Topics
2. Operations with Rational numbers
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United States of America
Grade 6

2.14 Compare and order fractions, decimals, percents

Lesson
Practice

Introduction

Now that we know how to  convert both fractions and decimals into percentages  , it's time to play around with them a bit and compare these different types of numbers.

Compare fractions, decimals, percents

First, let's review a few important terms:

Greater than

the symbol is written as \gt and will have the larger number on the left, for example, 5\gt2

Less than

the symbol is written as \lt and will have the larger number on the right, for example, 2\lt5

Ascending order

means smallest to largest, for example, -2, 3, 5, 8

Descending order

means largest to smallest, for example, 10, 5, 2, -1

When we need to compare a list of fractions, decimals and percents, we need to convert them to be in the same form. Begin by looking at the given list and deciding which form would be most helpful to make the comparisons in.

For example, when given the list:

10\%, \, 0.6, \, \dfrac{5}{10}

You may see it makes the most sense to make comparisons as decimals, changing them to be 0.1, 0.6, and 0.5. While someone else might see it makes the most sense to convert them all to percentages, such as 10\%, 60\%, and 50\%. Which form you choose doesn't matter as long as it is the same for each number in the list.

Examples

Example 1

Arrange \dfrac {9}{10} , 40\% and 0.5 in descending order using percentages.

a

First, convert \dfrac {9}{10} to a percentage.

Worked Solution
Create a strategy

Convert \dfrac{9}{10} to be a fraction out of 100.

Apply the idea
\displaystyle \dfrac{9}{10}\displaystyle =\displaystyle \dfrac{9}{10} \times \dfrac{10}{10}Multiply the numerator and denominator by 10
\displaystyle =\displaystyle \dfrac{9 \times 10}{10 \times 10}Multiply
\displaystyle =\displaystyle \dfrac{90}{100}Write as a fraction
\displaystyle =\displaystyle 90\%Rewrite as a percentage
b

Now convert 0.5 to a percentage.

Worked Solution
Create a strategy

Multiply the decimal by 100\%.

Apply the idea
\displaystyle 0.5\displaystyle =\displaystyle 0.5 \times 100\%Multiplying by 100\%
\displaystyle =\displaystyle 50\%Evaluate
c

Which of the following arranges \dfrac{9}{10}, \enspace 40\% and 0.5 in descending order?

A
40\%, \, \dfrac{9}{10}, \, 0.5
B
\dfrac{9}{10}, \, 0.5, \, 40\%
C
\dfrac{9}{10}, \, 40\%, \, 0.5
D
0.5, \, 40\%, \, \dfrac{9}{10}
Worked Solution
Create a strategy

Compare the percentages.

Apply the idea

The percentages in order are: 90\%, \, 50\%, \, 40\%

So the original numbers in order are: \dfrac{9}{10}, \, 0.5, \, 40\%

The answer is option B.

Idea summary

When we need to compare a list of fractions, decimals and percents, converting them to be in the same form can make it easier to compare. Look at the given list and decide which form would be most helpful to make the comparisons in.

Outcomes

6.NS.C.7

Understand ordering and absolute value of rational numbers.

6.NS.C.7.A

Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram.

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