Mathematics
Grade 7
15 min
Multiply unit fractions by whole numbers: word problems
Multiply unit fractions by whole numbers: word problems
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Introduction & Learning Objectives
Learning Objectives
Identify unit fractions and whole numbers within word problems.
Translate word problems involving unit fractions and whole numbers into mathematical expressions.
Accurately multiply unit fractions by whole numbers.
Interpret the product of a unit fraction and a whole number in the context of a word problem.
Solve real-world word problems involving the multiplication of unit fractions by whole numbers.
Simplify fractional answers to their simplest form.
Explain their reasoning and solution steps for word problems.
Ever wondered how much pizza you'd eat if you had 1/4 of a pizza every day for 3 days? 🍕 This lesson will show you how to solve problems like that!
In this lesson, you'll learn how to tackle word problems that require multiplying a...
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Key Concepts & Vocabulary
TermDefinitionExample
Unit FractionA fraction where the numerator is 1 and the denominator is a positive whole number (e.g., 1/2, 1/3, 1/8). It represents one part of a whole that has been divided into equal parts.In the fraction 1/5, '1' is the numerator and '5' is the denominator. It means one out of five equal parts.
Whole NumberAny non-negative number without a fractional or decimal part (e.g., 0, 1, 2, 3, ...).If you have 7 apples, '7' is a whole number.
ProductThe result obtained when two or more numbers are multiplied together.The product of 3 and 4 is 12, because 3 x 4 = 12.
Word ProblemA mathematical problem presented in a narrative or story format, requiring interpretation to identify the numbers and operations needed to solve it.If a recipe calls f...
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Core Formulas
Multiplying a Unit Fraction by a Whole Number
$$n \times \frac{1}{d} = \frac{n}{d}$$
To multiply a whole number ($n$) by a unit fraction ($\frac{1}{d}$), multiply the whole number by the numerator (which is always 1 for a unit fraction) and keep the denominator the same. This effectively places the whole number in the numerator position.
Interpreting 'of' as Multiplication
In word problems, the word 'of' often indicates multiplication, especially when dealing with fractions (e.g., '1/2 of 6' means '1/2 times 6').
When you see phrases like 'a fraction OF a quantity' or 'a number OF times a fraction', it's a strong clue that you need to multiply.
Simplifying Fractions
To simplify a fraction, divide both the...
5 more steps in this tutorial
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Challenging
A water tank is being filled. Each hour, 1/15 of the tank's capacity is added. After some number of hours, the tank is exactly 4/5 full. How many hours has the tank been filling?
A.4 hours
B.8 hours
C.12 hours
D.15 hours
Challenging
During a fundraiser, the 7th-grade class washes cars. For every car they wash, they earn 1/10 of their daily fundraising goal. On Saturday, they washed 12 cars. On Sunday, they washed 15 cars. How many times over their daily goal did they earn during the entire weekend?
A.27/20 times the goal
B.27/10 times the goal
C.2 7/10 times the goal
D.1 7/10 times the goal
Challenging
A machine can fill 15 bottles per minute. Each bottle uses 1/12 of a liter of juice. A container holds 2 liters of juice. Is there enough juice in the container to run the machine for one full minute?
A.Yes, because 15/12 is less than 2.
B.No, because 15/12 is greater than 2.
C.Yes, because 12/15 is less than 2.
D.No, because 2 is less than 15.
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