प्रतिशत की मूल बातें
Percentage Basics
Per cent means 'out of a hundred'. 25 per cent is 25 out of 100, that is 25/100 or 0.25 or one quarter. Percentages appear in Class 5 work on marks, discounts, and simple comparison, and they are the bridge between fractions and everyday life.
The three conversions
Percentage → fraction: divide by 100 | Fraction → percentage: multiply by 100
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 1/8 | 0.125 | 12.5% |
| 1/3 | 0.333... | 33.33% |
| 1/10 | 0.1 | 10% |
These seven should be known by sight; they remove most of the arithmetic from a percentage question.
The three standard problems
- Finding a percentage of a number — 15 per cent of 240 = 15/100 x 240 = 36.
- Expressing one number as a percentage of another — 36 out of 240 = 36/240 x 100 = 15 per cent.
- Finding the whole from a part — if 15 per cent is 36, the whole is 36 x 100/15 = 240.
Increase and decrease
Percentage change = (change / original value) x 100
If a price rises from 200 to 250, the change is 50 and the percentage increase is 50/200 x 100 = 25 per cent. The denominator is always the original value, which is the point most often missed.
A price raised by 10 per cent and then reduced by 10 per cent does not return to the original, because the second 10 per cent is calculated on a larger number: 100 becomes 110, then 99.
Percentage and fraction together
The fastest method in most percentage questions is to replace the percentage with its fraction. Twenty-five per cent of 84 becomes one quarter of 84, which is 21, with no multiplication at all. Similarly 12.5 per cent is one eighth and 33.33 per cent is one third. Children who learn percentages only as a formula never gain this speed.
In a Class 5 classroom
- Marks: 36 out of 50 in a test — what percentage?
- A shopkeeper's discount of 20 per cent on a 150-rupee bag.
- Attendance: 22 present out of 25 — is that above 85 per cent?
✗ A 20 per cent rise followed by a 20 per cent fall returns the price to the start. | ✓ It does not; the fall is calculated on the increased amount, so the price ends lower.
संकेत: प्रतिशत का अर्थ 'प्रति सौ'; प्रतिशत परिवर्तन हमेशा मूल मान पर निकाला जाता है।
Percentages give one question in the Maths section and often reappear inside a data-handling or measurement item. The reliable trap is calculating a percentage change on the new value instead of the original. A second trap is the successive increase-and-decrease question above. Learn the fraction-decimal-percentage table by heart, because it converts a two-minute calculation into a five-second one under exam pressure.
Frequently asked questions
How do you convert a fraction into a percentage?
Multiply the fraction by 100 and add the per cent sign. One eighth multiplied by 100 gives 12.5, so one eighth is 12.5 per cent. The reverse conversion is done by dividing the percentage by 100.
On which value is a percentage increase calculated?
Always on the original value, not on the new one. If a price goes from 200 to 250, the increase of 50 is divided by 200, giving a 25 per cent rise.
Does a 10 per cent rise followed by a 10 per cent fall cancel out?
No. The fall is calculated on the increased amount, so a price of 100 becomes 110 and then 99. Successive percentage changes never simply cancel each other.
60-second recap
- Per cent means out of a hundred; 25% = 25/100 = 0.25.
- Know the common fraction, decimal and percentage equivalents by sight.
- Three problems: percentage of a number, one number as a percentage of another, whole from a part.
- Percentage change is always calculated on the original value.
- Equal successive rise and fall do not cancel out.
Ab isi chapter ke questions CTET Paper 1 mock test me practice karo — fractions, decimals aur percentage ke sawaal wahin milenge.