Multiply fractions and mixed numbers: word problems

Learning Objectives Identify keywords and phrases in word problems that indicate multiplication of fractions or mixed numbers. Accurately convert mixed numbers to improper fractions and vice versa within word problem contexts. Set up and solve multiplication problems involving two fractions, a fraction and a mixed number, or two mixed numbers. Simplify fractional products to their simplest form or convert them to mixed numbers when appropriate. Interpret the solution of a fraction or mixed number multiplication problem in the context of the original word problem. Solve multi-step word problems involving multiplication of fractions and mixed numbers. Ever wondered how much flour you need if a recipe calls for 2 1/2 cups, but you only want to make 3/4 of the recipe? 🤔 This le...

TermDefinitionExample FractionA number representing a part of a whole, expressed as a numerator (top number) over a denominator (bottom number).In the fraction $\frac{3}{4}$, 3 is the numerator and 4 is the denominator, meaning 3 out of 4 equal parts. Mixed NumberA number consisting of a whole number and a proper fraction.$2\frac{1}{2}$ is a mixed number, representing 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.$\frac{5}{2}$ is an improper fraction, which is equivalent to the mixed number $2\frac{1}{2}$. ProductThe result obtained when two or more numbers are multiplied together.The product of $\frac{1}{2}$ and $\frac{1}{4}$ is $\frac{1}{8}$. Keywor...

Multiplying Fractions $\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$ To multiply two fractions, multiply the numerators together to get the new numerator, and multiply the denominators together to get the new denominator. Always simplify the result. Converting Mixed Numbers to Improper Fractions $A\frac{b}{c} = \frac{(A \times c) + b}{c}$ Before multiplying mixed numbers, convert them into improper fractions. Multiply the whole number by the denominator, add the numerator, and place this sum over the original denominator. Converting Improper Fractions to Mixed Numbers Divide the numerator by the denominator. The quotient is the whole number, the remainder is the new numerator, and the denominator stays the same. After multiplying, if your answer is...