How to Work Out Percentages Without a Calculator

Most percentage questions can be solved with one anchor trick: find 10%, then use it to build 1% and 5%. Once you can do those three in your head, the rest is addition, subtraction, and simple division.

The anchor trick: find 10%, then 1% and 5%

To find 10% of a number, move the decimal point one place to the left. For 240, 10% is 24. That single move is the foundation for almost every mental percentage problem.

From 10%, you can get 5% by halving it. If 10% of 240 is 24, then 5% of 240 is 12. To find 1%, move the decimal point two places left from the original number. For 240, 1% is 2.4.

Those three anchors — 10%, 5%, and 1% — let you build 15%, 17%, 20%, 25%, 30%, and many other percentages with simple adding or subtracting.

Work out a percent of a number

For 15% of 240, split 15% into 10% + 5%. You already know both pieces:

• 10% of 240 is 24.
• 5% of 240 is 12.
• Add them: 24 + 12 = 36.

So 15% of 240 is 36.

If you want 17% of something, use 10% + 5% + 1% + 1%. It feels like stacking blocks, but the blocks are just the three anchor amounts.

What percent is one number of another?

When you need to write one number as a percent of another, scale the fraction so the bottom becomes 100. For 43 out of 50, the fraction is 43/50.

The denominator 50 doubles to 100, so double the top as well:

43/50 × 2/2 = 86/100 = 86%.

That means 43 out of 50 is 86%. You did not need to divide 43 by 50 and then move a decimal — you just made the bottom number 100.

Percent increase and decrease

For an increase from 80 to 100:

• Change = 100 − 80 = 20.
• Original = 80.
• 20 ÷ 80 = 0.25, so the increase is 25%.

For a decrease from 120 to 90:

• Change = 120 − 90 = 30.
• Original = 120.
• 30 ÷ 120 = 0.25, so the decrease is 25%.

Both changes are 25%, but the actual change amounts differ because the starting bases differ. That is why the denominator always has to be the original number.

Reverse percentages: go from sale price back to original

A 25% discount means you pay 75% of the original price, because 100% − 25% = 75%.

If $90 is the price after 25% off, then $90 is 75% of the original. The original price is:

90 ÷ 0.75 = 120.

The original price was $120. You can also think of it as 0.75 × original = 90, so original = 90 ÷ 0.75.

Stacked discounts don't add

Two discounts should not be added together, because the second discount applies to a smaller remaining amount.

Take $120 and apply 25% off, then 10% off the reduced price:

Here is the math behind that table: 120 × 0.75 = 90, then 90 × 0.90 = 81. You saved 120 − 81 = 39. As a percent of the original price, 39 ÷ 120 = 0.325, or 32.5% off in total.

Adding 25% + 10% would suggest 35% off, but the real total is 32.5% because the second discount only applies to $90, not the original $120.

If you want the shopping version with tax, the Discount Calculator handles the receipt-style math.

Practice set

Try these three using the anchors and rules above:

1. Work out 15% of 240 using 10% and 5%.
2. Write 43 out of 50 as a percent.
3. A price after a 25% discount is $90. What was the original price?

Quick check: 15% of 240 is 36; 43 out of 50 is 86%; the original price was $120. If you want to check your mental steps or see the calculations update as you type, the Percentage Calculator has all six percentage modes in one tool.