About Comparing and Ordering Fractions
Introduction
Joseph and John are at the pizza store and they buy a pizza each. They bet on who can eat the most in the shortest amount of time. Dinner will be decided by the winner. Joseph claims he had eaten\(\frac{1}{2}\) the pizza. According to John, he had eaten up 75% of the pizza. Who gets to choose the dinner menu? To answer this question we must compare a fraction with a decimal. As a result, you’ll learn how to compare and order fractions, percentages and decimals in the sections below. By the end of this lesson, you will be able to figure out who will get to choose the dinner menu.
Because fractions, decimals, and percentages all have equivalents, comparing and ordering them is simple. It’s just a matter of converting them to the same format.
Fraction, Decimal and Percent
Let’s write \(\frac{4}{5}\), which is a fraction, in terms of a decimal and a percent.
- To convert a fraction to a decimal, we have to do division:
\(\frac{4}{5}=4\div 5=0.8\) (using long division for 4 divided by 5).
- To get a percent value, multiply by 100:
\(0.8\times 100=80%\)
So as you can see, \(\frac{4}{5}\), 0.8 and 80% all represent the same value but they are in fraction, decimal and percent form respectively.
Comparing Fractions, Decimals and Percents
You can use the symbols of greater than, less than and equal to symbols to compare fractions, decimals and percents. To compare values, convert fractions, decimals and percents to the same form.
For example,
Find the least number from 35%, \(\frac{3}{5}\) ,0.8 .
Firstly, convert all three numbers into the same form. Let us first convert the number to a percentage.
To convert \(\frac{3}{5}\) into a percentage, multiply both the numerator and denominator by ‘20’.
\(\frac{3\times 20}{5\times 20}=\frac{60}{100}=60%\)
To convert 0.8 into percentage.
Multiply 0.8 by 100%.
\(0.8\times 100%=80%\)
From 35%, 60%, 80% . 35% is the least
What are Ordering Fractions, Decimals and Percents?
When ordering fractions, decimals and percents, write them as all fractions or decimals or all percents. Then order them according to the question.
For example; which is the least number; 21%, \(\frac{2}{5}\) or 0.5 ? Find which is greater using a number line.
First, convert all three numbers into the same form. Let’s convert the number to percentage.
To convert \(\frac{2}{5}\) to percentage, multiply both the numerator and denominator by ‘20’.
\(\frac{2\times 20}{5\times 20}=\frac{40}{100}=40%\)
To convert 0.5 to percentage, move the decimal point two places to the right and add the percent sign.
0.5 = 50%
So now we have 21%, 40% and 50%.
Let’s order from least to greatest: 21% < 40% < 50%
We can also plot the values on a number line. Values to the right are greater than the values to the left of the number line.
Solved Ordering and Comparing Examples
Example 1: Katie, Courteney and Chloe were drinking juice from a 1 gallon carton. Katie drank 50% of the carton and Courteney drank 0.2 gallon whereas Chloe drank \(\frac{11}{50}\) gallon. Who drank the most juice?
Solution:
First, convert 50% and \(\frac{11}{50}\) into the decimal form.
Let’s convert 50% into a decimal.
Move the decimal point two places to the left.
\(50%=\frac{50}{100}=0.50\) gallon
Let’s convert \(\frac{11}{50}\) into a decimal.
Find the equivalent fraction of \(\frac{11}{50}\) as a fraction with denominator 100. Multiply both numerator and denominator by ‘2’.
\(\frac{11\times 2}{50\times 2}=\frac{22}{100}=0.22\) gallon.
We can plot 0.5, 0.22 and 0.2 on a number line and the number to the right-most would be the greatest, which is 0.5.
So out of 0.5 gallon, 0.22 gallon and 0.2 gallon we can identify that 0.5 gallons is the greatest amount and this means that Katie drank the most juice.
Example 2: Complete the table given below.
Solution:
Let’s convert \(\frac{15}{10}\) into a decimal and percentage.
To find the equivalent fraction of \(\frac{15}{10}\) as a fraction with denominator 100, multiply both the numerator and denominator by ‘10’.
\(\frac{15\times 10}{10\times 10}=\frac{150}{100}=1.5\).
To convert 1.5 to percentage, move the decimal point two places to the right and add the percentage sign.
1.5 = 150 %
Let’s convert \(\frac{4}{10}\) into a decimal.
To find the equivalent fraction of \(\frac{4}{10}\) as a fraction with denominator 100, multiply both the numerator and denominator by ‘10’.
\(\frac{4\times 10}{10\times 10}=\frac{40}{100}=0.4\).
Let’s convert \(\frac{11}{10}\) into a percent.
To find the equivalent fraction of \(\frac{11}{10}\) as a fraction with denominator 100, multiply both the numerator and denominator by ‘10’.
\(\frac{11\times 10}{10\times 10}=\frac{110}{100}=110%\).
The table is filled as below:
Fraction | Decimal | Percent |
|---|---|---|
| \(\frac{15}{10}\) | 1.5 | 150 % |
| \(\frac{4}{10}\) | 0.4 | 40 % |
| \(\frac{11}{10}\) | 1.1 | 110 % |
Descending order is the process of arranging things such as numbers, quantities, lengths and so on from a higher to a lower value. The decreasing order is another name for it.
Ascending order refers to the placement of numbers from smallest to largest.
Comparing fractions is difficult because there is an added step to convert fractions with common denominators. When comparing fractions with the same denominators, determining the greater or smaller fraction becomes easier as we can simply look for the fraction with the larger numerator.
To compare fractions with unlike denominators, we must first convert them to like denominators.
Let’s look at \(\frac{1}{3}\) and \(\frac{3}{5}\) as an example.
- Step 1: Look at the denominators of the fractions given: \(\frac{1}{3}\) and \(\frac{3}{5}\). They are distinct.
- Step 2: Let’s now convert them so that the denominators are the same. Multiply the first fraction by \(\frac{5}{5}\), which equals \(\frac{1}{3}\times \frac{5}{5}=\frac{5}{15}\).
- Step 3: Multiply the second fraction by \(\frac{3}{3}\), which equals \(\frac{3}{5}\times \frac{3}{3}=\frac{9}{15}\)
- Step 4: Make a comparison between the fractions \(\frac{5}{15}\) and \(\frac{9}{15}\). We can compare the numerators because the denominators are the same, and we can see that 5 < 9
- Step 5: The fraction with the larger numerator, \(\frac{5}{15}\) < \(\frac{9}{15}\), is the larger fraction. As a result,\(\frac{1}{3}\) < \(\frac{3}{5}\)
It’s worth noting that if the denominators differ but the numerators are the same, we can compare fractions by comparing their denominators.
For example in \(\frac{1}{3}\) and \(\frac{1}{9}\)
3 < 9 So \(\frac{1}{9}\) < \(\frac{1}{3}\)