3 Checking your answers
3.1 Have I done the right calculation?
Once you have done a calculation, with or without the aid of a calculator, it is important that you pause for a moment to check your calculation.
You need to ask yourself some questions.
Have I done the right calculation in the right order?
Have I given due consideration to units of measurement?
Is my answer reasonable?
Did I make a rough estimate to act as a check?
Your calculation will probably involve a mixture of operations, like addition, subtraction, multiplication and division. You should check that you have used the right operations in the correct order.
Example 8
Suppose you are one of five people going out for a meal and sharing the total bill. Your friend Val has done the accounts and shows you her calculation to check. Is she correct?
| £ | |
| Float from last outing | + 0.40 |
| Discount voucher for restaurant | + 5.00 |
| Contribution from Ali (who left early) | + 8.00 |
| Food | − 36.98 |
| Drinks beforehand | − 5.10 |
| Taxi | − 3.50 |
| Tip | − 3.00 |
| Total | − 35.18 |
| Share among the remaining four of us | ÷ 4 |
| − 8.795 | |
| Round up to nearest 10p | − 8.80 |
| Everybody owes £8.80. |
Answer
Yes, she is correct.
Note that Val has used positive numbers to represent money in hand and negative numbers to represent debts or payments due, but she could have done the reverse. Sharing among four people, she has used division by four. It is important that the total was calculated before the division by four.
Example 9
(a) Suppose somebody in the party queries the fact that Ali paid 80p less than everybody else, saying that everybody should pay the same. Somebody else suggests the order of the calculation needs to be changed as shown. Is this correct?
| £ | |
| Float from the last outing | + 0.40 |
| Discount voucher for restaurant | + 5.00 |
| Food | − 36.98 |
| Drinks beforehand | − 5.10 |
| Taxi | − 3.50 |
| Tip | − 3.00 |
| Total | − 43.18 |
| Share among the remaining four of us | ÷ 4 |
| − 10.795 | |
| Round up to nearest £0.10 | − 10.80 |
| Everybody owes £10.80 | |
| Contribution from Ali (left early) | + 8.00 |
| Ali still owes £2.80 | − 2.80 |
(b) Someone else, Paul, says, ‘No, this is not right! Rather than redo the calculation, it would be simpler for Ali to share the 80 p which he underpaid among the rest of us, so he owes us 20p each.’ Is this a better solution?
Answer
(a) There is something wrong here! The number of people sharing is now five not four and so you need to divide by five instead of four.
| £ | |
| Float from last outing | + 0.40 |
| Discount voucher for restaurant | + 5.00 |
| Food | − 36.98 |
| Drinks beforehand | − 5.10 |
| Taxi | − 3.50 |
| Tip | − 3.00 |
| Total | − 43.18 |
| Share among all five of us | ÷ 5 |
| − 8.636 | |
| Round up to the nearest 10p | − 8.70 |
| Everybody owes £8.70 | |
| Contribution from Ali (left early) | + 8.00 |
| Ali still owes 70p | − 0.70 |
(b) Paul's solution is unfair to Ali. The result of that redistribution would be that everyone would have paid £8.80 − 20p = £8.60, except for Ali who would have paid £8 + 4 × 20p = £8.80.