Calculation
Mathematical Formula For Calculating Percentage Of a Number
$$ \text{Percentage of Number} = \frac{\text{Percentage}}{100} \times \text{Number} $$
Example Broken Down With Steps
$$
\text{Given: Percentage = 25, Number = 200}
$$
$$
\text{Step 1: Divide 25 by 100: } \frac{25}{100} = 0.25
$$
$$
\text{Step 2: Multiply 0.25 by 200: } 0.25 \times 200 = 50
$$
$$
\text{Result: 25% of 200 is 50.}
$$
Further Explained
Example: Find 25% of 200.
Steps:
- Convert the percentage into a decimal: Divide 25 by 100 to represent the percentage in decimal form:
$$ \frac{25}{100} = 0.25 $$
This step is necessary because percentages are fractions out of 100. - Multiply the decimal by the number: Multiply ( 0.25 ) by ( 200 ) to find the value of 25% of 200:
$$ 0.25 \times 200 = 50 $$ - Conclusion: 25% of 200 is 50.
Quick Trick: Swap the Numbers
When you need to find a percentage of a number in your head, try swapping the two values. The result is always the same.
x% of y = y% of x
This works because percentage calculations are just multiplication, and multiplication can be done in any order:
(x / 100) × y = (y / 100) × x
Example Broken Down With Steps
Finding 4% of 75 in your head feels difficult. Swap the numbers instead:
$$\text{Step 1: Rewrite 4% of 75 as 75% of 4}$$
$$\text{Step 2: 75% means three quarters, so } \frac{3}{4} \times 4 = 3$$
$$\text{Result: 4% of 75 = 3}$$
More Examples
8% of 25 is tricky. Flip it: 25% of 8 = 2. Done.
18% of 50 is tricky. Flip it: 50% of 18 = 9. Done.
48% of 50 is tricky. Flip it: 50% of 48 = 24. Done.
6% of 200 is tricky. Flip it: 200% of 6 = 12. Done.
When Does This Help?
The trick is most useful when one of the two numbers happens to be a friendly percentage like 10, 20, 25, 50, 75, or 100. In those cases, the flipped version becomes simple mental math — no calculator needed.