Key takeaways
Reverse percentages answer "what was it before?". Divide by the multiplier that was applied, instead of subtracting the percentage.
- Original = result ÷ (1 ± rate).
- Subtracting the rate from the result is the classic error.
- Check by applying the rate forwards again.
The question in reverse
A coat is $72 after 20 % off. What did it cost? The sale price is 80 % of the original, so the original is $72 ÷ 0.80 = $90.
After an increase
A salary is $55,000 after a 10 % raise. Before the raise it was $55,000 ÷ 1.10 = $50,000, not $49,500.
From a part to the whole
30 students are 15 % of a school. The school has 30 ÷ 0.15 = 200 students.
Always check forwards
$90 × 0.80 = $72. $50,000 × 1.10 = $55,000. 200 × 0.15 = 30. If the forward calculation does not land on the number you started with, the division was wrong.
Related questions
- How do I find the original price before a 20 % discount?
