Comparing Quantities
Class 8 · Mathematics
5 ideas in Class 8 Mathematics, explained in plain words, with games and quizzes to practise.
Ratios and Percentages
Part of: Comparing quantities
A ratio compares two quantities, like 12 boys to 18 girls, which is 2 : 3 in simplest form. A percentage is a ratio out of 100, so 14 out of 40 is 35%. The unitary method finds one part first: if 30% is 12, then 1% is 0.4.
Why it matters. Ratios and percentages are everywhere: scores, offers, recipes and surveys. These are the base for discounts, taxes and interest in the rest of the chapter.
Try it in two minutes
- Ask your child to count how many red and blue items are in a pack of pencils or beads and write the ratio.
- Change the counts into a percentage of the total.
- Ask: if 10% of the pack is 3 items, how many items are there in all?
Try at home. Ask your child to find the percentage of vowels in their name.
Discounts
Part of: Comparing quantities
A discount is a reduction in the marked price of an item. Discount = marked price - sale price. A discount percentage is always worked out on the marked price. For a ₹ 500 shirt with 10% discount, the discount is ₹ 50 and you pay ₹ 450.
Why it matters. Discounts are part of everyday shopping. Knowing how to find the real saving helps children compare offers and avoid being misled by big-looking numbers.
Try it in two minutes
- At home, pick an item and imagine a sale price: for example ₹ 400 marked, ₹ 340 sale. Ask: what is the discount?
- Ask: what percentage of ₹ 400 is that discount?
- Ask the sale price of an item marked ₹ 600 with 20% off.
Try at home. Ask your child to compare two offers: 20% off ₹ 500, and ₹ 80 off ₹ 450. Which is better?
Sales Tax, VAT and GST
Part of: Comparing quantities
Sales tax is charged by the government on the selling price and added to the bill. VAT and GST are taxes included in or added to prices. With 10% tax, an item priced ₹ 100 costs ₹ 110, so a price of ₹ 330 including tax means ₹ 300 before tax.
Why it matters. Every bill a family pays has taxes. Children who understand how tax is added, and how to take it out again, can check bills and compare prices.
Try it in two minutes
- Look at a shop bill at home. Ask your child to find the tax line.
- Ask: which percentage was charged? Does it match 5%, 12% or 18% of the price?
- Try to work back from a total to the price before tax.
Try at home. Ask your child to work out the bill for an item priced ₹ 250 with 12% GST.
Simple and Compound Interest
Part of: Interest and growth
Simple interest is always worked out on the original sum. Compound interest is worked out on the amount at the end of the previous year, so the interest itself earns interest. On ₹ 100 at 10% for 3 years, simple interest gives ₹ 30 but compound interest gives ₹ 33.10.
Why it matters. Compound interest is how savings, loans and bank deposits really grow. Children who see how it works can understand why early saving, and clearing loans quickly, matter.
Try it in two minutes
- Take ₹ 100 and a rate of 10%. Work out simple interest for 3 years.
- Now work year by year: after year 1 you have ₹ 110. Find 10% of 110.
- Compare the two totals after 3 years.
Try at home. Ask your child to find the compound interest on ₹ 1000 at 10% for 2 years, year by year.
Compound Interest Formula and Applications
Part of: Interest and growth
For compound interest, the amount after n years is A = P × (1 + R/100)^n, where P is the sum, R the yearly rate and n the number of years. The compound interest is A - P. The same idea works for population growth. For falling values, called depreciation, we use (1 - R/100).
Why it matters. The formula saves time over year-by-year work and applies to savings, loans, populations and the value of items. It shows how repeated percentage change adds up.
Try it in two minutes
- Take ₹ 1000 at 10% for 2 years. Work out the amount year by year, then use 1000 × 1.1 × 1.1.
- Check that both methods give the same answer.
- Try a population of 2000 that grows 5% a year for 2 years.
Try at home. Ask your child to find the value of a ₹ 2000 bicycle after 2 years if it loses 10% of its value each year.
What your child will practise
- Compound Interest Formula and Applications: Space Puzzle (Clue Puzzle)
- Discounts: Jungle Quick Fire (Quick Fire)
- Ratios and Percentages: Number Quest (Collect the Answer)
- Sales Tax, VAT and GST: Candy Puzzle (Clue Puzzle)
- Simple and Compound Interest: Desert Puzzle (Clue Puzzle)
- Quiz: Compound Interest Formula and Applications (8 questions)
- Quiz: Discounts (8 questions)
- Quiz: Ratios and Percentages (8 questions)
- Quiz: Sales Tax, VAT and GST (8 questions)