Compare sums and differences of fractions with like denominators

Learning Objectives Accurately add and subtract fractions with like denominators. Compare the values of two fractions using inequality symbols (<, >, =). Evaluate and compare expressions involving sums and differences of fractions with like denominators. Apply the rules of comparing fractions to determine the relationship between two fractional expressions. Solve real-world problems that require comparing sums and differences of fractions. Justify the comparison of fractional expressions using mathematical reasoning. Ever wonder if sharing half a pizza and then eating another quarter is more or less than just eating three-quarters of a different pizza? 🍕 Let's find out how to compare these kinds of fractional amounts! In this lesson, you'll learn how to com...

TermDefinitionExample FractionA number representing a part of a whole, written as a numerator over a denominator.In \frac{3}{4}, 3 is the numerator and 4 is the denominator. NumeratorThe top number in a fraction, indicating how many parts of the whole are being considered.In \frac{5}{8}, the numerator is 5. DenominatorThe bottom number in a fraction, indicating the total number of equal parts the whole is divided into.In \frac{2}{7}, the denominator is 7. Like DenominatorsFractions that have the same denominator.\frac{1}{5} and \frac{3}{5} have like denominators. SumThe result of adding two or more numbers or fractions.The sum of \frac{1}{4} and \frac{2}{4} is \frac{3}{4}. DifferenceThe result of subtracting one number or fraction from another.The difference between \frac{5}{6} and \frac{...

Adding Fractions with Like Denominators \frac{a}{c} + \frac{b}{c} = \frac{a+b}{c} To add fractions with the same denominator, add the numerators and keep the denominator the same. Subtracting Fractions with Like Denominators \frac{a}{c} - \frac{b}{c} = \frac{a-b}{c} To subtract fractions with the same denominator, subtract the numerators and keep the denominator the same. Comparing Fractions with Like Denominators If c > 0, then \frac{a}{c} > \frac{b}{c} if and only if a > b. Similarly, \frac{a}{c} < \frac{b}{c} if and only if a < b, and \frac{a}{c} = \frac{b}{c} if and only if a = b. When comparing fractions with the same positive denominator, the fraction with the larger numerator is the larger fraction.