Compare sums and differences of fractions

Learning Objectives Add and subtract fractions with unlike denominators. Find a common denominator for two or more fractions. Convert mixed numbers to improper fractions and vice versa. Compare two fractions using common denominators or other strategies. Calculate the sum or difference of two fractions. Compare the results of two fractional expressions (sums or differences). Use comparison symbols (<, >, =) correctly to show relationships between fractional expressions. Have you ever wondered if sharing half a pizza and then another quarter is more or less than 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 add and subtract fractions, and then use those ski...

TermDefinitionExample FractionA number that represents a part of a whole. It is written as a numerator (top number) over a denominator (bottom number).In the fraction $\frac{3}{4}$, 3 is the numerator and 4 is the denominator, meaning 3 out of 4 equal parts. Common DenominatorA shared multiple of the denominators of two or more fractions. It's necessary for adding, subtracting, and easily comparing fractions.For $\frac{1}{2}$ and $\frac{1}{3}$, a common denominator is 6, because $2 \times 3 = 6$ and $3 \times 2 = 6$. SumThe result obtained when two or more numbers are added together.The sum of $\frac{1}{4}$ and $\frac{2}{4}$ is $\frac{3}{4}$. DifferenceThe result obtained when one number is subtracted from another.The difference between $\frac{5}{6}$ and $\frac{1}{6}$ is $\frac{4}{6}...

Adding/Subtracting Fractions with Unlike Denominators To add or subtract fractions with unlike denominators, first find a common denominator (preferably the least common denominator, LCD). Then, convert each fraction to an equivalent fraction with the LCD. Finally, add or subtract the numerators and keep the common denominator. Use this rule whenever you need to combine or find the difference between fractions that don't share the same bottom number. Example: $\frac{a}{b} \pm \frac{c}{d} = \frac{a \cdot k}{b \cdot k} \pm \frac{c \cdot m}{d \cdot m}$ where $b \cdot k = d \cdot m = \text{LCD}$. Comparing Fractions To compare two fractions, convert them to equivalent fractions with a common denominator. Then, compare their numerators. The fraction with the larger numerator i...