Fractions and percentages
Equivalence and comparison
The same value can be written as a fraction, a decimal or a percentage. In this section we simplify fractions, find equivalent values, and compare and order fractions, decimals and percentages.
Simplest form
A fraction is in its simplest form when the numerator and denominator have no common factor except 1. Simplify by dividing both the numerator and the denominator by the same number: 12/16 = 3/4 (divide both by 4), and 4/20 = 1/5 (divide both by 4).
Equivalent fractions, decimals and percentages
The same value can be written three ways. For example 7/10 = 0.7 = 70%. Tenths and hundredths make this easy: 57/100 = 0.57 = 57%, and 1/4 = 25/100 = 0.25 = 25%.
Comparing and ordering
To compare or order fractions, decimals and percentages, change them to the same form (usually decimals), then use =, > and <. For example 75% = 0.75 and 4/5 = 0.8, so 75% < 4/5.
Worked examples
Writing a fraction in its simplest form
- Look for a number that divides both 12 and 16.
- Both can be divided by 4.
- 12 divided by 4 = 3 and 16 divided by 4 = 4.
Answer: 12/16 = 3/4
Equivalent fraction, decimal and percentage
- 7/10 means 7 tenths, which is 0.7.
- 0.7 is the same as 70 hundredths.
- 70 out of 100 is 70%.
Answer: 7/10 = 0.7 = 70%
Comparing with <, > and =
- Change 75% to a decimal: 0.75.
- Change 4/5 to a decimal: 0.8.
- Compare: 0.75 is less than 0.8.
Answer: 75% < 4/5
Ordering fractions, decimals and percentages
- Change each number to a decimal: 50% = 0.5, 3/5 = 0.6, 0.65 stays, 7/10 = 0.7.
- Put the decimals in order from smallest to largest.
- Write them back in their original form.
Answer: 50%, 3/5, 0.65, 7/10
Where you see this in real life
- Checking whether 0.25 and 1/4 are the same amount.
- Comparing a 55% score with a 0.6 score.
- Putting results written as fractions, decimals and percentages in order of size.
Key words
- Equivalent fractions
- Fractions that have the same value, such as 6/10 and 3/5.
- Simplest form
- A fraction where the numerator and denominator have no common factor except 1.
- Simplify a fraction
- To divide the numerator and denominator by the same number to make an equal, simpler fraction.
- Percentage
- A number written as a part out of 100, such as 70%.