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Operations with Fractions

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Operations with Fractions

Study Guide

Key Definition

To add or subtract fractions, make sure denominators are the same. Use $\frac{a}{b} + \frac{c}{b} = \frac{a+c}{b}$ for like denominators.

Important Notes

Use $\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$ to multiply fractions.
To divide by a fraction, multiply by the reciprocal: $\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$.
Always simplify fractions when possible.
To add or subtract with different denominators, find the least common multiple.
Multiplying by a whole number is like multiplying by a fraction with 1 as the denominator.

Mathematical Notation

$\frac{a}{b}$ means division of a by b

$+$ represents addition

$-$ represents subtraction

$\times$ or $*$ represents multiplication

$\div$ or $/$ represents division

Remember to use proper notation when solving problems

Why It Works

Fractions represent parts of a whole. Understanding equivalent fractions helps in performing operations like addition and subtraction.

Remember

Finding common denominators is crucial for adding and subtracting fractions.

Quick Reference

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

Multiplication of Fractions:$\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$

Understanding Operations with Fractions

Choose your learning level

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Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

When adding or subtracting fractions with the same denominator, simply add or subtract the numerators and keep the denominator the same. For example, \frac{2}{5} + \frac{1}{5} = \frac{3}{5}.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

What is $\frac{2}{7} + \frac{4}{7}$?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

If you have $\frac{3}{4}$ of a pizza and your friend gives you $\frac{1}{4}$ more, how much pizza do you have in total?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Calculate $\frac{2}{3} \times 3$.

Challenge Quiz

Single Choice Quiz

Advanced

What is $\frac{3}{4} + \frac{5}{3}$?

Recap

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Review key concepts and takeaways