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Answers to Calculations Sections 1 & 2
Here we give the answers and some workings to the questions at the end of
each of the numbers worksheets. Answers are shown in bold.
CALCULATIONS 1: ANSWERS
A) Calculations with + and x. Try these without a calculator.
1)
2)
3)
4)
5)
6)
Check your answers using a calculator, if any answers disagree it’s really good
practice to find the problem.
B) Calculations with -, +, ÷, x, brackets and powers
1)
–
2)
–
3)
– –
4) –
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5) –
6)
7)
8)
–
–
–
9)
10)
11)
12)
13)
C) Calculations to try with a calculator
1)
2)
3)
4)
5)
6)
7)
8)
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D) Calculations with word problems
1) I get three twenty pound notes out of the bank. I need to buy presents for my
three nieces. I decide to get the same for all of them, and I buy them each three
packs of pens, and 4 colouring books. Use the letter P to mean pens and B to
mean books and write an expression for the total money you have left after
buying the presents.
ANSWER:
3 twenty pound notes = 3x20
Each niece gets 3 packs pens + 4 colouring books = 3P+4B
Three nieces = 3x(3P+4B)
Money I have left is 3x20 – 3x(3P+4B)
2) Using the answer to the first question calculate how much money you have
left by substituting the cost of pens which are £1.00 per pack and the books are
£2.00 each. Try to show each line of your workings and check your answer
using your calculator.
ANSWER:
If P=£1.00 and B=£2.00, then
3x20 – 3x(3x1.00 +4x2.00) = 60 – 3(3+8) = 60 – 3x11 =60 – 33 = 27
So I have £27 left
3) A family hire a holiday villa for two weeks at £100 per night. Then they hire
bikes for five people. The bikes are £10 a day and they hire them for three days.
They then hire two jet skis for a week which costs £80 each but they get a 15%
discount. Write the calculation and then calculate how much they spent.
ANSWER:
Cost of villa = 2 weeks (7 days each) at 100 for a day = 2x7x100
Cost of bikes = 5 people for 3 days at 10 a day = 5x3x10
Cost of jet-skis = 2 jet skis at 80 with reduction of 15% = 2x80x085
Total = 2x7x100+5x3x10 + 2x80x.85
Using a calculator this gives 1710.85
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4) A holiday caravan is available to rent throughout the year. It is booked for 13
weeks during the summer and 12 weeks during the winter season. Between
these dates is booked for 7 short breaks of three nights. Write the calculation
showing what percentage of the 365 days of the year the caravan is occupied.
ANSWER:
5) A patient is to receive 180 mg of a drug over four days. He is to take the
medication as tablets three times a day. Show how you would calculate the
number of mg the patient should take each time he takes his medication.
ANSWER:
6) In the above calculation the tablets are only available as 5mg tablets. How
many tablets should the patient take each time?
ANSWER
:
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7) There are 1,000 millilitres in a litre and 284 millilitres in a pint. If there are 18.2
grams of fat in one litre of milk, show how you would calculate the numbers of
grams of fat in a pint of milk?
ANSWER:
Now divided everything by 1000 to find out about 1 millilitre of milk
Now multiply everything by 284 to find out about 284ml which is one pint
8) The gear ratio in a car relates the number of teeth on the smaller gear to the
number of teeth on the larger gear. The ratio is 1:5 means the larger gear has 5
times more teeth than the smaller gear and so the smaller gear rotates five
times each time the larger one rotates once. The gear ratio on the 6 gear of an
Enzo Ferrari is 0.76:1 show how to calculate the number of times the smaller
gear rotates if the larger one rotates 286 times?
ANSWER: Gear ratio is 0.76 : 1
With any ratio we can multiply or divide by any number as long as we do the
same to both sides. If we divide both sides by 0.76 we will get the ratio
So the larger gear has 1.32 times the number of teeth on the smaller gear. This
means the smaller gear rotates 1.32 times for each rotation of the large gear, so
Now multiplying both sides by 286 we get
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CALCULATIONS 2: ANSWERS
A) Rounding including decimal places and significant figures
1) round 1.38972 to 1 d.p. = 1
2) round 14.90012 to 6 s.f. = 14.9001
3) round 0.056443 to 2 s.f. = 0.056
4) round 0.01507 to 2 d.p. = 0.015
5) round 500,419 to 3 s.f.= 500,000
6) round 0.099501 to 3 d.p. = 0.0995
7) round 10101 to 4 s.f. = 10100
8) round 0.992 to 1 d.p. =1.0
B) Write the following numbers in scientific notation
1)
2)
3)
4)
5)
6)
7)
8)
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C) Write the following numbers as one number in decimal format
1)
2)
3)
4)
5)
6)
= 1,200
7)
8)
D) Carry out the following calculations using your calculator
Answers given to 3 s.f.
1)
2)
3)
4)
5)
6)
7)
8)
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E) General word problems involving calculations, indices and rounding
1) The cost of a second hand Skoda car is £5975. What is this amount to the
nearest 10, to the nearest 100 and to the nearest 1,000?
ANSWER:
To the nearest 10 the cost is £5980
To the nearest 100 the cost is £6000
To the nearest 1,000 the cost is £6000
2) The GDP (Gross Domestic Product) is the market value of all final goods and
services from a country in one year. In millions of US Dollars the GDP of the UK
is 2,258,565 and the GDP of Japan is 5,390,897. Using the exchange rate of 1 US
Dollar = 0.6430 UK pounds, give both these numbers in pounds sterling in
scientific notation to 3 significant figures.
ANSWER:
The same method can be applied to calculate GDP of Japan
3) In Berlin in 2009 the 100m world record was broken by Usain Bolt. His time
was 9.58 seconds. The beat the previous world record of 9.69 seconds was
help by Tyson Gay. How much faster was Usain than Tyson and write this
number in scientific notation.
ANSWER:
Usain speed was smaller than Tyson by
–
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4) Most bacteria species are spherical, and have a radius of about a
micrometer. We can write 1 micrometer in scientific notation as
volume of a sphere can be calculate from the formula Volume =
the symbol r = radius, and
. If the
, where
= 3.14, calculate the volume of a single bacteria in
and give your answer to 3 s.f in scientific notation
ANSWER:
Using a calculator we can type in the whole expression to give
Rounding this to 3 s.f gives
This is already in scientific notation since there is only one number displayed
before the decimal point. So
5) For certain drugs the dosage for children will depend on their weight and
their temperature. For a fever less than
weight of the child. Above
the dose is 5mg per kilogram of
the dose is 10mg per kilogram of weight of the
child. The dose should be taken every 8 hours. If a child weighs 11kg and has a
temperature of
ANSWER:
how many milligrams of the drug do they take in one day.
The child has temperature
which is lower than
so
they need to take 5mg per kilogram of weight.
The child weighs 11 kg so has to take 11 x 5mg of dose = 55mg dose.
The dose is taken every 8 hours. If there are 24 hours in one day, then the child
needs to take the medicine 24/8 = 3 times a day.
The total amount of drug taken in one day is 3 x 55 = 165mg
www.mathsupport.wordpress.com Jackie Grant, Birkbeck College, 2011
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