Patterns of equivalent fractions

Learning Objectives Define and identify equivalent fractions. Generate equivalent fractions using multiplication. Generate equivalent fractions using division to simplify. Recognize and describe the patterns within sets of equivalent fractions. Express fractions in their simplest form. Apply the concept of equivalent fractions to compare fractions with different denominators. Have you ever shared a pizza and wondered if cutting it into 4 slices or 8 slices changes how much pizza you get? 🍕 Let's find out! In this lesson, we'll discover that fractions can look different but represent the exact same amount. We'll learn how to create these 'equivalent fractions' and uncover the cool patterns they follow, which will help us understand and compare fract...

TermDefinitionExample FractionA number that represents a part of a whole or a part of a collection. It is written as a numerator over a denominator.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 of the whole or collection are being considered.In $\frac{2}{5}$, the numerator is 2, meaning we have 2 out of 5 equal parts. DenominatorThe bottom number in a fraction, which tells you the total number of equal parts the whole or collection is divided into.In $\frac{2}{5}$, the denominator is 5, meaning the whole is divided into 5 equal parts. Equivalent FractionsFractions that represent the same value or the same amount, even though they have different numerators and denominators.$\frac{1}{2}$ and...

Generating Equivalent Fractions by Multiplication To find an equivalent fraction, multiply both the numerator and the denominator by the same non-zero number. This rule allows you to create fractions that look different but have the same value. It's like cutting each existing piece of a whole into smaller, equal pieces. The formula is: $\frac{a}{b} = \frac{a \times n}{b \times n}$ where $n \neq 0$. Generating Equivalent Fractions by Division (Simplifying) To find an equivalent fraction (or simplify a fraction), divide both the numerator and the denominator by the same non-zero common factor. This rule helps you reduce a fraction to a simpler form while keeping its value the same. It's like grouping smaller pieces of a whole into larger, equal pieces. The formula is...