BIRKBECK MATHS SUPPORT
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Answers to Numbers Sections 1, 2 & 3
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.
NUMBERS 1: ANSWERS
A) Adding and subtracting numbers
1) 2+3 = +5 = 5
4) –2–4 = –6
2) 2–3 = –1
5) 8–12 = –4
3) –6+7 = +1 = 1
6) –2–7 = –9
B) Multiplying and dividing whole numbers
1) 2 x 3 = 6
4) –10 ÷ –5 = –10/–5 = +2 = 2
2) 4 ÷ –2 = +4/–2 = – 4/2 = –2
5) –7 x 2 = –14
3) –4 x –2 = +8 = 8
6) 3 ÷ 6 =
C) Adding and subtracting with decimals
1) 1.0 + 0.5 = +1.5 = 1.5
4) –7.5 – 1.5 = –9.0
2) –0.5 + 2.5 = +2.0 = 2.0
5) 2.5 – 2.0 = +0.5 = 0.5
3) –3.0 + 1.5 = –1.5
6) –4.0 – 2.5 = –6.5
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D) Questions combining all types in word form
1) I buy a jacket for £15 but have a credit voucher for £7. How much do I pay?
ANSWER: Jacket costs £15 reduced by credit voucher £7 = 15 – 7= £8
I have to pay £8 in total.
2) I have a credit note for £20 and buy a skirt for £10. Do I have to pay extra or
do I get another credit note?
ANSWER: Credit note is £20 and we will use up £10 of that for a skirt.
£20-£10 = £10 is left, so therefore you get another credit note.
3) I have an overdraft of £12.50 and get charged £1.50. How much do I owe?
ANSWER: Overdraft is £12.50, this is a negative amount, so I have – £12.50. I
then get charge £1.50, which is taken away. So I can write – £12.50 – £1.50 = –
£14.00. So I now owe £14.00
4) I am £4.50 overdrawn and then spend £3.50 on my card. If I then pay £10 into
my account how much money do I have in my account?
ANSWER: So my overdraft is a negative number, then I remove £3.50, so this is
another negative number. They I pay £10, so this is positive. So I write
– £4.50 – £3.50 + £10.00 = – £7.00 + £10.00 = + £3.00 = £3.00
5) Three people agree to split the cost of lunch which is £12. How much do they
pay each?
ANSWER: The cost is £12.00, but this is divided by 3, so we write
£12.00 divided by 3 =
= 4.
So they have to pay £4 each
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NUMBERS 2: ANSWERS
A) Try to find the simplest equivalent fractions. The first one is an example
Example:
1)
6)
2)
7)
3)
8)
4)
9)
5)
10)
B) Add and subtract these fractions. Hint: do they have the same
denominator? As extra practice see if you can simplify your answer.
Example:
1)
7)
2)
8)
3)
4)
5)
9)
10)
6)
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C) Add and subtract the following fractions. Hint: how can you find common
denominator, the first one is an example. Also check to see if you can write your
answer in the simplest possible fraction
Example:
1)
2) In this question we notice that the answer can be written as an improper
fraction or a mixed fraction. Either answer is correct.
3)
4) In this question we notice that the denominators of the two fractions both go
into 8. So we can leave the first denominator as it is and change the second
one by multiplying the top and bottom by 4.
5) In this question we first convert the mixed fraction to an improper fraction.
6)
7)
8)
9)
10)
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D) Combining all types in word form. The first one is an example
Example: Eight out of ten people at the cinema bought an ice cream or popcorn. Write this number as a fraction, then simplify it into its simplest form.
1) At a wedding the bride gives half the cake to her mum and a quarter of the
cake to her sister. How much cake has she given away in total?
ANSWER: The wedding cake is one whole. The bride gives away a quarter and
a half, so the amount left is one whole take away half then take away a quarter
2) If the major shareholder owns four tenths of a company and the only other
investor owns half of the amount that the major shareholder owns, how much
of the company is not owned by these two combined?
ANSWER: There are only two people listed in this question
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3) If it takes Phil 3 days to build a brick wall and it takes Vasil 2 days to build a
wall, how much of the wall do they manage to finish in one day if they both
work together?
ANSWER:
4) Orange juice is sold in 600ml cartons, for a special promotion they offer 1/3
extra in each carton. What is the total amount in the promotional cartons?
ANSWER:
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NUMBERS 3: ANSWERS
A) Convert the following improper factions into mixed fractions
1)
4)
2)
5)
3)
6)
B) Multiplying and Dividing Fractions, try to simplify your answer too
1)
6)
2)
7)
3)
8)
4)
9)
5)
10)
C) Decimals, Percentages and Ratios
1)
2)
3)
4)
5)
6)
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7) Water is mixed with glue in the ratio 3:1. If I use 1 litre of glue, how much water do I
need? Need 3 litres of glue if 1 litre of water is used.
8) Orange juice is mixed in the ratio 1 parts juice to 4 parts water. How much water is
in 100ml of mixed juice?
The ratio is 1 part juice to 4 parts water, written as 1:4. This means there are 5
parts of total mixed juice. So every 5ml is made of 1ml juice and 4 ml water. In
100ml there is
lots of 5ml. So there are 20 lots of 1ml of juice and 20 lots
of 4ml =80ml of water. In 100ml mixed juice = 20ml juice + 80ml water.
We can write this mathematically as
9) The ratio of milk to dark chocolates is 3:4. If there are 140 chocolates in a bag, how
many are milk chocolates?
The ratio is 3:4 which means 7 parts in total. So for every 7 chocolates 3 are
milk and 4 are dark. So for 14 chocolates 6 are milk and 8 are dark. Continuing
with this process, in 140 chocolates 60 are milk and 80 are dark. We can write
this mathematically as
D) Working with indices, simplify the following
1)
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2)
3)
4)
5)
6)
7)
8)
9)
10)
E) Word Questions
1) In a restaurant each slice of cake sold is one eight of a total cake. If there are
three and a half cakes left how can you show mathematically how many slices
are left for sale?
ANSWER:
2) A suit has a price tag £100 and a shirt has a price tag £40. But there is a
special offer and everything is reduced by 15%. How much would the suit and
shirt cost with the reduction?
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ANSWER:
3) Humans produce 2 million red blood cells each second. If each blood cell
has mass of
. Show using indices the mass of blood cells produced
each second.
ANSWER:
4) Two brothers decide to share the cost of a car. One of them pays £800 and
the other one £200. Write these amounts as the simplest ratio possible.
ANSWER:
5) Jeans are sold for £30 each. The selling price is 50% more than the cost
price. What is the cost price of each pair of jeans?
ANSWER:
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6) The ratio of men to women working in a factory is 5:4. There are a total of 20
women. How many people work at the factory in total?
ANSWER:
7) A survey reports that one half of families living in a particular block of flats
have a pet. Of these people half had a fish, a quarter had a hamster and a
quarter had a dog. What fraction of families had a fish?
ANSWER:
8) A television has a mark up on the cost price of 40% and is then sold in the
sale for 10% discount. If the TV originally cost £100, how much was it sold for?
ANSWER:
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