Fractions in Disguise
Class 8 · Mathematics
5 ideas in Class 8 Mathematics, explained in plain words, with games and quizzes to practise.
Fractions as Percentages
Part of: Percentages in everyday life
A percentage is a fraction whose denominator is 100. The word per cent means out of every hundred. So 35% means 35 out of 100, which is the fraction 35/100 or 7/20 or the decimal 0.35. To turn any fraction into a percentage, make an equivalent fraction with denominator 100, or multiply the fraction by 100.
Why it matters. Shops, marks, discounts and news reports all use percentages. They make it easy to compare two things that have different totals, such as 9 out of 12 and 14 out of 20. Without this idea, children find such comparisons confusing.
Try it in two minutes
- Ask your child: if 20 of 25 children in a class are present, how many out of 100 would that be? Let them scale up by 4.
- Write 1/2, 1/4, 3/4 and 1/5 on paper and ask for the percentage of each. Check using 100 paise in a rupee.
- Ask which is larger, 3/8 or 40%, and let your child explain how they decided.
Try at home. Look at a price tag or a battery indicator and ask your child to say what the percentage means as a fraction.
Percentage of a Quantity
Part of: Percentages in everyday life
To find 35% of 240, multiply 240 by 35/100 or by 0.35. Handy shortcuts help: 10% is one tenth, 5% is half of 10%, 20% is double 10%. A percentage can also be more than 100. For example, 250% of a number is 2.5 times that number. If a part and its percentage are known, we can work backwards to the whole.
Why it matters. Percentages of quantities appear in marks, recipes, savings and sales targets. Seeing that 20% is double 10% lets children calculate quickly in their heads without a calculator.
Try it in two minutes
- Pick a number such as 120. Ask your child to find 10% of it, then 5%, then use these to find 15%.
- Ask: if 20% of a number is 30, what is 100% of it?
- Say a runner ran 150% of the planned distance and ask your child to say what that means in words.
Try at home. Ask your child to find 15% of the bill the next time you eat out, using 10% plus half of it.
Percentage Change, Profit and Discount
Part of: Percentages in everyday life
Percentage change is the change divided by the original amount, times 100. If a price goes from 40 to 46, the increase is 6 and 6/40 × 100 = 15%. Profit is selling price minus cost price, and profit percentage is usually found against the cost price. A discount reduces the marked price, and GST is a tax added on top of the price.
Why it matters. Children meet sale boards and bills every day. Knowing that the percentage is taken on the original amount stops them from making common mistakes in shopping, savings and comparing prices.
Try it in two minutes
- Pick an item at home with a price. Ask: if its price rises by 10%, what is the new price?
- Ask: a shop buys a pen for 20 rupees and sells it for 25. What is the profit, and what percentage of the cost is it?
- Look at a discount offer together. Find the amount saved and the final price.
Try at home. Next time you see a sale, ask your child to find the final price after the discount.
Interest and Compounding
Part of: Percentages in everyday life
When money is kept in a bank, the bank pays extra money called interest. The money deposited is the principal, and p.a. means per annum or each year. Without compounding, interest every year is the same: principal × rate. With compounding, the interest is added back, so next year interest is earned on a bigger amount. After t years the amount is principal × (1 + rate) multiplied t times.
Why it matters. Understanding interest helps children see why saving early works and why borrowed money can become costly. It also shows how steady percentage growth speeds up.
Try it in two minutes
- Ask: if you deposit 1000 rupees at 10% a year, how much is the interest after one year?
- Find the amount after two years if the interest is not added back, then if it is added back. Compare the two.
- Ask your child why the second year gives more interest when the interest is added back.
Try at home. Ask your child to find how much 5000 rupees becomes in 3 years at 10% a year with compounding.
Depreciation and Repeated Changes
Part of: Percentages in everyday life
Depreciation means the value of an item falls with use and age. If a scooter loses 10% of its value, it is worth 90% of what it was, so multiply by 0.9. When changes are applied one after another, they are multiplied, not added: a 20% rise then a 20% fall gives 1.2 × 0.8 = 0.96, so the final value is 4% lower than the start.
Why it matters. Many sales say things like 30% + 20% off. Children who know that repeated percentages multiply, not add, can judge such offers and avoid mistakes in money matters.
Try it in two minutes
- Take a price of 100 rupees. Increase it by 10%, then decrease the new price by 10%. Is the answer 100?
- Ask why 30% off then 20% off is not the same as 50% off.
- Ask your child to find the value of a 50000 rupee phone after it loses 10% each year for 2 years.
Try at home. Ask your child to compare a single 40% discount with two discounts of 20% each.
What your child will practise
- Depreciation and Repeated Changes: Jungle Quick Fire (Quick Fire)
- Fractions as Percentages: Number Quest (Match It Up)
- Interest and Compounding: Desert Puzzle (Clue Puzzle)
- Percentage Change, Profit and Discount: Space Quick Fire (Quick Fire)
- Percentage of a Quantity: Lab Explorer Quest (Collect the Answer)
- Quiz: Depreciation and Repeated Changes (8 questions)
- Quiz: Fractions as Percentages (8 questions)
- Quiz: Interest and Compounding (8 questions)
- Quiz: Percentage Change, Profit and Discount (8 questions)