Equations with brackets, decimals and fractions · Usually met around P6
Finding the original
Original = what you know ÷ its %.
How to do it
Method
Original = what you know ÷ its %
$32 after 20% off: 32 ÷ 80% = 40
Another way
As a fraction, one part first
80% = 45: 32 ÷ 4 = 8, 8 × 5 = 40
In full
If you know a number after a percentage change, you can work back to the number before. First, work out what percentage of the original the number you know is. 40% of a number is 18 → 40%. 20% off → 80%. Up 25% → 100% + 25% = 125%. Down 20% → 100% − 20% = 80%. Then the original = the number you know ÷ that percentage, which means × 100, then ÷ the percentage. $32 after 20% off: 32 ÷ 80% → 32 × 100 = 3200, 3200 ÷ 80 = 40, so it was $40. You can also write the percentage as a fraction in its simplest form and find one part first. 80% = 45, so 4 parts are $32. One part is 32 ÷ 4 = 8, and 5 parts are 8 × 5 = 40. Careful: if 150 is 25% more, don't take 25% of 150 away from 150. The 25% that was added was 25% of the original: 150 ÷ 125% = 120. Check by working forwards: 40 × 80% = 32.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
20% off is $48: was $?
Show the answer and working
Answer: 20% off is $48: was $60
20% off leaves 80% of the price, so the price = 48 ÷ 80%: 48 × 100 = 4800, 4800 ÷ 80 = 60
Example 2
70% of ? = 168
Show the answer and working
Answer: 70% of 240 = 168
168 is 70% of the number, so the number = 168 ÷ 70%: 168 × 100 = 16800, 16800 ÷ 70 = 240
Example 3
20% off is $640: was $?
Show the answer and working
Answer: 20% off is $640: was $800
20% off leaves 80% of the price, so the price = 640 ÷ 80%: 640 × 100 = 64000, 64000 ÷ 80 = 800
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