Lesson 7
Finding the Original Value
Work backwards from a percentage to find the original number.
- intermediate
Formula
Original = Result ÷ (Percentage ÷ 100)
📚 Finding the Original Value
Sometimes you know the result after a percentage change and need to find the original value.
Example: 30 is 25% of what number?
Real-world Example:
After a 20% discount, a shirt costs $40. What was the original price?
$40 is 80% of the original (100% - 20% = 80%)
Original = $40 ÷ 0.80 = $50
Frequently Asked Questions
How do I find the original value before a percentage change?
Divide the new value by 1 plus or minus the change as a decimal. If $60 is the price after a 25% discount, the original was $60 ÷ 0.75 = $80.
How do I find the original price from a total that includes tax?
Divide by 1 plus the tax rate: a $54 total with 8% tax means a pre-tax price of $54 ÷ 1.08 = $50.
Practice
Work each one out, then check yourself.
60 is 40% of what number?
Hint: Convert 40% to 0.40, then divide 60 by 0.40
Show answer
150
Final Quiz
0/3
Test what you learned. Pick the correct answer for each question.
After a 20% discount, an item costs $80. Original price?
$80 ÷ 0.80 = $100.
Total with 8% tax is $108. Pre-tax amount?
$108 ÷ 1.08 = $100.
After a 15% increase, the value is $230. Original?
$230 ÷ 1.15 = $200.