Write fractions in lowest terms

Learning Objectives Define 'lowest terms' for a fraction. Identify common factors between the numerator and denominator of a fraction. Find the greatest common factor (GCF) of two numbers. Simplify fractions to their lowest terms using the GCF method. Simplify fractions by dividing by common factors iteratively. Recognize when a fraction is already in lowest terms. Ever wonder why a recipe might say '1/2 cup' instead of '2/4 cup'? 🤔 It's all about making things simpler and easier to understand! In this lesson, you'll learn how to simplify fractions to their lowest terms, also known as reducing fractions. This skill is fundamental for working with rational numbers and will make future math topics, like solving equations and working wi...

TermDefinitionExample FractionA number representing a part of a whole, written as $\frac{a}{b}$ where $b \neq 0$.$\frac{3}{4}$ represents three out of four equal parts. NumeratorThe top number in a fraction, indicating how many parts are being considered.In $\frac{3}{4}$, 3 is the numerator. DenominatorThe bottom number in a fraction, indicating the total number of equal parts in the whole.In $\frac{3}{4}$, 4 is the denominator. Common FactorA number that divides exactly into two or more other numbers.The common factors of 12 and 18 are 1, 2, 3, and 6. Greatest Common Factor (GCF)The largest common factor of two or more numbers.The GCF of 12 and 18 is 6. Lowest Terms (Simplest Form)A fraction is in lowest terms when its numerator and denominator have no common factors other than 1.$\frac{...

Rule for Simplifying Fractions $\frac{a}{b} = \frac{a \div c}{b \div c}$, where $c$ is a common factor of $a$ and $b$, and $c \neq 0$. This rule allows you to create an equivalent fraction with smaller numbers. You apply it repeatedly until the fraction is in lowest terms. Rule for Finding the GCF (Prime Factorization Method) If $a = p_1^{e_1} p_2^{e_2} \dots$ and $b = p_1^{f_1} p_2^{f_2} \dots$, then $\text{GCF}(a,b) = p_1^{\min(e_1,f_1)} p_2^{\min(e_2,f_2)} \dots$. This method systematically finds the largest number that divides both the numerator and denominator, ensuring the fraction is reduced in a single step. Rule for Identifying Lowest Terms A fraction $\frac{a}{b}$ is in lowest terms if the Greatest Common Factor (GCF) of its numerator ($a$) and denominator ($...