Ratios & Proportional Relationships · Grade 7 · 7.RP.A.3
Roots of Reason
rootsofreason.org
Stuck? Scan for the anchor chart
Percent Change Forward and Backward
Name
Date
Correct / 10
1
Forward: Apply the Change
- write the change as ONE multiplier first. Up 8% is ×1.08. Down 25% is ×0.75.
1. 8% tax on a $50 game.
× → total $
2. 25% off a $48 hoodie.
× → price $
3. A $35 lamp, marked up 40%.
× → price $
2
Backward: Undo the Change
- the given price is the AFTER. Divide by the multiplier. Do not take the percent off the new price.
4. After 30% off, a jacket costs $42.
Original price: $
5. With 8% tax included, the receipt says $86.40.
Before tax: $
6. After a 20% raise, Amara earns $54 a day.
Before the raise: $
7. A phone's price dropped 15%, to $102.
Original price: $
8. A 5% booking fee brought a trip's total to $210.
Before the fee: $
Check: multiply each answer by its multiplier. It should give exactly the given price.
Ratios & Proportional Relationships · Grade 7 · 7.RP.A.3
Roots of Reason
rootsofreason.org
3
Two Changes and a Comparison
- each change uses a new base. Show the middle price.
9. A $100 skateboard is 10% off. At the register, a coupon takes another 10% off the sale price. What is the final price, and what total percent came off?
$100
→ after the first 10%:
→ after the second 10%:
Final price: $ Total off: %
10. A $40 sweater. You may use one coupon: 30% off or $15 off. Which saves more money, and by how much?
saves $ more
Ratios & Proportional Relationships · Grade 7 · 7.RP.A.3
Roots of Reason
rootsofreason.org
Percent Change Forward and Backward
1Forward: Apply the Change
1. 8% tax on a $50 game.
100% + 8% = 108%
× 1.08 → total $ 54.00
2. 25% off a $48 hoodie.
100% − 25% = 75%
× 0.75 → price $ 36.00
3. A $35 lamp, marked up 40%.
100% + 40% = 140%
× 1.40 → price $ 49.00
2Backward: Undo the Change
4. After 30% off, a jacket costs $42.
42 ÷ 0.70 = 60
check: 60 × 0.70 = 42
check: 60 × 0.70 = 42
Original price: $ 60
5. With 8% tax included, the receipt says $86.40.
86.40 ÷ 1.08 = 80
check: 80 × 1.08 = 86.40
check: 80 × 1.08 = 86.40
Before tax: $ 80
6. After a 20% raise, Amara earns $54 a day.
54 ÷ 1.20 = 45
NOT 54 minus 20%, that gives 43.20
NOT 54 minus 20%, that gives 43.20
Before the raise: $ 45
7. A phone's price dropped 15%, to $102.
102 ÷ 0.85 = 120
NOT 102 plus 15%, that gives 117.30
NOT 102 plus 15%, that gives 117.30
Original price: $ 120
8. A 5% booking fee brought a trip's total to $210.
210 ÷ 1.05 = 200
check: 200 × 1.05 = 210
check: 200 × 1.05 = 210
Before the fee: $ 200
A wrong answer fails the forward check.
Ratios & Proportional Relationships · Grade 7 · 7.RP.A.3
Roots of Reason
rootsofreason.org
3Two Changes and a Comparison
9. A $100 skateboard is 10% off, then another 10% off the sale price.
$100
→ after the first 10%:$90
→ after the second 10%:$81
100 × 0.90 = 90, then 90 × 0.90 = 81
the first 10% takes $10 off 100. The second takes $9 off the new base of 90
Final price: $ 81 Total off: 19 % not 20%
10. A $40 sweater: 30% off, or $15 off?
30% of 40 = $12 off, so you pay $28
$15 off means you pay $25. A percent is only as big as its base.
$15 off saves $ 3 more