Percentage Change with Multipliers · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

One number does the whole change

Mathematics · Ratio & Proportion · ages 15-16
Name ______________________   Date ____________

  1. Which multiplier would you use to increase an amount by 8%?

    • 0.08
    • 0.92
    • 1.08
    • 8.00

  2. A shop raises every price by 15%. What multiplier turns an old price into the new price?

    • 0.85
    • 1.15
    • 1.015
    • 15

  3. True or false: a 20% increase followed by a 20% decrease always brings a value back to where it started.

    Circle one:   True   False

  4. What multiplier cuts an amount by 20%?

    • 1.20
    • 0.80
    • 0.20

  5. A coat costs 68 pounds after 15% off. What was the original price in pounds?

    Answer: ______________

  6. A jacket is on sale for $68 after a 20% discount. What was the original price, in dollars?

    Answer: ______________

  7. A price drops 10%, then rises 10%. What is true about the final price compared to the original?

    • It's back to the original price
    • It's lower than the original
    • It's higher than the original
    • Not enough info

  8. A book is priced at $18 after a 25% discount. Which calculation finds the original price?

    • 18 × 0.75
    • 18 ÷ 0.75
    • 18 × 1.25
    • 18 ÷ 1.25

  9. A painting's value increases 25% one year, then decreases 25% the next. If it started at $400, what is its value now, in dollars?

    Answer: ______________

  10. A painting starts at 400 pounds, rises 25%, then falls 25%. What is it worth now in pounds?

    Answer: ______________

LightMySky · lightmysky.comW1-mt_uqclfF4OBR-s1

Answer key

For grown-ups. Fold this page away before handing over the rest.

One number does the whole change W1-mt_uqclfF4OBR-s1

  1. 1.08 · Keeping the whole amount and adding 8% more gives 108%, written as the decimal 1.08.
  2. 1.15 · You keep the whole original amount (100%) and add 15% more, so you multiply by 1.15.
  3. False · The decrease works on a bigger number after the increase, so multiplying 1.20 by 0.80 gives 0.96, which is less than 1.
  4. 0.80 · A 20% fall leaves 80%, which is 0.80.
  5. 80 · 15% off means times 0.85, so divide: 68 divided by 0.85 = 80.
  6. 85 · A 20% discount means the sale price is 80% of the original, so you divide the sale price by 0.80 to undo it.
  7. It's lower than the original · Multiplying 0.90 by 1.10 gives 0.99, so the final price ends up 1% below the start, not back to normal.
  8. 18 ÷ 0.75 · A 25% discount gives a multiplier of 0.75, and dividing the sale price by that multiplier undoes the discount.
  9. 375 · Chaining the two multipliers shows the painting ends up below its starting value, since the decrease applies to a bigger number.
  10. 375 · Chain the multipliers: 400 times 1.25 times 0.75 = 375.
Worksheet · LightMySky