Fractions, Decimals & Percentages
Discover how fractions, decimals and percentages are three different ways of showing the same value, and learn to convert between them.
The Big Connection
Fractions, decimals and percentages are three different ways of writing the same amount. Think of them as three languages that all say the same thing. Being able to convert between them is a powerful skill.
For example, 1/2 = 0.5 = 50%. They all mean "half of something."
Common Equivalents
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 1/10 | 0.1 | 10% |
| 1/1 (whole) | 1.0 | 100% |
Visual: Fraction Wall
Each row shows the same whole divided into different numbers of equal parts. Notice how 1/10 = 0.1 = 10%.
Visual: Decimal Grid (0.75 = 75%)
75 out of 100 squares shaded = 75/100 = 3/4 = 0.75 = 75%
Visual: Percentage Bar
How to Convert Between Them
Fraction to Decimal
Divide the numerator by the denominator.
Example: 3/4 = 3 ÷ 4 = 0.75
Decimal to Percentage
Multiply by 100 and add the % sign.
Example: 0.75 × 100 = 75%
Percentage to Fraction
Write over 100, then simplify.
Example: 75% = 75/100 = 3/4
Singapore Bar Model: Percentage Problem
Problem: There are 60 students in Year 5. 25% walk to school. How many walk?
Total: 60 students
Walk
Other
Step 1: 25% means 25/100 = 1/4
Step 2: 1/4 of 60 = 60 ÷ 4 = 15
Answer: 15 students walk to school.
Key Vocabulary
Fraction
A number showing parts of a whole, written as one number over another (e.g. 3/4).
Decimal
A number using a decimal point to show parts less than one (e.g. 0.75).
Percentage
A number showing how many out of 100, using the % symbol (e.g. 75%).
Equivalent
Equal in value. For example, 1/2, 0.5, and 50% are all equivalent.
Worked Examples
Convert 2/5 to a decimal and a percentage.
Step 1: Fraction to decimal: 2 ÷ 5 = 0.4
Step 2: Decimal to percentage: 0.4 × 100 = 40%
Answer: 2/5 = 0.4 = 40%
Convert 60% to a fraction in simplest form.
Step 1: Write as a fraction: 60% = 60/100
Step 2: Simplify by dividing both by 20: 60 ÷ 20/100 ÷ 20 = 3/5
Answer: 60% = 3/5
Convert 0.35 to a percentage and a fraction.
Step 1: Decimal to percentage: 0.35 × 100 = 35%
Step 2: Decimal to fraction: 0.35 = 35/100 = 7/20
Answer: 0.35 = 35% = 7/20
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
What is 3/10 as a decimal?
Question 2
What is 0.25 as a percentage?
Question 3
What is 50% as a fraction in simplest form?
Question 4
Which of these is equivalent to 4/5?
Question 5
A shop has a 20% off sale. A book costs $40. How much do you save?
Key Concepts Summary
- ●Fractions, decimals and percentages are three ways of writing the same value.
- ●Fraction to decimal: divide the numerator by the denominator.
- ●Decimal to percentage: multiply by 100.
- ●Percentage to fraction: write over 100, then simplify.
- ●Memorise key equivalents: 1/2 = 0.5 = 50%, 1/4 = 0.25 = 25%, 1/5 = 0.2 = 20%.