Compare and order fractions

Learning Objectives Identify the greater or lesser of two fractions with different denominators. Convert fractions to equivalent fractions with a common denominator. Compare and order a set of three or more fractions, including mixed numbers and negative fractions. Utilize benchmarks (0, 1/2, 1) to estimate the relative size of fractions. Apply knowledge of comparing fractions to solve real-world problems. Explain the process of comparing fractions using various strategies. Ever wondered which slice of pizza is bigger if they're cut into different numbers of pieces? 🍕 Let's find out how to compare fractions accurately! In this lesson, you'll learn powerful techniques to compare the sizes of fractions and arrange them in order, even when they look tricky. Thi...

TermDefinitionExample FractionA number representing a part of a whole, written as $\frac{a}{b}$, where $a$ is the numerator and $b$ is the denominator.$\frac{3}{4}$ represents 3 out of 4 equal parts of a whole. NumeratorThe top number in a fraction, indicating how many parts of the whole are being considered.In $\frac{2}{5}$, the numerator is 2. DenominatorThe bottom number in a fraction, indicating the total number of equal parts the whole is divided into.In $\frac{2}{5}$, the denominator is 5. Common DenominatorA shared denominator for two or more fractions, usually the Least Common Denominator (LCD), which is the Least Common Multiple (LCM) of the original denominators.For $\frac{1}{3}$ and $\frac{1}{4}$, a common denominator is 12. Equivalent FractionsFractions that represent the same...

Comparing Fractions with Common Denominators If two fractions have the same denominator, the fraction with the larger numerator is the greater fraction. For example, if $b > 0$, then $\frac{a}{b} > \frac{c}{b}$ if and only if $a > c$. This rule is straightforward. Once fractions share a common 'size' of parts, you just compare how many parts each has. This also applies to negative fractions: for example, $\frac{-3}{5} < \frac{-2}{5}$ because $-3 < -2$. Comparing Fractions with Different Denominators To compare fractions with different denominators, first find the Least Common Denominator (LCD) and convert each fraction to an equivalent fraction with the LCD. Then, compare their numerators. This is the primary method for comparing fractions that don&#...