Check reasonableness of calculations

Checking if an answer is reasonable means we check to see whether an answer is a good approximation or estimate to the question. This is really important because it allows us to check whether our calculations make sense.

For example, if I said $\$10$$10 was shared between $2$2 people and they both got $\$50$$50, this would NOT be a reasonable estimate as my answer ($\$50$$50) is even more money than the total at the start ($\$10$$10)!

How do we check if an answer is reasonable?

Well, one of the best things to do is to round the numbers in the question so you can do a quick mental calculation. If the given answer is close to your estimate, then it is a reasonable calculation. 

You can also put the answer into context, ask yourself does it make sense that the answer is this big, or this small?

Worked Examples

Question 1

Is $6000$6000 a reasonable estimate for $57\times11$57×11?

Think: Let's round both these numbers to the nearest ten and see if it's close to $6000$6000.

Do: If we round $57$57 to the nearest ten, it's $60$60 and if we round $11$11 to the nearest ten, it's $10$10.

So, our estimate can be rewritten as $60\times10$60×10.

$60\times10=600$60×10=600

$600$600 is way less than $6000$6000 so NO $6000$6000 is not a reasonable estimate.

Worked Examples

Question 2

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Question 5