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Fractions, decimals, and percentages are three different ways of representing parts of a whole. In the GL 11+ exam, you need to be able to convert between them, compare them, and perform calculations with each. This lesson covers everything you need to know.
A fraction has two parts:
¾ means "3 out of 4 equal parts."
| Type | Description | Example |
|---|---|---|
| Proper fraction | Numerator < Denominator | 3/4 |
| Improper fraction | Numerator ≥ Denominator | 7/4 |
| Mixed number | Whole number + proper fraction | 1 ¾ |
Mixed to improper: Multiply the whole number by the denominator, then add the numerator.
Improper to mixed: Divide the numerator by the denominator.
Fractions that represent the same amount are called equivalent fractions. You create them by multiplying or dividing both the numerator and denominator by the same number.
| Original | × 2 | × 3 | × 4 |
|---|---|---|---|
| 1/2 | 2/4 | 3/6 | 4/8 |
| 2/3 | 4/6 | 6/9 | 8/12 |
| 3/5 | 6/10 | 9/15 | 12/20 |
Divide both the numerator and denominator by their Highest Common Factor (HCF).
Simplify 18/24:
To compare fractions, make the denominators the same (find a common denominator).
Which is larger: 3/5 or 2/3?
Just add or subtract the numerators.
Step 1: Find a common denominator. Step 2: Convert both fractions. Step 3: Add or subtract the numerators.
Worked Example: 2/3 + 1/4
Worked Example: 3 ²⁄₅ - 1 ³⁄₄
Multiply the numerators together and the denominators together.
Worked Example: 3/4 × 2/5
Tip: Cancel common factors before multiplying to keep numbers small. In this example: ³⁄₄ × ²⁄₅ — the 2 and 4 share a factor of 2, so cancel to get ³⁄₂ × ¹⁄₅ = 3/10.
Keep, Change, Flip: Keep the first fraction, change ÷ to ×, flip the second fraction.
Worked Example: 3/5 ÷ 2/7
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