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Fractions, decimals, and percentages are three different ways of expressing parts of a whole. The FSCE 11+ exam tests your ability to convert between them, calculate with them, and apply them to real-world problems. This lesson covers everything you need to know, with six fully worked examples and a conversion reference table you should memorise.
A fraction has two parts:
So 3/8 means "3 parts out of 8 equal parts."
Mixed to improper: Multiply the whole number by the denominator, add the numerator. Keep the same denominator.
Improper to mixed: Divide the numerator by the denominator. The quotient is the whole number, the remainder is the new numerator.
Two fractions are equivalent if they represent the same value: 2/4 = 1/2 = 3/6 = 50/100.
To simplify a fraction, divide both numerator and denominator by their highest common factor (HCF).
Rule: You can only add or subtract fractions when they have the same denominator (common denominator).
Steps:
Example: 2/3 + 1/4
Rule: Multiply the numerators together and multiply the denominators together.
3/4 x 2/5 = (3 x 2)/(4 x 5) = 6/20 = 3/10
To multiply by a whole number, write the whole number as a fraction over 1:
Rule: To divide by a fraction, flip the second fraction (find its reciprocal) and multiply.
3/4 ÷ 2/3 = 3/4 x 3/2 = 9/8 = 1 1/8
Memory aid: "Keep, Change, Flip" — keep the first fraction, change ÷ to x, flip the second fraction.
Decimals use a decimal point to represent parts of a whole:
| Ones | . | Tenths | Hundredths | Thousandths |
|---|---|---|---|---|
| 3 | . | 4 | 5 | 2 |
This represents 3.452 = 3 + 4/10 + 5/100 + 2/1000.
"Per cent" means "out of 100." So 45% means 45 out of 100, or 45/100, or 0.45.
To find 15% of 240:
This table is essential. Memorise these conversions:
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 2/5 | 0.4 | 40% |
| 3/5 | 0.6 | 60% |
| 1/10 | 0.1 | 10% |
| 1/3 | 0.333... | 33.3...% |
| 2/3 | 0.666... | 66.6...% |
| 1/8 | 0.125 | 12.5% |
| 3/8 | 0.375 | 37.5% |
| 1/100 | 0.01 | 1% |
Fraction to decimal: Divide the numerator by the denominator. 3/8 = 3 ÷ 8 = 0.375.
Decimal to percentage: Multiply by 100. 0.375 x 100 = 37.5%.
Percentage to fraction: Write over 100 and simplify. 45% = 45/100 = 9/20.
Percentage to decimal: Divide by 100. 37.5% ÷ 100 = 0.375.
Decimal to fraction: Use the place value. 0.375 = 375/1000 = 3/8.
Question: Convert 7/20 to a percentage.
Step-by-step solution:
Answer: 35%
Question: Calculate 3/4 + 5/6. Give your answer as a mixed number in its simplest form.
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