Percentages
Out of a hundred, and how to switch between fractions, decimals and per cent.
What per cent means
Per cent literally means "out of 100". The symbol is %.
So 35% means 35 out of every 100, which is the fraction 35/100 and the decimal 0.35. Three ways of saying exactly the same thing.
Converting between the three forms
Per cent → decimal: divide by 100. So 45% = 0.45.
Decimal → per cent: multiply by 100. So 0.7 = 70%.
Per cent → fraction: put it over 100 and simplify. 25% = 25/100 = 1/4.
Percentages worth knowing by heart
50% = 1/2, 25% = 1/4, 75% = 3/4, 10% = 1/10, 20% = 1/5.
Knowing these turns many questions into single steps: 25% of 60 is just a quarter of 60, which is 15. No calculator needed.
Finding a percentage of an amount
Two reliable methods. Decimal method: 35% of 80 = 0.35 × 80 = 28.
Building-block method: 10% of 80 is 8, so 30% is 24, and 5% is 4, total 28. Same answer, and this one works in your head.
Increase and decrease
To increase by a percentage, find the amount and add it. A 20% rise on Rs 500: 20% is 100, so the new price is Rs 600.
To decrease, subtract instead. A 20% discount on Rs 500 gives Rs 400.
Writing one amount as a percentage of another
Make a fraction, then multiply by 100.
You scored 18 out of 25. That is 18/25, and 18 ÷ 25 × 100 = 72%. Always check which number is the total. It goes on the bottom.
Percentages in real life
Discounts, sales tax, exam marks, interest on savings, battery level, statistics in the news, percentages are everywhere.
They matter because they let you compare fairly: 18 out of 25 and 30 out of 40 are hard to rank until you convert both to 72% and 75%.
Where marks go
- "A 20% rise then a 20% fall returns to the start." It does not: the second 20% is of a bigger number.
- Confusing 0.5 with 5%. 0.5 = 50%. Watch the decimal point.
- Putting the wrong number on the bottom. The total is the denominator.
What to remember
- Per cent = out of 100. Divide by 100 for a decimal; multiply by 100 to go back.
- Learn 50%, 25%, 75%, 10%, 20% as fractions.
- Percentage of an amount: use the decimal, or build from 10%.
- One amount as a percentage: part ÷ total × 100.
Watch one worked through
Here is one done slowly, with the reason for every move. Then one for you.
A shirt costs Rs 1200. In a sale it is 15% off. What do you pay?
- Find 10% first by moving the digits one place right.10% of 1200 = 12010% is always the number divided by 10, which you can do in your head. Build other percentages from it.
- Halve that to get 5%.5% = 120 ÷ 2 = 605% is half of 10%, 20% is double it, 1% is a tenth of it. Three facts cover most percentage questions.
- Add them for 15%.15% = 120 + 60 = 180Percentages add, so 10% + 5% really is 15% of the same amount.
- The question asks what you pay, not the discount.1200 − 180 = Rs 1020This is where the marks go. Read the question again before writing the answer: discount or final price.
Answer: Rs 1020
A bag costs Rs 800 with 20% off. What do you pay in rupees?
Show the answer
640
Practise Percentages
Everything on QuizByt for Class 6 Mathematics that goes with this lesson: read it first, then test yourself while it is fresh.
🧠 5 quizzes on Percentages (2 easy, 2 medium, 1 hard)
Work up from easy to hard: the hard quiz asks the Class 6 exam-style questions on Percentages.
🖨️ Printable worksheet
Percentages on paper for Class 6, with room to write the working out. Preview the first page free.
🎮 Games for Class 6 Mathematics
Number and logic games at the right level for Class 6. Passing a quiz on Percentages earns the credits that open them.
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