Page 44 - Mathematics Coursebook

3.8 Estimating and approximating

When you are asked to solve a problem, as well as using an estimate or an inverse operation to check
your answer, you should present your work clearly and neatly.

When you are writing out your solution, imagine someone else is looking over your shoulder. Make
sure that when they read your work they can understand exactly what you have done and why.

Worked example 3.8C
a Madai runs in a marathon. The total distance is 26.2 miles. After 1 hour Madai has run 8.7 miles.
How much further has she got to run?
b There are 1125 portable toilets along the marathon route. They are arranged into 12 toilet blocks.
How many toilets should be in each toilet block?

a 26.2 − 8.7 = 17.5 Work out the answer and make sure you write
down the complete calculation
She has to run another 17.5 miles. Write your answer in a sentence that explains
what you have worked out. Make sure you include
the units (miles).
Check: 17.5 + 8.7 = 26.2 Use an inverse operation to check your answer.
b 1125 ÷ 12 = 93.75 Work out the answer and make sure you write
down the complete calculation.
There will be about 94 toilets in each toilet block. Write your answer in a sentence that explains
what you have worked out. Make sure your
answer is sensible.
You can’t have 93.75 toilets so choose 93 or 94
as your answer.
Check: 1000 ÷ 10 = 100 Use estimation to check your answer. 100 is close
to 94 so the answer is probably right.

) Exercise 3.8

1 Work out an estimate for each calculation.
a 69 + 47 b 81 − 38 c 72 × 49 d 63 ÷ 18 Don’t work out the accurate
e 137 + 912 f 292 − 64 g 289 × 23 h 672 ÷ 21 answer yet.
2 Work out the accurate answer for each of the parts of question 1.
Compare your estimates with your accurate answers to check your accurate answers are correct.
3 For each of these questions:
i work out an estimate of the answer
ii work out the correct answer, to one decimal place
iii compare your estimate with the accurate answer to check your answer is correct.
. ×
×
+
−
.
.
.
.
a 194 45 7 b 618 2785 c 36 54 d 85827
14 39 76 23
4 For each of these questions:
i work out the accurate answer
ii use an inverse operation to check your answer.
a 27.9 + 132.5 b 67.09 − 39.52 c 7 × 13.8 d 46.29 ÷ 3

3 Place value, ordering and rounding 43