Percentage: ICSE Class 7 Complete Guide

A parent once told me that her ten year old could recite the multiplication table to twenty but could not figure out whether a 'buy one get one fifty percent off' deal at Decathlon was actually better than a flat twenty five percent discount. That moment was her wake up call. Mental maths without percent literacy is like knowing all the alphabet but not being able to read words.

Percentage is the first chapter in the ICSE Class 7 commercial maths trilogy (followed by profit loss discount, and then simple interest). Every single future chapter, every commercial calculation, every real world maths problem that any Class 7 student will encounter in adult life uses percentages. If you master this chapter, the next two chapters will feel almost trivial.

The good news is percentage is not hard. It is just a different way of writing fractions with a fixed denominator of 100. Once you see that, the conversion rules and the word problems fall into place. This guide walks through every idea Selina covers, with six worked examples and a study plan you can start tomorrow.

The word percent literally means 'per hundred'. It comes from the Latin per centum. So $25\%$ means 25 per 100, or 25 out of every 100 parts, or the fraction $\frac{25}{100}$.

The symbol $\%$ is just a shortcut. Wherever you see it, you can mentally replace it with $/100$. So $60\% = \frac{60}{100}$ and $7\% = \frac{7}{100}$.

Why do we bother with percentages when we already have fractions? Because a fixed denominator of 100 makes numbers instantly comparable. 'My daughter scored $\frac{53}{62}$ in maths' is hard to evaluate. '$85\%$' is instantly clear. Percentage is the common currency of numerical comparison.

One more thing: percentages can be more than 100. If a company's profit grew from 50 to 125, the growth is $150\%$ of the original. This might look strange the first time, but it just means 'the new value is one and a half times the old value'. Similarly, percentages can be fractional: $12.5\%$ is perfectly valid and equals $\frac{12.5}{100} = \frac{1}{8}$.

To find $x\%$ of a quantity $Q$, use the formula:

Worked example 1: Find $15\%$ of Rs 800.

Solution:

Worked example 2: In a class of 40 students, $30\%$ are girls. How many girls are there?

Solution:

So there are 12 girls in the class. By subtraction, there are $40 - 12 = 28$ boys.

Worked example 3: Sonia spent $40\%$ of her pocket money on books and $25\%$ on snacks. If she had Rs 500 to start, how much does she have left?

Solution: Total spent percent $= 40 + 25 = 65\%$. Amount spent:

Amount left $= 500 - 325 = \text{Rs } 175$.

Alternatively, amount left is $100 - 65 = 35\%$ of 500, which is $\frac{35}{100} \times 500 = 175$. Both methods give the same answer. Pick whichever feels faster for you.

Sometimes the question is reversed: instead of 'what is $15\%$ of 800', you are asked 'what percent of 800 is 120'. The formula is:

Worked example 4: In an exam, Rahul scored 72 marks out of 80. What percent did he score?

Solution:

So Rahul scored $90\%$.

Worked example 5: A shirt originally priced at Rs 600 is sold for Rs 450. What percent of the original price is the selling price?

Solution:

The selling price is $75\%$ of the original. That means a discount of $100 - 75 = 25\%$ was applied. This kind of calculation is the bridge into the next chapter on profit loss and discount.

When a quantity changes from one value to another, the change as a percent of the original is called the percentage change. If the new value is bigger, we call it a percentage increase. If smaller, a percentage decrease.

Formulas:

Notice the denominator is always the original value, not the new one. This is the single most common mistake students make.

Worked example 6: The price of rice increased from Rs 40 per kg to Rs 50 per kg. Find the percentage increase.

Solution:
Increase $= 50 - 40 = 10$.
Original $= 40$.

The price increased by $25\%$.

Another example: Anita's weight decreased from 60 kg to 54 kg. Find the percentage decrease.

Decrease $= 60 - 54 = 6$.

Anita's weight decreased by $10\%$.

A tricky question Selina loves: If a number is increased by $20\%$ and then decreased by $20\%$, do we get back the original number?

Answer: no. Say the number is 100. Increased by $20\%$ it becomes 120. Now decrease 120 by $20\%$: $20\%$ of 120 is 24, so we get $120 - 24 = 96$. We lost 4 compared to the original 100. The reason is that the percent decrease was calculated on 120, not 100. This kind of question shows up in almost every ICSE Class 7 exam.

Here are a few more application problems in the Selina style.

Example: A shopkeeper reduces the price of a TV by $15\%$. If the original price was Rs 24000, what is the new price?

Solution: Reduction $= 15\%$ of $24000 = \frac{15}{100} \times 24000 = 3600$.
New price $= 24000 - 3600 = 21600$.

Or, new price is $100 - 15 = 85\%$ of original $= \frac{85}{100} \times 24000 = 20400$. Wait, that gives 20400, not 21600. Let me recompute. $85 \times 240 = 20400$. And $3600$ off $24000$ is $20400$. So the answer is Rs 20400. I made an arithmetic slip earlier. Check your work always.

Example: A salesman gets $5\%$ commission on all his sales. In a month he sold goods worth Rs 80000. How much commission did he earn?

Solution: $5\%$ of $80000 = \frac{5}{100} \times 80000 = 4000$. His commission is Rs 4000.

Example: A farmer's crop yield increased from 2000 kg to 2500 kg after switching to a new method. Find the percentage increase.

Solution: Increase $= 500$ kg. Percent $= \frac{500}{2000} \times 100 = 25\%$.

Seven errors that keep eating marks in Class 7 percentage tests.

1. Forgetting to divide by 100 when converting percent to fraction. Writing $40\%$ as $40$ instead of $\frac{40}{100}$.

2. Using the new value as the denominator in percent change. The denominator must be the original value.

3. Missing the subtraction step. When asked for the amount left after spending, students stop at the amount spent.

4. Confusing 'percent of' with 'percent more than'. $120\%$ of a number is not $20\%$ more than it, it is exactly that number plus twenty percent. Be careful with the language.

5. Successive percent errors. Assuming a $20\%$ increase followed by a $20\%$ decrease cancels out. It does not, as we showed above.

6. Sloppy arithmetic in the final step. Getting the formula right but miscalculating $\frac{15}{100} \times 800$. Always double check.

7. Dropping the percent sign. Writing '$60$' in the final answer when the question asked for a percent. The answer should be '$60\%$'.

* Percent means per hundred. $x\% = \frac{x}{100}$.
* Convert between fractions, decimals and percent by multiplying or dividing by 100.
* Percent of a quantity: $x\% \text{ of } Q = \frac{x}{100} \times Q$.
* One quantity as percent of another: $\frac{\text{part}}{\text{whole}} \times 100\%$.
* Percentage change denominator is always the original value.
* Memorise the common fractions like $\frac{1}{4} = 25\%$, $\frac{1}{5} = 20\%$, $\frac{1}{8} = 12.5\%$.
* Successive percent changes do not cancel. An increase followed by a decrease leaves you with less than the original.