Warm-up
Three quick ones from earlier work. Try each in your head or on paper before you open the answer.
- (Lesson 3) How many millilitres are there in 2.4 litres?
Answer
2400 mL. 2.4 × 1000 = 2400. - (Year 7, Unit 2, lesson 5) Increase 80 rupees by 25%.
Answer
100 rupees. 25% of 80 is 20, and 80 + 20 = 100. - (Lesson 1) 250 g of cashews cost 90 rupees. What is the price per 100 g?
Answer
36 rupees. 250 g is 2.5 lots of 100 g, and 90 ÷ 2.5 = 36.
Words used in this lesson
- exchange rate
- how much of one currency one unit of another is worth. For example: 1 peso = 5 rupees.
- currency
- the money of a country. For example: dirham, rupee, taka.
- convert
- change from one unit or currency to another. For example: 12 pesos to rupees.
- reciprocal
- the number you multiply by to get 1. For example: 4 and 0.25.
- break-even
- the point where two things are equal. For example: 10 dirhams = 250 rupees at 25.
- per kilogram
- for each one kilogram. For example: 80 rupees per kilogram.
Which is cheaper?
A pair of headphones costs 15 dirhams in Dubai and 330 rupees in Chennai. The rates on this page are invented for practice; they are not real rates. Predict first: which pair is cheaper, 15 or 330? What is the one fact you would need before you could say?
The figure uses a backpack: 18 dirhams in Dubai, 396 rupees in Chennai. Move the exchange rate and watch the Dubai price in rupees.
At 1 dirham = 24 rupees, 18 dirhams is 18 × 24 = 432 rupees. Chennai asks 396 rupees, so Chennai is cheaper by 36 rupees.
Show me the steps
- 1 dirham = 24 rupees: 18 × 24 = 432 rupees, which is 36 more than 396. Chennai is cheaper.
- 1 dirham = 22 rupees: 18 × 22 = 396 rupees. The two prices are the same.
- 1 dirham = 19 rupees: 18 × 19 = 342 rupees, which is 54 less than 396. Dubai is cheaper.
- 1 dirham = 27 rupees: 18 × 27 = 486 rupees, which is 90 more than 396. Chennai is much cheaper.
An exchange rate is a conversion factor: 1 dirham = 22 rupees. To change dirhams into rupees, multiply by 22. To change rupees into dirhams, divide by 22.
Compare prices only in the same currency, and for the same amount. Change one price into the other's currency, or both into a third, then compare. For different pack sizes, find the price for one kilogram, or one litre, first.
The answer holds at that exchange rate only: when the rate moves, a price in another currency moves with it.
Back to the headphones: at 1 dirham = 22 rupees, 15 dirhams is 15 × 22 = 330 rupees, exactly the same. At 21 rupees to the dirham Dubai is cheaper (315 rupees) and at 23 it is dearer (345 rupees). The numbers 15 and 330 could not tell you that.
A common mistake: “15 is much smaller than 330, so the Dubai price is the lower one.” The two numbers are counted in different units, so they cannot be compared as they stand. Dirhams are worth many rupees each, so a small number of dirhams can be a large price.
Worked example: back the other way
1 dirham = 22 rupees. How many dirhams is 770 rupees?
- A dirham is worth more than a rupee, so the number of dirhams will be smaller: divide.
- 770 ÷ 22 = 35.
- 35 dirhams. Check by going forward: 35 × 22 = 770.
Worked example: two pack sizes
Rice is sold as 750 g for 60 rupees or 2 kg for 150 rupees. Which is cheaper per kilogram?
- 750 g is 0.75 kg. Price per kilogram: 60 ÷ 0.75 = 80 rupees.
- The 2 kg pack: 150 ÷ 2 = 75 rupees per kilogram.
- The 2 kg pack is cheaper, by 5 rupees for each kilogram.
Your go. The first step is given. Tea is sold as 250 g for 95 rupees or 1 kg for 360 rupees. Which is cheaper per kilogram?
- 250 g is a quarter of a kilogram, so four packs make a kilogram: 95 × 4 = 380 rupees per kilogram.
- Now find the price per kilogram of the large pack, compare, then check.
Check the answer
The 1 kg pack is 360 rupees per kilogram. 360 < 380, so the 1 kg pack is cheaper, by 20 rupees for each kilogram.
Check before you go on
1. The exchange rate is 1 dirham = 20 rupees. How do you change 60 rupees into dirhams?
Your turn
Start at Level 1 and go as far as you can. Type negative numbers with a minus sign, for example -7. A wrong answer gets a reason, not just a cross: read it, then try again.
Level 1 · Getting started
2. A scarf costs 12 dirhams. The rate is 1 dirham = 22 rupees. What is the price in rupees?
3. The rate is 1 dirham = 22 rupees. How many dirhams is 440 rupees?
Level 2 · Building
4. A shirt costs 15 dirhams in a shop in Dubai. The rate is 1 dirham = 32 taka. A shop in Dhaka sells the same shirt for 450 taka. How many taka cheaper is the shirt in Dhaka?
5. At one exchange, 1 rupee = 0.05 dirham. How many rupees is 1 dirham?
6. Cooking oil is sold as 500 mL for 90 rupees or as 2 litres for 340 rupees. How many rupees per litre cheaper is the 2 litre bottle?
Level 3 · Stretch
7. A watch costs 28 dirhams in Dubai and 560 rupees in Chennai. At what exchange rate, in rupees for 1 dirham, do the two cost the same?
8. A change office buys dirhams at 20 rupees each and sells them at 25 rupees each. Ravi sells the office 200 dirhams, then at once uses all the rupees to buy dirhams back. How many dirhams does he finish with?
Something to think about
The rate moves from 1 dirham = 22 rupees to 1 dirham = 24 rupees. For someone in India buying from a Dubai shop, does the Dubai shop become cheaper or dearer? Explain, then say what the new price is for an item that costs 15 dirhams.
One way to think about it
Dearer. Each dirham now costs 24 rupees instead of 22, so the same number of dirhams costs more rupees. An item priced at 15 dirhams costs 15 × 24 = 360 rupees instead of 15 × 22 = 330 rupees, which is 30 more.
Exit ticket
9. Rice costs 9 dirhams for a 2 kg bag in Sharjah and 475 rupees for a 5 kg bag in Kochi. The rate is 1 dirham = 22 rupees. Which is cheaper per kilogram, and why?