Understanding fractions: word problems

Learning Objectives Identify key information and operations required to solve fraction word problems. Translate real-world scenarios into mathematical expressions involving fractions and mixed numbers. Accurately perform addition, subtraction, multiplication, and division of fractions and mixed numbers within word problems. Convert between mixed numbers and improper fractions as needed to solve problems. Solve multi-step fraction word problems involving various operations. Check the reasonableness of their answers in the context of the word problem. Ever wonder how much pizza is left after your friends eat their share, or how to split a recipe in half? 🍕 Fractions are everywhere! In this lesson, you'll learn how to tackle word problems involving fractions and mixed nu...

TermDefinitionExample FractionA number representing a part of a whole or a part of a collection. It is written as a numerator over a denominator.In the fraction $\frac{3}{4}$, 3 is the numerator (parts we have) and 4 is the denominator (total parts). Mixed NumberA number consisting of a whole number and a proper fraction.$2\frac{1}{2}$ represents two whole units and an additional half unit. Improper FractionA fraction where the numerator is greater than or equal to the denominator, representing a value of one or more whole units.$\frac{7}{3}$ is an improper fraction, which is equivalent to the mixed number $2\frac{1}{3}$. Keywords for OperationsSpecific words or phrases in a word problem that indicate which mathematical operation (addition, subtraction, multiplication, division) to use.&#...

Adding and Subtracting Fractions $\frac{a}{b} \pm \frac{c}{d} = \frac{ad \pm bc}{bd}$ (after finding a common denominator, add/subtract numerators and keep the common denominator) To add or subtract fractions, they must have the same denominator. If they don't, find a common denominator (often the least common multiple), convert the fractions, then add or subtract the numerators. Keep the denominator the same. Multiplying Fractions $\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$ To multiply fractions, multiply the numerators together and multiply the denominators together. Simplify the resulting fraction if possible. Mixed numbers should first be converted to improper fractions. Dividing Fractions $\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times...