Reduce fractions to lowest terms

Learning Objectives Define 'lowest terms' or 'simplest form' for a fraction. Identify common factors of the numerator and denominator of a fraction. Use division to simplify a fraction to an equivalent fraction. Reduce a fraction to its lowest terms using the greatest common factor (GCF). Explain why reducing fractions to lowest terms is useful. Simplify fractions that require multiple steps of division. Have you ever shared a pizza or a cake and wondered if there's a simpler way to describe your slice? 🍕 Sometimes fractions can look complicated, but we can make them easier to understand! In this lesson, you'll learn how to make fractions as simple as possible, which is called 'reducing to lowest terms'. This skill helps us compare f...

TermDefinitionExample FractionA number that represents a part of a whole or a part of a collection. It has a numerator (top number) and a denominator (bottom number).In the fraction $\frac{3}{4}$, 3 is the numerator and 4 is the denominator. NumeratorThe top number in a fraction, which tells you how many parts you have.In $\frac{5}{8}$, the numerator is 5, meaning you have 5 parts. DenominatorThe bottom number in a fraction, which tells you the total number of equal parts the whole is divided into.In $\frac{5}{8}$, the denominator is 8, meaning the whole is divided into 8 equal parts. FactorA number that divides another number evenly, without leaving a remainder.The factors of 12 are 1, 2, 3, 4, 6, and 12. Common FactorA factor that two or more numbers share.For 6 and 9, the common factor...

The Division Rule for Simplifying Fractions To reduce a fraction, divide both the numerator and the denominator by the same common factor (a number that divides both evenly). This rule creates an equivalent fraction that looks simpler. You can keep dividing by common factors until the fraction is in its lowest terms. Mathematically, if $c$ is a common factor of $a$ and $b$, then $\frac{a}{b} = \frac{a \div c}{b \div c}$. Using the Greatest Common Factor (GCF) To reduce a fraction to its lowest terms in one step, divide both the numerator and the denominator by their Greatest Common Factor (GCF). Finding the GCF first ensures that you only need to divide once to get to the simplest form. If $g$ is the GCF of $a$ and $b$, then $\frac{a}{b} = \frac{a \div g}{b \div g}$.