Unit 1 section 2.5 checking
your answers
24 September 2015
23:53
If your answer is very different
from your estimate, then you know to look for a mistake. The mistake could be
in your working, or it might have occurred then you use your calculator.
If you were totting up a weekly
shopping bill for a family of 4 then you might expect an answer between £100
and £200.
To estimate an answer is to round
all the numbers in the calculation- perhaps 21 significant figure, or to nearby
numbers that are easy to work with and carry out the calculation with the
rounded numbers.
Should be possible to this fairly
quickly, either in your head or on a piece of paper. But it will help you to
spot mistakes that happen when you use your calculator.
Example
6 estimating an answer
the road distances in kilometres
between 3 places in Scotland. Suppose you are planning around trip in which you
start at Edinburgh, visit Perth and Glasgow, and returned to Edinburgh, in a
minibus whose fuel consumption is 12 km per litre of fuel.
(A) estimate the amount of fuel
needed for the trip.
(B) use your calculator to work
out the amount of fuel needed, to the nearest litre.
Solution
(A) Round the numbers to one
significant figure.
An
estimate for the total distance km is
70+100+80=
250
the minibus
can travel around 10 km on 1 litre of fuel, so the amount of fuel needed in
litres is approximately
250÷ 10= 25. So an
estimate for the amount of fuel needed is 25 litres.
(B) the amount of fuel needed, in
litres is
(69+95+83)÷12= 21 (to the nearest
whole number).
So the amount of fuel needed is
21 litres, to the nearest litre. The answer is fairly close to the estimate so
is no evidence of a mistake.
Checking
for calculator mistakes
The 1st thing to check
is whether you have mistyped something. If the calculation is displayed on your
calculator screen, and you should check the numbers and operations carefully,
and edit the calculation to correct any errors.
The next thing to check is
whether the calculation you entered was the correct one. You need to think
about the BIDMAS rules. For example, if you have intended to carry out the
calculation in example 6b and had typed 69+95+82÷ 12, then you would have
obtained the wrong answer, because your calculator would do the division before
the addition. You need to include the brackets, as in the solution above.
If you still cannot find a
mistake, then you can try breaking the calculation into simpler steps. You
could 1st work out the total distance, which is 247 km and then
divide 247 by 12 to find the amount of fuel in litres.
Checking
your answer is when using your calculator.
v Have you entered the calculation
correctly?
v Have you used brackets were
needed?
v If the answer reasonable? Think
about the context or work out an estimate.
Activity
11 sporting errors in a calculation
(A) Estimate the number of days
needed.
(B) A student typed the
calculation shown below into a calculator, and concluded that the number of
days needed is 12 try to identify the 2 mistakes.
(C) Use your calculator to find
how many days are needed and round your answer appropriately.
Answer
(A) Each jewellery box takes
about 4 hours to make and decorate. The working day is 8 hours so about 2
jewellery boxes can be completed in a working day. So it would take about 24
days to complete 48 jewellery boxes.
(B) The students 1st
mistake was to forget to include brackets around 2.30+1.45’. So the calculator
will 1st multiply 1.4 5 x 48 then divide by 7.5, and then add 2.30,
which is not what the student intended. The students at the mistake was to
assume that if you add 2 hours and 30 minutes to 1 hour and 45 minutes then the
total number of hours is 2.30+1.45. This is not correct since 2 hours and 30
minutes is 2.5 hours, not 2.30 hours, and 1 hour and 45 minutes is 1.75 hours
not 1.45 hours.
(C) The time needed to make and
decorate the jewellery box is 2 hours and 30 minutes +1 hour and 45 minutes
equals 4 hours and 15 minutes= 4.25 hours. The number has been rounded up
because all 48 boxes must be finished. So 28 days are needed.
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