Currency Conversions

Worked example

1. 1

   $\pounds 250\to \text{euros}$ — The question. Pounds are the side with the 1 (£1 = €1.16), so we start from that side.

2. 2

   $250\times 1.16=290\text{ euros}$ — Each pound gives 1.16 euros, so 250 pounds give 250 lots of 1.16. Multiply.

3. 3

   $290>250$ — Check the size: one pound buys more than one euro, so the euro number should be the bigger one. It is.

4. 4

   $348\text{ euros}\to \pounds$ — Now go the other way, from euros back to the side with the 1.

5. 5

   $348÷1.16=\pounds 300$ — Every 1.16 euros makes one pound, so count how many 1.16s fit in 348. Divide.

6. 6

   $300\times 1.16=348$ — Check by multiplying back. It gives the 348 euros we started with, so £300 is right.

Worked example

1. 1

   $87\text{ euros}\to \pounds$ — The prices are in different currencies, so they cannot be compared yet. Change one so both are in pounds.

2. 2

   $87÷1.16=\pounds 75$ — Euros back to pounds, so divide by the rate. Paris costs £75.

3. 3

   $\pounds 70$ — London is already in pounds, so it stays as it is.

4. 4

   $75-70=\pounds 5$ — Both prices are now in pounds, so subtract the smaller from the bigger to find the difference.

5. 5

   $\text{London, by }\pounds 5$ — London has the smaller price. The question asks where and by how much, so give both, with the £ sign.

Worked example

1. 1

   $\text{euros}\to \pounds \to \text{AED}$ — No rate links euros and AED directly, but both are given against pounds. So go through pounds.

2. 2

   $580÷1.16=\pounds 500$ — Euros back to pounds: the 1 is on the pounds side, so divide.

3. 3

   $500\times 4.6=2300\text{ AED}$ — Pounds out to AED: £1 = 4.6 AED starts from pounds, so multiply the £500 from the line before.

Worked example

1. 1

   $46÷40=1.15$ — The same bag is £40 or 46 CHF. Divide the CHF by the pounds to get the rate: CHF for one pound.

2. 2

   $\pounds 1=1.15\text{ CHF}$ — Write the rate with the 1 on the pounds side, so you can see which way to go.

3. 3

   $60\times 1.15=69\text{ CHF}$ — The coat is in pounds, the side with the 1, so multiply by the rate.

Worked example

1. 1

   $500\times 1.16=580\text{ euros}$ — Bank A has the 1 on the pounds side, so multiply.

2. 2

   $500÷0.85=588.235\dots$ — Bank B has the 1 on the euros side: each euro costs £0.85. Count how many 0.85s fit in 500, so divide.

3. 3

   $\approx 588.24\text{ euros}$ — Money uses 2 decimal places, so round to the nearest cent.

4. 4

   $588.24-580=8.24$ — Subtract to compare. Bank B gives 8.24 euros more, so Bank B is the better deal.

Worked example

1. 1

   $\pounds 1=1.16\text{ euros},\pounds 1=4.6\text{ AED}$ — Both rates start from £1, so 1.16 euros and 4.6 AED are worth the same.

2. 2

   $1.16\text{ euros}=4.6\text{ AED}$ — Write them equal to each other, because each is worth exactly £1.

3. 3

   $1\text{ euro}=\frac{4.6}{1.16}\text{ AED}$ — We want 1 euro, so divide both sides by 1.16.

4. 4

   $1\text{ euro}=3.9655\dots \approx 3.97\text{ AED}$ — Work it out. Keep the full number for any later step; round only the final answer.

5. 5

   $580\times 3.9655\dots =2300\text{ AED}$ — Check with the Through a Middle Currency card: 580 euros gave 2300 AED there too.

Worked example

1. 1

   $400\times 1.16=464\text{ euros}$ — Pounds to euros: pounds have the 1, so multiply. This is the money she takes.

2. 2

   $464-350=114\text{ euros}$ — She spends 350 euros. Both numbers are in euros, so subtract to find what is left.

3. 3

   $114÷1.16=98.2758\dots$ — Change only the euros left back to pounds. Euros back to pounds, so divide.

4. 4

   $\approx \pounds 98.28$ — Money uses 2 decimal places, so round to the nearest penny.

Worked example

1. 1

   $230\times 1.16=266.8\text{ euros}$ — Pounds to euros: multiply. This is the most he could get.

2. 2

   $260\text{ euros}$ — The bank only gives €10 notes, so round down to a multiple of 10. €270 would cost more than £230.

3. 3

   $260÷1.16=224.1379\dots$ — Find what the €260 costs in pounds: euros back to pounds, so divide.

4. 4

   $230-224.1379\dots =5.862\dots$ — Take that cost from the £230 he brought. What is left comes back as change.

5. 5

   $\approx \pounds 5.86$ — Round to the nearest penny, 2 decimal places, as the very last move.