Daily Maths
Currency conversion and exchange rates
In this note
- 1.12Convert money between currencies, in either direction, with an exchange rate.
- 1.12Use a rate given per 100, find a rate, and go through a common currency.
- 1.12Handle commission and compare prices in different currencies.
Before you start: rates and percentages.
Formula bank
Multiply or divide?
General methodHow to convert any amount of money
- Write the rate with a 1 on one side: 1 A = r B.
- Going AWAY from the 1 (A → B): multiply by r. Going TOWARDS the 1 (B → A): divide by r.
- Sense check: you get MORE units of the currency that is worth less.
- Round money to 2 d.p. (or whole units / whole notes if the question says).
Example $1 = €0.92. Change €161 to dollars.
Euros → dollars goes towards the 1: divide.
- \(161\div0.92=175\)
Answer $175
Try it yourself
Show answer
Answer €230
Show answer
Answer £400
Show answer
Answer ¥8910
Rates per 100, finding a rate, two rates, commission
General methodHow to handle the harder types
- Rate given for 100: divide by 100 to get the rate for 1.
- Find a rate: amount received ÷ amount changed (divide by the side that should be 1).
- Two rates with a common currency: change INTO the common currency, then OUT of it.
- Commission: take the percentage off the money BEFORE converting.
- Comparing prices: change both into ONE currency first.
Example €1 = £0.85 and $1 = £0.79. Change €400 into dollars.
Pounds are the bridge: € → £ → $.
- \(400\times0.85=£340\)
- \(340\div0.79=430.379\ldots\)
Answer $430.38
Try it yourself
Show answer
Answer $50
Show answer
Answer 148.5
Show answer
Answer €724.96
Rounding money
| Situation | Round to | Example |
|---|---|---|
| Dollars, pounds, euros | 2 d.p. | $179.533… → $179.53 |
| Currency with no small coins (yen) | whole units | ¥8910.4 → ¥8910 |
| Only whole notes or dollars given | DOWN | 152.67 SGD in whole dollars → 152 |
Ways they test it
Type 1 Both directions
"£1 = €1.16. (a) Change £450 to euros. (b) Change €87 to pounds." (3 marks)
Spot it a rate and two amounts.
- (a) × the rate.
- (b) ÷ the rate.
For example £1 = €1.16
- (a) \(450\times1.16=522\)
- (b) \(87\div1.16=75\)
Answer €522 and £75
Type 2 Rate from a table (per 100)
"For 100 SGD you get 1310 rand. Change 65 SGD to rand."
Spot it "for 100".
- ÷ 100 for the rate for 1.
- Then × or ÷.
Type 3 Whole notes / whole units
"She receives only whole dollars. How many?"
Spot it "whole dollars", "only $10 notes".
- Convert.
- Round DOWN.
For example 2000 rand at 13.10 rand per SGD
- \(2000\div13.10=152.67\ldots\)
Answer 152 SGD
Type 4 Two rates
"€1 = £0.85, $1 = £x. €600 gives $645.57. Find x." (3 marks)
Spot it two rates sharing a currency.
- Convert into the common currency.
- Divide to find the missing rate.
For example €600 → £510
- \(x=510\div645.57\)
Answer \(x=0.79\)
Type 5 Which is cheaper?
"$420 in the USA or £350 in the UK? £1 = $1.27."
Spot it prices in two currencies.
- Change one price into the other currency.
- Compare; give the difference with its currency.
Mistakes to avoid
- ✗ €87 → £ at £1 = €1.16: 87 × 1.16✓ 87 ÷ 1.16Towards the 1: divide.
- ✗ Using a 'per 100' rate as the rate for 1✓ ÷ 100 first$100 = 27 850 means $1 = 278.5.
- ✗ Comparing $420 with £350✓ change one into the otherDifferent currencies can't be compared.
- ✗ Rounding up to whole notes✓ round downThe bank won't give money you haven't paid for.
Summary
- 1 A = r B: A → B multiply, B → A divide.
- Per 100: ÷ 100 for the rate for 1.
- Two rates: go through the common currency.
- Commission comes off first.
- Money to 2 d.p.; whole notes round down.
If you see …
- "for 100 ..."÷ 100 first.
- two currencies to compareone currency first.
- "whole dollars only"round down.
Practice
Practice: easy, medium, hard
Easy
Show working
- \(120\times0.9\)
Answer €108
Show working
- \(90\div0.9\)
Answer $100
Show working
- \(15\,600\div100\)
Answer 156
Medium
Guide me
What is it asking? pounds
What do we know? dollars → pounds
Plan ÷ 1.36
Show working
- \(150\div1.36=110.29\)
Answer £110.29
Guide me
What is it asking? the rate the other way
What do we know? $1 = £0.8
Plan 1 ÷ 0.8
Show working
- \(1\div0.8=1.25\)
Answer $1.25
Guide me
What is it asking? yen received
What do we know? 3% taken off the dollars first
Plan 485 × 150
Show working
- commission $15
- \(485\times150=72\,750\)
Answer ¥72 750
Hard
Guide me
What is it asking? pounds back
What do we know? £75 → $, spend, → £
Plan × 1.36, subtract 68, ÷ 1.36
Show working
- \(75\times1.36=102\)
- \(102-68=34\)
- \(34\div1.36=25\)
Answer £25
| Part | Answer / working | Marks | Guidance |
|---|---|---|---|
| 102 | B1 | ||
| \(34\div1.36\) | M1 | ||
| 25 | A1 | ||
| Total: 3 marks | |||
Guide me
What is it asking? x
What do we know? pounds are common
Plan €500 → £, then £ ÷ $
Show working
- \(500\times0.88=440\)
- \(440\div473.12=0.93\)
Answer 0.93
| Part | Answer / working | Marks | Guidance |
|---|---|---|---|
| 440 | M1 | ||
| \(440\div473.12\) | M1 | ||
| 0.93 | A1 | ||
| Total: 3 marks | |||
Guide me
What is it asking? cheaper option and difference
What do we know? rupees and dollars
Plan change rupees to dollars, compare
Show working
- \(5400\div278.5=19.39\)
- \(20.50-19.39=1.11\)
Answer the shop, by $1.11
| Part | Answer / working | Marks | Guidance |
|---|---|---|---|
| \(5400\div278.5\) | M1 | ||
| 19.39 | A1 | ||
| shop, by $1.11 | A1 | ||
| Total: 3 marks | |||
Can I do this?
- I can convert money in both directions.
- I can use a rate per 100 and find an exchange rate.
- I can combine two rates through a common currency.
- I can handle commission and compare prices.
- I can round money correctly, including down to whole notes.
Anything unticked: revise that section first. All ticked: take the quiz.
Quiz
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