Money questions are everyday arithmetic done carefully: bills, change, wages and prices, always to the nearest cent. An exchange rate is a rate like any other, so multiply one way and divide the other.
If $1 = €0.92, then dollars \(\times 0.92\) gives euros and euros \(\div 0.92\) gives dollars. Check the answer makes sense: one dollar buys LESS than one euro, so the number of euros is smaller.
Fig. 1: a conversion graph for $1 = €0.92. Reading up from $350 and across gives €322
Section 01
Calculating with money.
Bills, change and wages are a chain of simple steps. Write each step with its units, and give money answers to the nearest cent (2 decimal places).
Two decimal places: \(\$7.8\) is written \(\$7.80\); \(160.898\) dollars rounds to \(\$160.90\).
Change \(=\) amount given \(-\) total cost.
Bills often have a fixed charge plus a cost per unit used.
Worked example Change from a note
Zara buys 3 notebooks at \(\$2.35\) each and 2 pens at \(\$0.85\) each. She pays with a \(\$20\) note. How much change does she get?
An electricity bill is a fixed charge of \(\$18.50\) plus \(\$0.21\) per unit. A family uses 640 units. Find the bill.
Units: \(640 \times 0.21 = \$134.40\).
Add the fixed charge: \(134.40 + 18.50\).
Answer: \(\$152.90\)
Examiner trap
Mixing dollars and cents in one calculation causes errors of 100 times. Work entirely in dollars (\(85\) cents \(= \$0.85\)) or entirely in cents.
Section 02
Converting currencies.
Open the lab on Exchange rate and move the rate and amount sliders. Notice that converting one way multiplies by the rate and converting back divides by it, and that the conversion graph is a straight line through zero (Fig. 1).
Worked example Both directions
The exchange rate is $1 = €0.92. (a) Change \(\$350\) to euros. (b) Change €230 to dollars.
(a) Each dollar is worth €0.92: \(350 \times 0.92 = 322\).
(b) Each €0.92 is one dollar, so divide: \(230 \div 0.92 = 250\).
Check (b): \(250 \times 0.92 = 230\). Correct.
Answer: (a) €322 (b) \(\$250\)
Worked example With commission
A bank changes dollars to yen at $1 = ¥148.6 and takes 2% of the dollars as commission. Lee changes \(\$500\). How many yen does he receive?
Commission: \(2\%\) of \(\$500 = \$10\), so \(\$490\) is changed.
Multiplying when you should divide gives \(230 \times 0.92 = \$211.60\) for part (b). Sense-check first: $1 buys only €0.92, so a euro is worth MORE than a dollar, and €230 must be MORE than 230 dollars.
Stage 1 · Learn
Check your understanding
Four quick checks. Each correct answer earns XP and records this skill on your profile.
Quick check+10 XP
Using $1 = €0.92, change \(\$50\) into euros.
Quick check+10 XP
Ali pays for a \(\$6.35\) sandwich with a \(\$10\) note. How much change does he get?
Quick check+10 XP
Using $1 = €0.92, change €69 into dollars.
Quick check+10 XP
Find the cost of 4 items at \(\$1.95\) each.
Section 03
Comparing prices in different currencies.
To compare, change both prices into the SAME currency first, then subtract.
Worked example Where is it cheaper?
A watch costs \(\$185\) in the USA and £150 in the UK. The rate is £1 = $1.27. Where is it cheaper, and by how many dollars?
Change the UK price to dollars: \(150 \times 1.27 = \$190.50\).
Compare: \(\$185 < \$190.50\).
Difference: \(190.50 - 185 = \$5.50\).
Answer: Cheaper in the USA, by \(\$5.50\)
Examiner trap
Do not subtract prices in different currencies: \(185 - 150 = 35\) has no meaning because dollars and pounds are different units.
Stage 2 · Exam
Exam-style questions
Unlocks once the four checks above are done. Worth more XP, written to IGCSE Paper 2 and Paper 4 standard.
Finish the four checks above to unlock the exam questions
Exam style+20 XP
Headphones cost £84 in the UK and €99 in France. The rate is £1 = €1.17. Which is cheaper, and by how much in pounds?
Exam style+20 XP
A bank changes dollars to euros at $1 = €0.92 and charges 1.5% commission on the dollars. How many euros do you get for \(\$600\)?
Exam style+20 XP
A phone plan costs \(\$24\) a month and includes 300 minutes. Extra minutes cost \(\$0.08\) each. Sita uses 465 minutes in a month. What is her bill?
Exam style+20 XP
Kim changes \(\$400\) to euros at $1 = €0.92. She spends €250, then changes the rest back at €1 = $1.05. How many dollars does she get back?
Skill unlocked
Money, sorted.
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