Add and subtract fractions with unlike denominators: word problems

Learning Objectives Deconstruct complex word problems to identify the required fractional operations. Accurately determine the least common denominator (LCD) for two or more fractions. Convert fractions to equivalent forms with a common denominator to perform addition or subtraction. Set up and solve multi-step problems involving both addition and subtraction of fractions. Express the solution in its simplest form, including converting improper fractions to mixed numbers when appropriate. Apply fractional arithmetic to solve problems in contexts such as geometry, resource allocation, and data analysis. A team is building a robot. The chassis takes up 1/3 of the budget, and the electronics take up 2/5. Do they have enough left for a sensor package that costs 1/4 of the budget...

TermDefinitionExample Unlike DenominatorsDenominators of two or more fractions that are not equal. Direct addition or subtraction is not possible until a common denominator is found.In the fractions 1/3 and 3/5, the denominators 3 and 5 are unlike. Least Common Denominator (LCD)The smallest positive integer that is a multiple of all the denominators of a set of fractions. It is the Least Common Multiple (LCM) of the denominators.For the fractions 1/6 and 3/8, the multiples of 6 are 6, 12, 18, 24... and the multiples of 8 are 8, 16, 24... The LCD is 24. Equivalent FractionsFractions that represent the same value, even though they have different numerators and denominators. To create an equivalent fraction, multiply the numerator and denominator by the same non-zero number.1/2 is equivalent...

Addition of Fractions with Unlike Denominators \frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd} This is the general formula for adding two fractions. To use it, you find a common denominator by multiplying the two denominators (b*d), then create equivalent numerators (a*d and b*c) and add them. Subtraction of Fractions with Unlike Denominators \frac{a}{b} - \frac{c}{d} = \frac{ad - bc}{bd} This is the general formula for subtracting two fractions. It follows the same process as addition, but the equivalent numerators are subtracted. Least Common Denominator (LCD) Method \frac{a}{b} \pm \frac{c}{d} = \frac{a \cdot \frac{LCD(b,d)}{b} \pm c \cdot \frac{LCD(b,d)}{d}}{LCD(b,d)} A more efficient method for complex fractions. Find the LCD of the denominators. For each fractio...