Percentages and fractions are two ways of expressing parts of a whole.
- A fraction shows a part of something using two numbers: the numerator (top) and the denominator (bottom). For example, 1/2 means one out of two equal parts.
- A percentage expresses a part out of 100. For example, 50% means 50 out of 100, which is the same as 1/2.
At the A1/A2 level, you typically learn how to:
- Understand simple fractions and percentages.
- Convert between fractions and percentages for common cases (e.g., 1/2 = 50%).
- Calculate basic percentages of numbers (e.g., 10% of 50 = 5).
Simple meanings, conversions, and basic calculations are A1/A2 topics.
Fractions: Parts of a Whole
A fraction expresses a part of a whole using two numbers.
A fraction divides something into parts.
- Numerator: Number of parts you have
- Denominator: Total equal parts
Examples:
- 1/2 = 1 part out of 2 (half)
- 3/4 = 3 parts out of 4 (three quarters)
3/5 means three parts out of five equal parts.
Percentages: Parts out of 100
A percentage expresses parts per hundred.
A percentage shows how many parts out of 100 you have.
- 50% = 50 out of 100 (half)
- 25% = 25 out of 100 (one quarter)
You can convert a fraction into a percentage by making the denominator 100 (if possible) or by dividing and multiplying by 100:
\[
\text{Percentage} = \left(\frac{\text{Numerator}}{\text{Denominator}}\right) \times 100\%
\]
Divide the fraction and multiply by 100 to get a percentage.
Percentages include a number followed by %, e.g., 25%, 100%, 0%.
Equivalence: Fractions and Percentages
Correct pairs match when fraction is converted to percentage.
Some common equivalences:
| Fraction | Percentage | Decimal |
|---|---|---|
| 1/2 | 50% | 0.5 |
| 1/4 | 25% | 0.25 |
| 3/4 | 75% | 0.75 |
| 1/5 | 20% | 0.2 |
1/2 is equal to 50%.
Only common equivalents like 1/2=50%, 1/4=25%, 3/4=75% are correct.
Basic Calculations
Fraction of a Number
To find a fraction of a number, multiply the number by the fraction:
\[
\text{Fraction of number} = \text{Number} \times \frac{\text{Numerator}}{\text{Denominator}}
\]
Example: 1/2 of 40 = 40 × 1/2 = 20
Percentage of a Number
To find a percentage of a number, convert the percentage to a decimal and multiply:
\[
\text{Percentage of number} = \text{Number} \times \frac{\text{Percentage}}{100}
\]
Example: 25% of 80 = 80 × 0.25 = 20
Multiply the number by the fraction (90 × 1/3).
Convert 20% to 0.20 and multiply (50 × 0.20).
Conclusion
Percentages and fractions are fundamental ways to express parts of a whole, and understanding their relationship is key to mastering basic math.
- Fraction: numerator/denominator, parts of a whole.
- Percentage: parts per 100, can be converted from fractions.
- You can calculate both fractions and percentages of any number by multiplying.
Common equivalents include 1/2=50%, 1/4=25%, 3/4=75%.
Convert 10% to 0.10 and multiply (200 × 0.10).
'Three quarters' is 3/4.