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Equivalent Fractions and Comparing Fractions

Carl Roberts, 15.08.2022

1. Equivalent Fractions
2. Fractions to Mixed Numbers

1.

Equivalent Fractions

Introduction

Equivalent fractions can be useful when working with fractions (e.g. adding, subtracting, comparing).[br][br]You may use the applet below to help you with the following questions.

Equivalent Fractions Applet

Question 1)

Which of the following are equivalent to [math]\frac{1}{3}[/math]?

[math]\frac{2}{6}[/math] [math]\frac{2}{4}[/math] [math]\frac{6}{18}[/math] [math]\frac{4}{9}[/math]

Question 2)

You are told that [math]\frac{3}{4}=\frac{?}{16}[/math] . What is the missing number?

12 4 16 3

Question 3)

You are told that [math]\frac{4}{7}=\frac{20}{?}[/math] . What is the missing number?

35 7 5 140

Question 4)

Assuming a fraction with whole numbers in the numerator and the denominator, which of the following are true?

[math]\frac{1}{16}[/math] has an equivalent fraction of the form [math]\frac{?}{8}[/math] [math]\frac{8}{17}[/math] has an equivalent fraction of the form [math]\frac{12}{?}[/math] [math]\frac{1}{8}[/math] has an equivalent faction of the form [math]\frac{?}{16}[/math] [math]\frac{2}{5}[/math] has an equivalent fraction of the form [math]\frac{?}{12}[/math]

Question 5)

What relationship is there between the denominators of equivalent fractions for a [i]simplified[/i] fraction?

[b]Hint:[br][br][/b]Think about how equivalent fractions are found. What do we do with the numerator and denominator of a fraction to find equivalent fractions?

– Carl Roberts

2.

Fractions to Mixed Numbers

Introduction

We will often be working with numbers that involve fractions, but that are bigger than 1. To get the best of both worlds, we can use mixed numbers.[br][br]How can we write five halves? As a fraction? As a mixed number? Complete the following activities to find out.

An Applet to Allow Fractions to be Converted to Mixed Numbers

Question 1

Which of the following are ways to write five halves?

[math]\frac{5}{2}[/math] [math]5\frac{1}{2}[/math] [math]5\times\frac{1}{2}[/math] [math]2\frac{1}{2}[/math] [math]2\div5[/math] [math]5\div2[/math] [math]\frac{10}{2}[/math] [math]\frac{1}{2}\times5[/math]

Question 2

Write the following in order of size, from smallest to largest:[br][br][math]1\frac{1}{2}[/math], [math]2\frac{1}{4}[/math], [math]2\frac{1}{2}[/math], [math]1\frac{3}{4}[/math], [math]\frac{11}{4}[/math][br]

Question 3

Write [math]\frac{10}{4}[/math] as a mixed number, in its simplest form:

[math]\frac{5}{2}[/math] [math]2\frac{2}{4}[/math] [math]1\frac{2}{4}[/math] [math]1\frac{1}{2}[/math] [math]2\frac{1}{2}[/math] [math]10\frac{1}{4}[/math]

– Carl Roberts

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