Comparing fractions, decimals and percentages | Year 6 Mathematics PDF Download

Comparing Fractions, Percentages, and Decimals

• Fractions, decimals, and percentages are different ways to represent parts of a whole.
• They are all interconnected and can be converted into each other.
• Converting them into the same form makes it easier to compare and order them.
• Percentages are often used for comparison as they provide a clear indication of size relationships.

Conversion Methods

• From Fractions to Decimals: Divide the numerator by the denominator. For example, 1/4 = 0.25.
• From Decimals to Percentages: Multiply the decimal by 100 and add a percentage symbol. For example, 0.75 = 75%.
• From Percentages to Fractions: Remove the percentage sign and express the number over 100. For example, 25% = 25/100 = 1/4.
• From Percentages to Decimals: Divide the percentage value by 100. For example, 50% = 0.50.

Converting Fractions into Percentages

• Percentages represent values out of 100. When dealing with fractions that don't have a denominator of 100, conversion is necessary.

Examples

Example 1: What is ¹²⁄₂₅ as a percentage?
Sol: 12/25 = 48/100
If you multiply both the numerator and denominator by 4 you find the equivalent fraction with a denominator of 100.
48/100 = 48%
You can see that ¹²⁄₂₅ written as a percentage is 48%.
Another method you could use to convert a fraction to a percentage, is to divide the numerator by the denominator and multiply the answer by 100.

Example 2: What is ¹⁄₈ as a percentage?
Sol: First divide the numerator by the denominator…
1 ÷ 8 = 0.125
then multiply the answer by 100.
0.125 x 100 = 12.5%
Therefore, you can see that ¹⁄₈ written as a percentage is 12.5%

Converting Decimals into Percentages

• Converting a decimal to a percentage is a simple process. You just need to multiply the decimal by 100 to obtain the percentage equivalent.

Example 

Example: What is 0.67 as a percentage?
Sol: 0.67 x 100 = 67
Therefore
0.67 = 67%

More Examples

Example 1: Now try these ones. Can you convert and order these into descending order?

• Convert these numbers and put them in descending order.
  
• Step 1: Convert the decimals and fractions into percentages.
  
• Step 2: Order the original fractions, decimals and percentages in descending order using the new conversions to guide you. Now the original numbers are arranged in descending order with the biggest number on the left and the smallest on the right.

Example 2: Now here's a few for you to try.
Can you convert and order these into ascending order?

• Convert these numbers and then put them in ascending order.
  
• Step 1: Convert the decimals and fractions into percentages using the methods above.
  
• Step 2: Order the original fractions, decimals and percentages in ascending order using the new conversions to guide you. Now the numbers are arranged in ascending order with the smallest number on the left and the biggest on the right. Did you get it right?