Mathematics
Grade 6
15 min
Multiply fractions: word problems
Multiply fractions: word problems
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1
Introduction & Learning Objectives
Learning Objectives
Identify keywords and phrases that indicate multiplication in fraction word problems.
Translate real-world scenarios involving fractions into mathematical multiplication expressions.
Accurately multiply fractions by fractions and fractions by whole numbers within word problems.
Simplify fraction products to their simplest form.
Interpret the numerical answer of a fraction multiplication problem in the context of the original word problem.
Solve multi-step word problems involving the multiplication of fractions.
Ever wondered how much of a cake is left if your friend ate half of half? 🍰 Today, we'll learn how to solve these kinds of real-world puzzles using fraction multiplication!
In this lesson, you'll discover how to tackle word problems tha...
2
Key Concepts & Vocabulary
TermDefinitionExample
FractionA number that represents a part of a whole. It is written 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 parts out of 4 equal parts.
NumeratorThe top number in a fraction, representing how many parts of the whole are being considered.In $\frac{2}{5}$, the numerator is 2.
DenominatorThe bottom number in a fraction, representing the total number of equal parts that make up the whole.In $\frac{2}{5}$, the denominator is 5.
ProductThe result obtained when two or more numbers are multiplied together.The product of 2 and 3 is 6. The product of $\frac{1}{2}$ and $\frac{1}{3}$ is $\frac{1}{6}$.
Of (as multiplication)In word problems, the word 'of' often ind...
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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. Always simplify the product to its simplest form.
Rule for Multiplying a Fraction by a Whole Number
$\frac{a}{b} \times c = \frac{a}{b} \times \frac{c}{1} = \frac{a \times c}{b}$
To multiply a fraction by a whole number, first write the whole number as a fraction with a denominator of 1. Then, multiply the numerators and the denominators as you would with two fractions. Simplify the product if possible.
Rule for Interpreting 'Of' in Word Problems
"fraction of a quantity" $\implies$ fraction $\times$ quant...
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Challenging
A rectangular garden has a length of 4/5 meters and a width of 1/2 meter. A section of this garden, covering 3/4 of its area, is planted with carrots. What is the area of the section with carrots?
A.3/10 square meters
B.2/5 square meters
C.23/20 square meters
D.7/9 square meters
Challenging
A company has a budget of $60 million. 3/5 of the budget is allocated to research. Of the research budget, 1/4 is for developing a new product. Of the new product development budget, 2/3 is for hiring new engineers. How much money is allocated for hiring new engineers?
A.$12 million
B.$9 million
C.$18 million
D.$6 million
Challenging
In a school with 400 students, 3/5 of the students are girls. If 25% of the girls play on a sports team, what fraction of the *total student population* are girls who play on a sports team?
A.1/4
B.3/20
C.1/5
D.3/5
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