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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.

Original = Result ÷ (Percentage ÷ 100)

Example: 30 is 25% of what number?

1
Convert percentage to decimal: 25 ÷ 100 = 0.25
2
Divide the result by the decimal: 30 ÷ 0.25 = 120

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.

  1. 60 is 40% of what number?

    Hint: Convert 40% to 0.40, then divide 60 by 0.40

    Show answer

    150

Final Quiz

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Test what you learned. Pick the correct answer for each question.

  1. After a 20% discount, an item costs $80. Original price?

    After a 20% discount, an item costs $80. Original price?
  2. Total with 8% tax is $108. Pre-tax amount?

    Total with 8% tax is $108. Pre-tax amount?
  3. After a 15% increase, the value is $230. Original?

    After a 15% increase, the value is $230. Original?