing Fractions:$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} = \frac{ad}{bc}$

Understanding Fraction Operations

Choose your learning level

Watch & Learn

Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

Fractions are parts of a whole, and operations on fractions can include addition, subtraction, multiplication, and division.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

What is $\frac{1}{3} + \frac{1}{6}$?

Real-World Problem

Question Exercise

Intermediate

Pizza Party

You have $\frac{1}{2}$ of a pizza and your friend brings $\frac{1}{3}$ of another pizza. How much pizza do you have in total?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Consider the fractions $\frac{2}{5}$ and $\frac{3}{4}$. What is the product of these fractions?

Challenge Quiz

Single Choice Quiz

Advanced

What is $\frac{3}{4} \div \frac{2}{5}$?

Recap

Watch & Learn

Review key concepts and takeaways