Mathematics
Grade 7
15 min
Multiply fractions and whole numbers
Multiply fractions and whole numbers
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1
Introduction & Learning Objectives
Learning Objectives
Represent multiplication of a fraction by a whole number using visual models.
Convert whole numbers into fractional form to facilitate multiplication.
Apply the standard algorithm to multiply fractions by whole numbers.
Simplify products to their simplest form, including converting improper fractions to mixed numbers.
Solve real-world problems that require multiplying fractions and whole numbers.
Explain the meaning of multiplying a fraction by a whole number in various contexts.
Ever needed to double a recipe that calls for 'half a cup' of flour? 🥣 Or figure out how much ribbon you need if each of your 5 friends wants 'one-third of a meter'? This lesson will show you how!
In this lesson, you'll learn how to multiply fractions b...
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Key Concepts & Vocabulary
TermDefinitionExample
FractionA number representing a part of a whole, written as $\frac{a}{b}$, where 'a' is the numerator and 'b' is the denominator.$\frac{3}{4}$ represents 3 parts out of 4 equal parts.
Whole NumberA number without fractions or decimals, including 0, 1, 2, 3, and so on.5, 12, 100 are whole numbers.
NumeratorThe top number in a fraction, indicating how many parts of the whole are being considered.In $\frac{2}{3}$, the numerator is 2.
DenominatorThe bottom number in a fraction, indicating the total number of equal parts the whole is divided into.In $\frac{2}{3}$, the denominator is 3.
ProductThe result obtained when two or more numbers are multiplied together.The product of 3 and 4 is 12.
Improper FractionA fraction where the numerator is greater than...
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Core Formulas
Multiplying a Fraction by a Whole Number
$\frac{a}{b} \times c = \frac{a \times c}{b}$
To multiply a fraction by a whole number, multiply the numerator of the fraction by the whole number, and keep the denominator the same.
Representing a Whole Number as a Fraction
$c = \frac{c}{1}$
Any whole number can be written as a fraction by placing it over a denominator of 1. This helps visualize multiplication with fractions.
Simplifying Products
After multiplying, divide both the numerator and denominator by their greatest common factor (GCF) to reduce the fraction to its simplest form. If the result is an improper fraction, convert it to a mixed number.
Simplifying makes fractions easier to understand and work with. It's often done at the end, but sometimes you can sim...
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Challenging
A rectangular park is 6 kilometers long. Its width is 2/5 of its length. A path goes around the entire perimeter of the park. If a person walks around the park 3 times, what is the total distance they have walked?
A.16 4/5 km
B.25 1/5 km
C.50 2/5 km
D.28 4/5 km
Challenging
A student's work to solve 12 x 5/8 is shown below.
Step 1: 12 x 5/8 = (12 x 5) / (12 x 8)
Step 2: = 60/96
Step 3: = 5/8
Which statement best describes the student's error?
A.The error is in Step 1; the whole number should only be multiplied by the numerator.
B.The error is in Step 2; the product of 12 and 8 is incorrect.
C.The error is in Step 3; the GCF of 60 and 96 is not 12.
D.There is no error; the final answer is correct.
Challenging
Consider the expression N x 3/4, where N is a whole number greater than 1. Which statement is always true about the product?
A.The product is always greater than N.
B.The product is always less than N.
C.The product is always a whole number.
D.The product is always an improper fraction.
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