C1.15, C1.11; E1.15, E1.11 - Money and currency conversion

C1.15, C1.11; E1.15, E1.11 - Money and currency conversion

Is a price of €72 cheaper than a price of $86? The digits alone cannot tell you: first put both prices into the same currency. This lesson combines money calculations in C1.15 and E1.15 with exchange-rate reasoning in C1.11 and E1.11, so you can calculate totals, change and fair price comparisons.

Money calculations

A price is an amount of a particular currency. Before deciding which of the opening prices is cheaper, practise keeping currency values and decimal places clear.

Total cost and change

The total cost is the sum of all the charges. Change is the amount paid minus the total cost. For dollars and euros in this lesson, 100 cents make one dollar or one euro.

Multiply each unit price by its quantity, then add the costs. Keep the decimal points aligned in addition and subtraction. A calculator display of 4.84.8 dollars means 4.80,not4.80, not 4.08.

Worked example 1: several purchases

Question. A student buys 3 notebooks at 2.45eachand2pensat2.45 each and 2 pens at 1.30 each. Calculate the change from $20.

Plan. Find the cost of each group, add, then subtract from the payment.

notebooks=3×2.45=7.35 dollarspens=2×1.30=2.60 dollarstotal=7.35+2.60=9.95 dollarschange=20.00−9.95=10.05 dollars\begin{aligned} \text{notebooks}&=3\times2.45=7.35\text{ dollars}\\ \text{pens}&=2\times1.30=2.60\text{ dollars}\\ \text{total}&=7.35+2.60=9.95\text{ dollars}\\ \text{change}&=20.00-9.95=10.05\text{ dollars} \end{aligned}

Answer. $10.05 change.

Check. 9.95+10.05=20.009.95+10.05=20.00. The cost is just below 10,sothechangeshouldbejustabove10, so the change should be just above 10.

The next quantity is a measured length, so it need not be a whole number.

Worked example 2: a cost per metre

Question. Ribbon costs 4.60permetre.Calculatethechangefrom4.60 per metre. Calculate the change from 20 when buying 2.75 m2.75\,\mathrm{m}.

Plan. Multiply the price per metre by the length, then find the change.

cost=4.60×2.75=12.65 dollarschange=20.00−12.65=7.35 dollars\begin{aligned} \text{cost}&=4.60\times2.75=12.65\text{ dollars}\\ \text{change}&=20.00-12.65=7.35\text{ dollars} \end{aligned}

Answer. $7.35 change.

Check. 12.65÷2.75=4.6012.65\div2.75=4.60, recovering the price per metre, and 12.65+7.35=20.0012.65+7.35=20.00.

When a calculation gives part of a cent, follow the stated payment rule; normally give a final money amount to the nearest cent. Keep unrounded values during the calculation.

Watch out

Write 7.30forsevendollarsandthirtycents.Thezerorecordsthehundredthsplace;7.30 for seven dollars and thirty cents. The zero records the hundredths place; 7.03 means three cents.

Calculate all the purchases before finding the change.

Exchange rates

An exchange rate is a statement about equal values, not a command to multiply every amount you see. Use the rate given in the question: here, 1=€0.921 = €0.92.

Exchange rate

An exchange rate gives the amount of one currency equivalent to an amount of another. If 1=€0.92,multiplydollarsby1 = €0.92, multiply dollars by 0.92toobtaineuros;divideeurosbyto obtain euros; divide euros by0.92$ to obtain dollars.

The unitary method explains both directions. One dollar buys €0.92, so many dollars buy that many lots of €0.92. Reversing the conversion asks how many €0.92 lots fit into the euro amount.

Worked example 3: dollars to euros

Question. Convert 250toeurosat250 to euros at 1 = €0.92. There are no fees.

Plan. Scale the euro value of one dollar by 250.

1 dollar=0.92 euros250 dollars=250×0.92=230 euros\begin{aligned} 1\text{ dollar}&=0.92\text{ euros}\\ 250\text{ dollars}&=250\times0.92=230\text{ euros} \end{aligned}

Answer. €230.

Check. 230÷0.92=250230\div0.92=250. Since each dollar gives less than one euro, the euro numeral should be smaller than 250.

The rate stays the same in the next example; only the direction changes.

Worked example 4: euros to dollars

Question. Convert €322 to dollars at 1=€0.92.Therearenofees1 = €0.92. There are no fees.

Plan. Divide by the euro amount equivalent to one dollar.

dollars=322÷0.92=350\begin{aligned} \text{dollars}&=322\div0.92\\ &=350 \end{aligned}

Answer. $350.

Check. 350×0.92=322350\times0.92=322 euros. Multiplying 322×0.92322\times0.92 would move in the wrong direction.

The operation follows the wording of the quoted rate. A different quotation, such as €1 = $1.08, gives a different multiplier direction.

Problem-solving

Write a one-unit line before calculating. Label the starting currency and the required currency, then check by converting your answer back.

Use the direction in the question rather than memorising “currency means multiply”.

Comparing currency costs

A fair comparison uses the complete cost, the same quantity and the same currency. Add postage or a fixed conversion fee exactly where the question says it is charged.

You already know

For 1=€0.92,divideaeuropriceby1 = €0.92, divide a euro price by 0.92$ to obtain dollars. Keep the full quotient until the last step.

This resolves the opening price comparison.

Worked example 5: two prices in different currencies

Question. The same bag costs 86inoneshopand€72inanother.Theexchangerateis86 in one shop and €72 in another. The exchange rate is 1 = €0.92, with no other charges. Which shop is cheaper, and by how much in dollars?

Plan. Convert the euro price to dollars, then subtract from $86.

euro shop in dollars=72÷0.92=78.260869…difference=86−78.260869…=7.739130…\begin{aligned} \text{euro shop in dollars}&=72\div0.92=78.260869\ldots\\ \text{difference}&=86-78.260869\ldots\\ &=7.739130\ldots \end{aligned}

Answer. The euro shop is cheaper by $7.74, to the nearest cent.

Check. In euros, 86is86 is 86\times0.92=79.12.Thedifferenceis€7.12,and. The difference is €7.12, and 7.12\div0.92=7.739130\ldots$ dollars.

Now an extra charge makes the advertised foreign price incomplete.

Worked example 6: include delivery before comparing

Question. A game costs 96locally,includingdelivery.Abroaditcosts€82plus€5.50delivery.At96 locally, including delivery. Abroad it costs €82 plus €5.50 delivery. At 1 = €0.92, which complete price is cheaper, and by how much in dollars? There are no other charges.

Plan. Add the euro charges, convert the total, then compare.

foreign total=82+5.50=87.50 eurosdollar equivalent=87.50÷0.92=95.108695…saving=96−95.108695…=0.891304…\begin{aligned} \text{foreign total}&=82+5.50=87.50\text{ euros}\\ \text{dollar equivalent}&=87.50\div0.92=95.108695\ldots\\ \text{saving}&=96-95.108695\ldots=0.891304\ldots \end{aligned}

Answer. The foreign shop is cheaper by $0.89, to the nearest cent.

Check. The local price is 96×0.92=88.3296\times0.92=88.32 euros. It exceeds €87.50 by €0.82, equivalent to 0.82÷0.92=0.891304…0.82\div0.92=0.891304\ldots dollars.

Context can require a different kind of rounding. If a converted budget buys 7.87.8 whole tickets, you can buy at most 7 tickets. If a minimum payment must cover a cost of 8.431,paying8.431, paying 8.43 is insufficient: at least $8.44 is needed. Distinguish “nearest cent” from “at least enough”.

Watch out

Do not compare $96 with €82 directly, or forget the €5.50 delivery. Convert complete costs into one currency and state which choice your calculation supports.

Check whether the advertised price includes every charge.

Quick Recap

  • Multiply each unit price by its quantity; add costs before finding change.
  • Let the quoted one-unit exchange rate determine the conversion direction.
  • Compare complete costs in the same currency, keeping intermediate values unrounded.
  • Round a final money amount as requested; whole purchases and minimum payments need contextual decisions.

At 1=€0.92withnofees,theopening€72priceischeaperthan1 = €0.92 with no fees, the opening €72 price is cheaper than 86 by $7.74.