Understanding the concept
A fraction represents part of a whole divided into equal parts. The numerator tells how many parts are selected; the denominator tells how many equal parts make the whole.
Start by identifying the quantities and units. Use a small example to understand the idea before attempting larger calculations.
Step-by-step method
To add or subtract fractions, first use a common denominator. To multiply fractions, multiply the numerators and multiply the denominators.
- Read the question and underline what you must find.
- Write down the given values and check their units.
- Apply the relevant method one step at a time.
- Estimate or reverse-check your answer before presenting it.
Quick-reference table
Use this reference to recognise common situations.
| Example | Meaning or method | Result |
|---|---|---|
| 1/2 | One of two equal parts | 0.5 |
| 1/4 | One of four equal parts | 0.25 |
| 3/4 | Three of four equal parts | 0.75 |
| 2/3 | Two of three equal parts | 0.666… |
Four worked examples
Compare the different types of questions and the steps used to answer them.
Example 1: Share a pizza
Question or method: Three of eight equal slices are eaten.
Example 2: Equivalent fractions
Question or method: Multiply the numerator and denominator of 2/3 by 2.
Example 3: Add fractions
Question or method: Calculate 1/4 + 2/4.
Example 4: Unlike denominators
Question or method: Calculate 1/2 + 1/4 by converting 1/2 to 2/4.
Common mistakes
These errors are easy to make. Read each one and check your working.
- Adding denominators when adding fractions: 1/4 + 1/4 is 2/4, not 2/8.
- Comparing numerators without checking denominators.
- Forgetting that pieces must be equal sizes.
Always ask whether your answer is reasonable for the original situation.
Practice questions
Try each question on paper before revealing the answer.
Question 1. Simplify 6/8.
Show answer and explanation
Divide numerator and denominator by 2: 3/4.
Question 2. What is 1/3 + 1/6?
Show answer and explanation
Convert 1/3 to 2/6; answer 3/6 = 1/2.
Question 3. What is 3/4 of 20?
Show answer and explanation
20 ÷ 4 × 3 = 15.
Question 4. Which is larger, 2/3 or 3/5?
Show answer and explanation
10/15 versus 9/15; 2/3 is larger.
Question 5. Calculate 2/5 × 3/4.
Show answer and explanation
6/20 = 3/10.
Review checklist
- Can you explain the key idea in your own words?
- Can you complete a worked example without looking at the solution?
- Can you identify a common mistake and correct it?
- Can you estimate whether your result is sensible?