Multiplying distances
If a school van covers 18 km every day, how much does it cover in 6 days? Adding 18 + 18 + 18 + 18 + 18 + 18 works , but multiplication is faster.
What is this?
Multiplication is repeated addition. When the same distance happens many times, we multiply.
We line up the numbers like in addition and multiply column by column, carrying when a column gives a number bigger than 9.
For example, 235 × 4:
2 3 5
× 4
-------
9 4 0
- 4 × 5 = 20. Write 0, carry 2.
- 4 × 3 = 12, plus 2 = 14. Write 4, carry 1.
- 4 × 2 = 8, plus 1 = 9.
So 235 × 4 = 940.
When multiplying by a two-digit number, we do two rows and add them up. For 123 × 14:
- 123 × 4 = 492.
- 123 × 10 = 1,230.
- Add: 492 + 1,230 = 1,722.
So 123 × 14 = 1,722.
This same trick helps us calculate fares (₹85 per ticket × 12 tickets), petrol cost (₹100 per litre × 25 litres), or any "rate" problem.
Worked examples
Example 1. A bus covers 95 km in one hour. How far in 7 hours?
- 95 × 7.
- 7 × 5 = 35 → 5, carry 3.
- 7 × 9 = 63 + 3 = 66.
- Answer: 665 km.
Example 2. A petrol pump sells 235 litres of petrol per hour. How much in 8 hours?
- 235 × 8.
- 8 × 5 = 40 → 0, carry 4.
- 8 × 3 = 24 + 4 = 28 → 8, carry 2.
- 8 × 2 = 16 + 2 = 18.
- Answer: 1,880 litres.
Example 3. A taxi charges ₹15 per km. A trip is 24 km. What is the fare?
- 15 × 24 = ?
- 15 × 4 = 60.
- 15 × 20 = 300.
- 60 + 300 = ₹360.
Try it
- 132 × 5.
- 268 × 7.
- 145 × 12.
- A car covers 65 km per hour. How far in 9 hours?
- Auto fare is ₹14 per km. A 25 km trip costs how much?
Hands-on
Rate calculator. Pick anything in your home that has a "per-something" rate , for instance, a tap fills a bucket of about 12 litres per minute. Compute the litres for 15 minutes. Verify by measuring (carefully).
Journey planner. Pick a city you'd like to visit. Suppose a bus travels at 50 km per hour. How long will it take if the city is 300 km away? Multiply or divide as needed and write the answer in your notebook.