Cogito
Grade 7 Math · Chapter 3 · Lesson 5
Finding the Original Price
Undoing a percent change.
10 problems · about 19 minutes · 7.RP.A.3
What this lesson teaches
The child finds an original amount given the amount after a percent increase or decrease.
- A percent change multiplies the original by a fixed multiplier.
- To go backwards, divide by that multiplier.
- Adding the percent back on is a different, and wrong, calculation.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
3 problemsReview — Simple Interest: £600 at 5% for 2 years. Interest in pounds?
Answer 60
Why £60.
Review — Discounts and Sale Prices: £70 with 20% off. Pay in pounds?
Answer 56
Why £56.
Review — Tax, Tips, and Markup: £90 with 20% added. Total in pounds?
Answer 108
Why £108.
Warm Up
Straightforward practice. Get the method working first.
3 problems£64 after 20% off. Original in pounds?
Answer 80
Why £80.
£90 after 10% off. Original in pounds?
Answer 100
Why 90 ÷ 0.9.
£75 after 25% off. Original in pounds?
Answer 100
Why 75 ÷ 0.75.
Build It Up
The same ideas with more to keep track of.
2 problems£120 after a 20% rise. Original in pounds?
Answer 100
Why 120 ÷ 1.2.
Is adding 20% back to a discounted price correct? Answer 1 for yes, 0 for no.
Answer 0
Why The percent was of the original.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Sale Tag: £40 after 20% off. What was the original, in pounds?
Answer 50
Why £50.
The Rise: £110 after a 10% rise. What was the original, in pounds?
Answer 100
Why £100.