Add and subtract fractions: word problems

Learning Objectives Identify keywords in word problems that indicate addition or subtraction of fractions. Translate real-world scenarios involving fractions into mathematical expressions. Determine the appropriate operation (addition or subtraction) to solve fraction word problems. Solve word problems involving the addition of fractions with like and unlike denominators. Solve word problems involving the subtraction of fractions with like and unlike denominators. Simplify fractional answers to their simplest form in the context of word problems. Interpret and state the final answer to a word problem in a complete sentence with appropriate units. Ever wonder how much pizza is left after your friends eat some, or how much flour you need for a recipe? 🍕 Math helps us figure...

TermDefinitionExample FractionA number representing a part of a whole or a collection.If a pizza is cut into 8 slices and you eat 3, you've eaten 3/8 of the pizza. NumeratorThe top number in a fraction, indicating how many parts are being considered.In the fraction 3/8, 3 is the numerator. DenominatorThe bottom number in a fraction, indicating the total number of equal parts the whole is divided into.In the fraction 3/8, 8 is the denominator. Common DenominatorA shared multiple of the denominators of two or more fractions, necessary for adding or subtracting them.For 1/2 and 1/3, a common denominator is 6, so we convert them to 3/6 and 2/6. Mixed NumberA number consisting of a whole number and a proper fraction.2 1/2 (two and a half) represents two whole units and one half of another...

Rule for Adding/Subtracting Fractions To add or subtract fractions, they must have a common denominator: $\frac{a}{b} \pm \frac{c}{d} = \frac{ad}{bd} \pm \frac{bc}{bd} = \frac{ad \pm bc}{bd}$ Find the least common multiple (LCM) of the denominators to use as the common denominator. Convert each fraction to an equivalent fraction with this common denominator, then add or subtract the numerators. Rule for Converting Mixed Numbers to Improper Fractions To perform operations, mixed numbers are often converted to improper fractions: $A \frac{b}{c} = \frac{(A \times c) + b}{c}$ Multiply the whole number by the denominator, add the numerator, and place the result over the original denominator. This simplifies calculations, especially in subtraction. Rule for Interpreting Word P...