Mathematics
Grade 7
15 min
Multiply unit fractions and whole numbers: sorting
Multiply unit fractions and whole numbers: sorting
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1
Introduction & Learning Objectives
Learning Objectives
Define unit fractions and whole numbers.
Multiply a unit fraction by a whole number.
Express the product of a unit fraction and a whole number in simplest form.
Compare and order fractions, including those resulting from multiplication.
Apply the concept of multiplying unit fractions and whole numbers to solve real-world problems.
Understand the relationship between multiplication of unit fractions and repeated addition.
Ever wondered how to calculate a fraction of a whole amount, like sharing 🍕 or figuring out a portion of a recipe? Let's find out!
In this lesson, you'll learn how to multiply unit fractions by whole numbers, simplify your answers, and then sort these fractional products. This skill is crucial for understanding proportions and...
2
Key Concepts & Vocabulary
TermDefinitionExample
Unit FractionA fraction where the numerator (the top number) is 1. It represents one part of a whole that has been divided into equal parts.1/2, 1/7, 1/100
Whole NumberA counting number without fractional or decimal parts. These are 0, 1, 2, 3, and so on.5, 12, 0, 28
ProductThe result obtained when two or more numbers are multiplied together.In 3 x 4 = 12, the product is 12.
NumeratorThe top number in a fraction, which indicates how many parts of the whole are being considered.In the fraction 3/4, the numerator is 3.
DenominatorThe bottom number in a fraction, which indicates the total number of equal parts into which the whole has been divided.In the fraction 3/4, the denominator is 4.
Simplest FormA fraction is in its simplest form (or lowest terms) when its numera...
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Core Formulas
Multiplying a Unit Fraction by a Whole Number
$\frac{1}{b} \times a = \frac{a}{b}$
To multiply a unit fraction by a whole number, multiply the whole number by the numerator (which is always 1), and keep the denominator the same. The result is a fraction with the whole number as the numerator and the original denominator.
Whole Number as a Fraction
$a = \frac{a}{1}$
Any whole number can be expressed as a fraction by placing it over 1. This can be helpful when visualizing multiplication of fractions, as it makes both numbers appear as fractions.
Simplifying Fractions
$\frac{a}{b} = \frac{a \div \text{GCF}(a,b)}{b \div \text{GCF}(a,b)}$
To simplify a fraction, divide both the numerator and the denominator by their Greatest Common Factor (GCF) until they have no common f...
5 more steps in this tutorial
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Challenging
Calculate and sort the following values from least to greatest: W = $\frac{1}{3} \times 8$, X = $\frac{1}{5} \times 12$, Y = $\frac{1}{2} \times 5$, Z = $\frac{1}{4} \times 9$.
A.Z, X, Y, W
B.X, Z, Y, W
C.Z, Y, X, W
D.W, X, Y, Z
Challenging
Three friends are reading the same 360-page book. Alice has read $\frac{1}{9}$ of the book. Ben has read $\frac{1}{10}$ of the book. Chloe has read $\frac{1}{8}$ of the book. Sort the friends by the number of pages they have read, from greatest to least.
A.Ben, Alice, Chloe
B.Chloe, Alice, Ben
C.Alice, Chloe, Ben
D.Chloe, Ben, Alice
Challenging
Find an integer value for 'n' that makes the following compound inequality true: $\frac{1}{5} \times 25 < \frac{1}{4} \times n < \frac{1}{3} \times 21$.
A.16
B.20
C.24
D.28
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