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Equivalent Fractions

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Equivalent Fractions

Study Guide

Key Definition

Equivalent fractions are fractions that represent the same value even though they have different numerators and denominators. For example, $\frac{1}{2}$, $\frac{2}{4}$, and $\frac{4}{8}$ are all equivalent because they represent the same portion of a whole.

Important Notes

Multiplying the numerator and denominator of a fraction by the same non-zero number gives an equivalent fraction.
Equivalent fractions represent the same part of a whole.
To find an equivalent fraction, multiply or divide both the numerator and the denominator by the same number.
$\frac{a}{b} \times \frac{c}{c} = \frac{ac}{bc}$ is an equivalent fraction
Equivalent fractions simplify to the same simplest fraction.

Mathematical Notation

$\frac{1}{2}$ means one-half

$\times$ represents multiplication

$\div$ represents division

$=$ represents equality

Remember to use proper notation when solving problems

Why It Works

Multiplying a fraction by a fraction equal to 1, like $\frac{2}{2}$, maintains its value because multiplying by 1 does not change the original value.

Remember

To identify equivalent fractions, check if the cross-multiplication of two fractions results in the same product: $a \times d = b \times c$ for $\frac{a}{b}$ and $\frac{c}{d}$.

Quick Reference

Equivalent Fractions Formula:$\frac{a \times n}{b \times n} = \frac{a}{b}, \quad n \neq 0$

Understanding Equivalent Fractions

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Video explanation of this concept

Beginner

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Beginner Explanation

Equivalent fractions are fractions that have the same value. For example, $\frac{1}{2}$ and $\frac{2}{4}$ are equivalent because they both represent half of a whole.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

Which of the following is equivalent to $\frac{3}{6}$?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

Imagine you have a pizza sliced into 8 pieces. You've eaten 4 pieces, which is $\frac{4}{8}$. How would you express this as an equivalent fraction?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Can you find two different fractions equivalent to $\frac{5}{10}$ by multiplying or dividing?

Recap

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Review key concepts and takeaways