Mathematics
Grade 5
15 min
Multiply two fractions: word problems
Multiply two fractions: word problems
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1
Introduction & Learning Objectives
Learning Objectives
Identify key information and fractions within word problems.
Translate word problems involving 'of' into mathematical expressions for multiplying fractions.
Accurately multiply two proper fractions.
Simplify the product of two fractions to its simplest form.
Interpret the final fraction product in the context of the original word problem.
Solve multi-step word problems that require multiplying two fractions.
Ever wonder how much of a pizza is left if you eat a fraction of a fraction? 🍕 Let's find out how to solve these tricky fraction puzzles!
In this lesson, you'll learn how to tackle word problems that ask you to multiply two fractions. Understanding these problems helps you solve real-life situations where you need to find a part...
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Key Concepts & Vocabulary
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, which tells you how many parts of the whole you have.In $\frac{2}{5}$, the numerator is 2, meaning you have 2 out of 5 equal parts.
DenominatorThe bottom number in a fraction, which tells you the total number of equal parts the whole is divided into.In $\frac{2}{5}$, the denominator is 5, meaning the whole is divided into 5 equal parts.
ProductThe answer you get when you multiply two or more numbers together.The product of 3 and 4 is 12 ($3 \times 4 = 12$).
"Of" in Word ProblemsIn fraction word problems, the word 'of' often means to mul...
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Core Formulas
Rule for 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. Then, simplify the resulting fraction if possible.
Interpreting "Of" as Multiplication
Fraction 1 'of' Fraction 2 $\implies$ Fraction 1 $\times$ Fraction 2
When a word problem asks for a 'fraction of another fraction' or 'a fraction of a quantity', the word 'of' is a strong clue that you need to multiply.
Simplifying Fractions
Divide both the numerator and the denominator by their greatest common factor (GCF).
Always simplify your final answer to its simplest form unless ot...
4 more steps in this tutorial
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Challenging
A library's collection is 3/5 fiction books. Of the non-fiction books, 1/4 are biographies. What fraction of the total library collection are biographies?
A.3/20
B.1/10
C.7/20
D.1/5
Challenging
A full gas tank holds 10 gallons. The gas gauge shows the tank is 3/4 full. A trip to the store uses 1/6 of the gas that was in the tank. What fraction of a *full tank* of gas was used on the trip?
A.1/8
B.1/10
C.2/5
D.1/6
Challenging
At a park, 4/7 of the trees are maple trees. Of the remaining trees, 2/3 are oak trees. What fraction of all the trees in the park are oak trees?
A.8/21
B.2/7
C.1/3
D.3/7
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