Example 1
Write 'increase a by 5%' as one multiplication.
- The increase is 0.05a.
- a + 0.05a = 1a + 0.05a.
- Combine like terms: 1.05a.
Answer: 1.05a
⚖️ Grade 7 · equations · session 3 of 12 · 60 minutes · ⭐ Plus
Rewriting expressions: percent increase, discounts and meaning
The same quantity can be written in different ways, and each way tells you something. a + 0.05a shows the 5% added on; 1.05a shows it as one multiplication. Both are equal.
A complete lesson · 60 minutes
Teach it, see it, practise it, all on this page.
Open this page with your learner and work down it, or press Teach this lesson to go through it one step at a time on a big screen. Every section has something to do.
- Warm-up4 min
- Percent increase9 min
- Discounts9 min
- What each form shows9 min
- Activity 17 min
- Activity 27 min
- Activity 35 min
- Quiz6 min
- Set the project4 min
By the end you can
- Rewrite a percent increase or decrease as one multiplication
- Explain what each form of an expression shows
- Use the quicker form to solve a problem
- NJSLS-M 7.EE.A.2 (Common Core 7.EE.2)
Before you start
- Percent of a number
- Combining like terms
Have ready
- A calculator (for checking only)
Grade 7 · Unit 2 · NJSLS-M and Common Core 7.EE
Warm-up · think first
A ₹200 game goes up by 10%. Show two ways to find the new price.
Show the answer
200 + 0.10 × 200 = 220, or 1.10 × 200 = 220. Adding 10% on is the same as multiplying by 1.10.
Teacher tip: Ask: which way is quicker for 15 different prices?
Part 1 of 3 · learn, see, practise
Increase by p% = multiply by (1 + p/100)
Increase a by 5%: a + 0.05a = (1 + 0.05)a = 1.05a.
The 1 keeps the original amount; the 0.05 is the extra.
Increase by 30%: × 1.30. Increase by 100%: × 2.
Practise it
Start with the warm-up and go as far as you can. The stretch questions are meant to be hard.
Warm-up
Warm-up
Core
Core
Stretch 🔥
Answers (for the teacher)
- 1.1
- 1.25
- 1.08x
- 460
- 1.075
⭐ Part of Pure Faith Plus
The rest of this lesson is in Plus
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You have seen the plan, the warm-up and part 1. With Plus you also get:
- Part 2: Decrease and discounts: multiply by (1 − p/100), with practice at three levels
- Part 3: What does each form tell you?, with practice at three levels
- Class activity 1: Multiplier match
- Class activity 2: Shop the sale
- Class activity 3: Two forms, one story
- A 8-question quiz
- After-class project: Price tracker
- Homework and a printable practice sheet with answers
- Teach mode and the minute-by-minute teacher's plan
The first 2 lessons of every course, every game and all maths practice stay free.
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FAQ
Rewriting expressions: percent increase, discounts and meaning: questions
Why is a 5% increase the same as multiplying by 1.05?
Because a + 0.05a = (1 + 0.05)a = 1.05a: the 1 keeps the original and 0.05 adds the 5%.
How do you write a discount as a multiplication?
Subtract the percent from 100%: 20% off means paying 80%, so multiply by 0.8.
Which standard is this?
New Jersey 7.EE.A.2 (Common Core 7.EE.2): rewriting expressions in different forms to show how the quantities are related.
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