Add and subtract fractions with unlike denominators: word problems

Learning Objectives Identify the mathematical operation (addition or subtraction) required in a fraction word problem. Find a common denominator for two or more fractions with unlike denominators. Convert fractions to equivalent fractions with a common denominator. Add or subtract fractions with unlike denominators accurately. Solve multi-step word problems involving the addition and subtraction of fractions with unlike denominators. Express answers to fraction word problems in simplest form or as mixed numbers when appropriate. Ever wondered how to share a pizza fairly when everyone wants different amounts, or how much paint is left after a big art project? 🍕🎨 In this lesson, you'll learn how to tackle real-world challenges by adding and subtracting fractions that h...

TermDefinitionExample FractionA number that represents a part of a whole. It has a numerator (top number) and a denominator (bottom number).In the fraction $\frac{3}{4}$, 3 is the numerator and 4 is the denominator. Unlike DenominatorsFractions that have different numbers in their denominators (the bottom part of the fraction).$\frac{1}{2}$ and $\frac{1}{3}$ have unlike denominators (2 and 3). Common DenominatorA shared denominator for two or more fractions, found by identifying a common multiple of the original denominators.For $\frac{1}{2}$ and $\frac{1}{3}$, a common denominator is 6. Equivalent FractionsFractions that represent the same value, even though they have different numerators and denominators.$\frac{1}{2}$ is equivalent to $\frac{2}{4}$ and $\frac{3}{6}$. Word ProblemA math...

Finding a Common Denominator To add or subtract fractions with unlike denominators, you must first find a common denominator. This is often the least common multiple (LCM) of the original denominators. Multiply the numerator and denominator of each fraction by the factor that makes its denominator equal to the common denominator. For example, to add $\frac{a}{b} + \frac{c}{d}$, find the LCM of $b$ and $d$, let's call it $L$. Then, rewrite the fractions as $\frac{a \cdot (L/b)}{b \cdot (L/b)} + \frac{c \cdot (L/d)}{d \cdot (L/d)}$. Adding Fractions with Like Denominators Once fractions have a common denominator, add the numerators and keep the common denominator. $\frac{a}{c} + \frac{b}{c} = \frac{a+b}{c}$ This rule applies after you've converted fractions with unli...