Percentage basics: what % really means, with shortcuts

A percentage means "how many out of every 100". In this lesson you will learn fraction, decimal and percentage pairs, how to find x% of a number, how to get the whole from a part, and how to choose the right base.

Start here: which test went better?

In a maths test you scored 40 out of 50. In an English test you scored 60 out of 80. Which test went better?

At first glance 60 looks bigger. But the two tests have different totals, so comparing the marks directly misleads you. For a fair comparison, bring both to one scale: "out of 100".

• Maths: 40 out of 50. Multiply both by 2 and you get 80 out of 100, that is 80%.
• English: 60 out of 80. Divide both by 4 and you get 15 out of 20. Now multiply by 5: 75 out of 100, that is 75%.

Now it is clear: you did better in maths, even though the marks looked smaller. This is exactly what a percentage does. It puts things with different totals on the same scale.

Your exam speaks this language too. The Elementary Mathematics syllabus in the SSC GD notice of 2026 includes Percentages, and the notice gives its minimum marks as percentages. So this lesson answers one question: how do you see any number "out of 100", and how do you get back from there to the real number?

What a percentage really means: out of every 100

"Per cent" means "for every hundred". So 25% means 25 out of every 100.

The % sign is itself a signal to divide by 100: x% = x/100. Whenever you see %, read "÷ 100" in your mind.

Below is a square made of 100 small boxes. Each box is 1% of the square, and each row (10 boxes) is 10%.

The 25 boxes in the top-left corner are filled, so that is 25%. Now look closely: the filled block is half the width and half the height of the square, so it is exactly one quarter of it. That is why 25% = 1/4. A percentage and a fraction are two forms of the same thing.

100% means the whole thing. A percentage can also go above 100: 200% means double, and 150% means one and a half times. If this year's crop is 150% of last year's, it is one and a half times as big.

Fraction and percentage pairs

Fraction to percentage: multiply the fraction by 100. For example, 3/4 × 100 = 75, so 3/4 = 75%.

Why? 3/4 means "3 out of 4". We want "out of 100". Split 100 into 4 equal parts and each part is 25, so 3 parts make 75.

Percentage to fraction: write the number over 100 and simplify. For example, 40% = 40/100 = 2/5.

You do not need to cram these pairs. They come in three families, which start with 1/2, 1/5 and 1/3. Each family follows one rule: halve the fraction and the percentage halves too, because a percentage is just the fraction × 100.

Fraction	Percentage	How to remember
1/2	50%	First family: half
1/4	25%	half of 50 (chavanni)
1/8	12.5%	half of 25
1/16	6.25%	half of 12.5
1/5	20%	Second family: 100 ÷ 5
1/10	10%	half of 20
1/20	5%	half of 10
1/3	33⅓%	Third family: 100 ÷ 3
1/6	16⅔%	half of 33⅓
1/12	8⅓%	half of 16⅔

Bigger pairs come from multiplying. 3/8 is three pieces of 1/8, so its percentage is three times 12.5%:

• 3/8 → 3 × 12.5% = 37.5%
• 2/3 → 2 × 33⅓% = 66⅔%
• 4/5 → 4 × 20% = 80%
• 7/8 → 100% − 12.5% = 87.5% (the whole minus 1/8)

Go deeper: the 9, 11 and 7 pairs

Their multiples work the same way: 2/9 is two pieces of 1/9. The multiples of 1/9 and 1/11 repeat their digits, so they are easy to remember. 1/7 has no such easy pattern, so simply remember it.

• 1/9 is about 11.11% (exactly $11\tfrac{1}{9}\%$). Its multiples repeat one digit too: 2/9 is about 22.22%, and 4/9 is about 44.44%.
• 1/11 is about 9.09% (exactly $9\tfrac{1}{11}\%$). In its multiples, a number from the 9 times table appears twice: 2/11 is about 18.18% (9 × 2 = 18), and 3/11 is about 27.27% (9 × 3 = 27).
• 1/7 is about 14.29% (exactly $14\tfrac{2}{7}\%$).

Decimals and percentages

Decimal to percentage: multiply by 100, that is, move the decimal point two places to the right. For example, 0.35 = 35%, 0.07 = 7% and 1.2 = 120%.

Percentage to decimal: divide by 100, that is, move the point two places to the left. For example, 8% = 0.08, 0.5% = 0.005 and 150% = 1.5.

A slip of one place makes the answer 10 times too big or too small:

Decimal	Percentage
0.5	50%
0.05	5%
0.005	0.5%
1.5	150%

Finding x% of a number

The standard way: to find x% of y, multiply x by y, then divide by 100. For 15% of 360: 15 × 360 = 5400, and 5400 ÷ 100 = 54.

Why? x% is x/100, and "of" here means multiply. Just as half of 360 = 360 × 1/2 = 180, 15% of 360 means 360 × 15/100 = 54.

This always works, but big multiplication takes time without a calculator. As per the SSC GD notice of 2026, calculators were not allowed in the exam. So learn the quick ways too.

Build it from bricks: 10%, 5% and 1%

Any percentage can be built from three small bricks:

Why does this work? 10% = 10/100 = 1/10, that is, divide by 10, so the point moves one place. 1% = 1/100, that is, divide by 100, so the point moves two places. And the bricks add and subtract directly because all these percentages are parts of the same whole (360): 10 parts and 5 parts make 15 parts, out of every 100.

The swap trick

What is 8% of 50? Now ask it the other way round: what is 50% of 8? Half of 8 is 4. Both answers are the same: 4.

From a part to the whole: find 1% first

Sometimes you are given a percentage and its part, and asked for the whole. For example: in a village, 30% of the houses have solar panels on the roof, and there are 45 such houses. How many houses are there in the village?

How to think: 45 is not the whole. It is only the 30% part. We need 100%. So first find a small piece (1%), then climb to 100%.

• 30% = 45 houses
• 1% = 45 ÷ 30 = 1.5 houses
• 100% = 1.5 × 100 = 150 houses

Does 1.5 houses sound odd? It is only a step in the working. There is an easier road too: stop at 10% instead of 1%.

flowchart TD
  A["30% = 45 houses"] -->|"divide by 3"| B["10% = 15 houses"]
  B -->|"multiply by 10"| C["100% = 150 houses"]

So 30% = 45; divide by 3 to get 10% = 15, then multiply by 10 to get 100% = 150. Check: 30% of 150 = 45. Correct.

Why does this work? The percentage and the part grow and shrink together. If you divide 30% by 3, you must divide 45 by 3 as well. This is called the unitary method.

The same idea as a one-line formula: whole = part × 100 ÷ percentage. For the question above: 45 × 100 ÷ 30 = 150.

A is what % of B? Choose the right base

Formula: A ÷ B × 100. For example, 18 is what percent of 24? 18 ÷ 24 × 100 = 75%.

Why? A ÷ B is the fraction that tells you what part of B the number A is. Multiplying by 100 turns it into "out of 100", just as 3/4 × 100 = 75.

The most important question here is: which number is the base? The base is the number whose percentage is asked. It is taken as 100%, and it goes at the bottom of the division.

• Spotting it in English: the number after "of". "of 24" means the base is 24.
• Spotting it in Hindi: the number just before "का/के/की". "24 का" means the base is 24.

Change the base and the answer changes:

Question	Base	Answer
18 is what % of 24?	24	75%
24 is what % of 18?	18	133⅓%

The second answer is more than 100%, and that is perfectly fine. When the first number is bigger than the base, the percentage goes above 100.

In daily life: your recharge gives you 1.5 GB of data a day, and today you used 1.2 GB. What percentage of today's data did you use? The base is 1.5 GB, because its percentage is asked: 1.2 ÷ 1.5 × 100 = 80%.

Put both in the same unit first

A comparison is fair only when both amounts are in the same unit. You cannot divide grams by kilograms, or minutes by hours, directly.

For example: 300 grams is what percent of 1.5 kilograms? First change 1.5 kilograms into grams: 1.5 × 1000 = 1500 grams. Now 300 ÷ 1500 × 100 = 20%. Check: 10% of 1500 = 150, so 20% = 300.

Skip the change of unit and 300 ÷ 1.5 × 100 gives 20000%. But 300 grams is less than 1.5 kilograms, so the answer must be under 100%. If an answer looks absurd, check the units first.

Useful units:

• 1 kilogram (kg) = 1000 grams
• 1 quintal = 100 kilograms, and 1 tonne = 1000 kilograms
• 1 hour = 60 minutes
• 1 kilometre (km) = 1000 metres
• 1 rupee = 100 paise

A part of a part: the base changes at every step

When a question says "of these" or "of them", the next percentage is not of the whole but of the part before it. So the base changes at every step.

For example: a village has 1200 families. 75% of them farm, and 40% of the farming families own a tractor. How many families own a tractor?

• Farming families = 75% of 1200 = 900
• Families with a tractor = 40% of 900 = 360. Here the base is 900, not 1200.
• And those without a tractor? They are the other 100% − 40% = 60% of the farming families, that is 60% of 900 = 540.

The next lesson has questions like "what percent more or less". The same rule works there: the base is the number you compare with.

Worked examples: from easy to exam level

The first step of every example is "How to think". Stop there and think for yourself before you read the solution.

Where students often go wrong

Learn to spot these eight mistakes. Each one comes with the right way and a way to avoid it.

1. Taking the base the wrong way round. Question: 18 is what percent of 24?
   • Wrong: 24 ÷ 18 × 100 → 133⅓%
   • Right: 18 ÷ 24 × 100 → 75%
   • Avoid it: the question says "of 24", so 24 goes at the bottom. Do not put the bigger number at the bottom out of habit; a percentage can be more than 100.
2. Using the other part as the base instead of the total. Question: a village has 25 pucca houses and 15 kuccha houses. What percentage of all the houses are kuccha?
   • Wrong: 15 ÷ 25 × 100 → 60%
   • Right: 15 ÷ 40 × 100 → 37.5%
   • Avoid it: the question says "of all the houses", so add up the total first: 25 + 15 = 40.
3. Treating the part as the whole. Question: 20% of a number is 18. What is the number?
   • Wrong: finding 20% of 18 → 3.6
   • Right: 20% = 18, so 10% = 9 and 100% = 90
   • Avoid it: the 18 you are given is the part, so the whole must be bigger.
4. Moving the decimal point the wrong number of places.
   • Wrong: writing 0.5 as 5%, or 4% as 0.4
   • Right: 0.5 = 50%, and 4% = 0.04
   • Avoid it: the point always moves two places, never one. The percentage form always looks 100 times bigger.
5. Using a wrong or incomplete fraction pair.
   • Wrong: taking 1/8 as 8%, or 1/3 as just 33%
   • Right: 1/8 is 12.5%, and 1/3 is 33⅓%
   • Avoid it: the bottom number of a fraction is not its percentage. And dropping the ⅓ changes answers: 33% of 600 = 198, but one third of 600 is 200.
6. Subtracting or dividing a percentage like an ordinary number. Question: what is 30% of 90?
   • Wrong: 90 − 30 = 60, or 90 ÷ 30 = 3
   • Right: 10% of 90 = 9, so 30% = 3 × 9 = 27
   • Avoid it: % means "divide by 100". Find 10% first, then multiply.
7. Dividing without changing the unit. Question: 250 grams is what percent of 2 kilograms?
   • Wrong: 250 ÷ 2 × 100 → 12500%
   • Right: 2 kilograms = 2000 grams, so 250 ÷ 2000 × 100 → 12.5%
   • Avoid it: put both amounts in the same unit first. 250 grams is less than 2 kilograms, so the answer must be under 100%.
8. Not changing the base for a part of a part. Question: of 1200 families, 75% farm, and 40% of these own a tractor. How many families own a tractor?
   • Wrong: 40% of 1200 → 480
   • Right: first 75% of 1200 = 900, then 40% of 900 → 360
   • Avoid it: when the question says "of these", the next percentage is of the part before it, not of the whole.

Try it yourself

Solve each one in your notebook first, then check your answer. Every wrong option comes from a real mistake, so read the explanation to see which mistake your answer came from.

Quick reference

What next: the next lesson shows how things grow and shrink by a percentage; after it, take the practice set and the mock test on both lessons.