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Fractions in Lowest Terms

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Fractions in Lowest Terms

Study Guide

Key Definition

A fraction is in lowest terms if its numerator and denominator are relatively prime, meaning they have no common factors other than 1. For example, $\frac{5}{9}$ is in lowest terms, but $\frac{6}{9}$ is not.

Important Notes

To reduce a fraction, divide both the numerator and the denominator by their greatest common factor.
Fractions like $\frac{6}{9}$ can be reduced to $\frac{2}{3}$.
The process of finding the lowest terms is also known as reducing fractions.
The greatest common factor (GCF) is the largest factor shared by two numbers.
Relatively prime numbers have no common factors other than 1.

Mathematical Notation

$\frac{a}{b}$ represents a fraction with numerator $a$ and denominator $b$

$\div$ represents division

$\times$ represents multiplication

$+$ represents addition

$-$ represents subtraction

Remember to use proper notation when solving problems

Why It Works

Reducing fractions to their lowest terms ensures that they are in their simplest form, making them easier to understand and work with in calculations.

Remember

Always check for the greatest common factor to simplify fractions efficiently.

Quick Reference

Greatest Common Factor:The largest factor that divides both the numerator and the denominator.

Understanding Fractions in Lowest Terms

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Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

Fractions are in lowest terms when they cannot be reduced further. For example, $\frac{5}{9}$ is in lowest terms.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

What is $\frac{12}{16}$ in lowest terms?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

You have $\frac{8}{12}$ of a pizza left. How can you express it in simplest form?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

How would you simplify $\frac{45}{60}$?

Challenge Quiz

Single Choice Quiz

Advanced

Which of the following fractions is already in lowest terms?

Recap

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Review key concepts and takeaways