Subtract fractions with unlike denominators

Learning Objectives Identify fractions that have unlike denominators. Determine the least common multiple (LCM) of two or more denominators. Convert fractions into equivalent fractions with a common denominator. Subtract fractions once they share a common denominator. Simplify the resulting fractional answer to its lowest terms. Solve real-world problems involving the subtraction of fractions with unlike denominators. Ever tried to figure out how much more of a cake was eaten by one person than another, if they ate different-sized slices? 🍰 It's not as simple as just subtracting the top numbers! In this lesson, you'll learn the essential steps to subtract fractions that have different denominators. This skill is crucial for understanding quantities and solving pr...

TermDefinitionExample FractionA number that represents a part of a whole. 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, indicating how many parts of the whole 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, indicating the total number of equal parts that make up the whole.In $\frac{2}{5}$, the denominator is 5, meaning the whole is divided into 5 equal parts. Unlike DenominatorsWhen two or more fractions have different numbers in their denominators.$\frac{1}{2}$ and $\frac{3}{4}$ have unlike denominators (2 and 4). Equivalent FractionsFractions that represent the same value, even...

Finding the Least Common Denominator (LCD) To subtract fractions with unlike denominators, first find the Least Common Multiple (LCM) of the denominators. This LCM will be your LCD. The LCD is the smallest common multiple that both original denominators divide into evenly. It allows you to rewrite both fractions with the same denominator, which is a necessary step before subtraction. Converting to Equivalent Fractions $\frac{a}{b} - \frac{c}{d} = \frac{a \times k_1}{b \times k_1} - \frac{c \times k_2}{d \times k_2}$ where $b \times k_1 = d \times k_2 = \text{LCD}$. After finding the LCD, multiply the numerator and denominator of each fraction by the factor (k) needed to change its denominator to the LCD. This creates equivalent fractions that can now be subtracted. Subtr...