Example 1
Convert 3/5 into a percentage.
- Multiply 3/5 by 100.
- (3 / 5) × 100 = 3 × 20 = 60%.
Answer: 60%
📗 Class 7 maths · session 7 of 12 · 60 minutes · 🎁 free with an account
Comparing quantities: percentages and profit
Welcome aboard the Captain Calc Math Squad! Today we are mastering percentages and finding out how shopkeepers calculate profit and loss.
🤖 Written with Google's Gemini AI. A second AI solved all 55 questions without seeing the answers, and both agree. One of our teachers has not read it yet, so if something looks wrong, please tell us.
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-up3 min
- Warm-up games5 min
- Understanding Percentages and Conversions8 min
- Finding Quantities and Percentage Change7 min
- Cost Price, Selling Price, Profit, and Loss7 min
- Calculating Profit Percentage and Loss Percentage7 min
- Super Market Special Offers6 min
- Profit Protector5 min
- Percentage Power-Up6 min
- Quiz5 min
- Set the project1 min
By the end you can
- Convert fractions and decimals into percentages and vice versa
- Calculate the percentage increase or decrease of a quantity
- Identify Cost Price, Selling Price, Profit, and Loss
- Calculate Profit percentage and Loss percentage on Cost Price
Before you start
- Basic operations with whole numbers, fractions, and decimals
- Understanding of simple ratio concept
Have ready
- Notebook and pencil
- Ruler
Class 7 · CBSE, ICSE and state boards
Warm-up · think first
Captain Calc bought a superhero cape for ₹400 and sold it to a friend for ₹500. Did he make a profit or a loss, and by how much?
Show the answer
He made a profit of ₹100 because the selling price is ₹100 higher than the cost price.
Teacher tip: Ask students to explain how they knew it was a profit before doing any calculation.
🎮 Warm-up games · 5 quick games
Play with Captain Calc
Six minutes with Captain Calc. Vote, say why, then show the answer.
- Which one does not belong with the others: 50%, 1/2, 0.5, 0.05? (50% · 1/2 · 0.5 · 0.05)
Answer: 0.05 - Would you rather get 20% off on a comic book worth ₹500, or get ₹80 cash back on the same book? (20% off · ₹80 cash back)
Answer: 20% off - Profit percentage is calculated using the Selling Price as the base. (Always · Sometimes · Never)
Answer: Never. Profit percentage is always calculated using the Cost Price as the base. - Captain Calc bought 4 comic books for ₹50 each. He sold all 4 together for ₹260. What was his total profit in ₹?
Answer: 60 - Where do you see percentages used in daily life outside the math classroom?
Answer: Shopping discounts, exam marks, phone battery level, bank interest, and sports statistics.
Part 1 of 4 · learn, see, practise
Understanding Percentages and Conversions
Percent means per hundred. We write it using the % symbol.
To convert a fraction or decimal to a percentage, multiply it by 100.
To convert a percentage to a simple fraction, divide it by 100 and simplify.
Example 2
Convert 45% into a simple fraction.
- Write 45% as 45/100.
- Divide top and bottom by 5 to get 9/20.
Answer: 9/20
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 🔥
Stretch 🔥
Answers (for the teacher)
- 25
- 35
- 35
- 4/5
- 37.5
- 3/50
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Unlocking the rest of this lesson gives you:
- Part 2: Finding Quantities and Percentage Change, with practice at three levels
- Part 3: Cost Price, Selling Price, Profit, and Loss, with practice at three levels
- Part 4: Calculating Profit Percentage and Loss Percentage, with practice at three levels
- Class activity 1: Super Market Special Offers
- Class activity 2: Profit Protector
- Class activity 3: Percentage Power-Up
- A 10-question quiz
- After-class project: Comic Store Business Report
- Homework and a printable practice sheet with answers
- Teach mode and the minute-by-minute teacher's plan
It takes a minute. Anyone under 13 signs up with a parent. The first 2 lessons of every course, every game and all maths practice stay free.
FAQ
Comparing quantities: percentages and profit: questions
Why do we calculate profit percentage on cost price?
Cost price represents your original investment. Profit percentage measures how much your money grew compared to what you spent.
How do I quickly convert a fraction into a percentage?
Multiply the fraction by 100 and simplify the numbers by dividing common factors.
What is the difference between profit amount and profit percentage?
Profit amount is the actual gain in rupees, while profit percentage compares that gain to the original cost per hundred.
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