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Comparing Fractions

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Comparing Fractions

Study Guide

Key Definition

A fraction represents a part of a whole. The numerator represents the number of parts we have, while the denominator represents the total number of parts in the whole. For example, in the fraction $\frac{3}{5}$, the numerator is 3 and the denominator is 5.

Important Notes

A common denominator is important when adding or subtracting fractions with different denominators. You can find a common denominator by finding a multiple that both denominators share.
When comparing fractions, you can make the denominators the same, or make the numerators the same, whichever is easier.
If the denominators are the same, the fraction with the larger numerator is greater.
If the numerators are the same, the fraction with the smaller denominator is greater.

Mathematical Notation

$\frac{a}{b}$ means a fraction where a is the numerator and b is the denominator.

Remember to use proper notation when solving problems

Why It Works

When we talk about fractions, we're talking about parts of a whole. So when we compare fractions, we're comparing how much of the whole we have in one fraction versus the other.

Remember

A fraction is greater if its numerator is larger when the denominators are the same, or if its denominator is smaller when the numerators are the same.

Quick Reference

Fraction:$\frac{a}{b}$

Understanding Comparing Fractions

Choose your learning level

Watch & Learn

Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

In simple terms, when you compare fractions, you're trying to find out which fraction represents a larger quantity.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

Which is greater: $\frac{4}{7}$ or $\frac{5}{9}$?

Real-World Problem

Question Exercise

Intermediate

Baking Scenario

You're baking cookies and the recipe calls for $\frac{3}{4}$ cups of sugar. You only have $\frac{2}{3}$ cups of sugar. Do you have enough?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Without finding a common denominator or using a calculator, can you determine if $\frac{7}{8}$ is greater than $\frac{5}{6}$?

Challenge Quiz

Single Choice Quiz

Advanced

If a and b are positive and a > b, is $\frac{a}{b}$ always greater than 1?

Recap

Watch & Learn

Review key concepts and takeaways