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t h o m a s w h i t h a m . p b w o r k s . c o m
Year 8
Number Mathematics
S J Cooper
Thomas Whitham Sixth Form
Number (1) Addition and Subtraction of numbers
Work out each of the following:
1. 243 + 648
2. 377 + 6012
3. 1870 + 587
4. 791 - 658
5. 5984 + 258 + 7842
6. 6078 - 3824
7. 11457 - 8788
8. 12000 - 9782
9. 4581 + 3874 + 34
10. 273 – 157
11. 8117 + 452 + 929
12. 231 + 382 + 926
13. 17083 - 12263
14. 746 – 609
15. 4560 - 999
16. 12747 + 28585
17. 5634 - 894
18. 3000 – 1576
19. Add together nine thousand eight hundred and sixty two, and forty eight thousand six hundred
and one.
20. At a general election 8462 voted Conservative, 14 621 voted Labour and 3405 voted Liberal.
(a) How many votes were cast altogether?
(b) How many more people voted for Labour rather than Conservative?
21. Subtract eight hundred and forty three from one thousand six hundred and nine.
22. Work out five thousand six hundred and forty minus three thousand eight hundred and forty
one.
23. In Nelson on Wednesday 73 486 were watching Coronation Street on television. When the
adverts can on 21 968 people switched off. How many were watching the adverts?
24. In a game of darts Simon scored 133 with his first three darts. If he had scored 82 with his first
two darts, what score did he achieve with his third dart?
25. In the annual Christmas fair Albian High School raised £1 846 and Blacko High School raised
£1 297
(a) What was the difference between the two amounts?
Both schools decide to donate the monies raised to a local charity.
(b) How much will the charity receive from the two schools altogether?
26. Look at this set of numbers and then subtract
(a) the smallest from the largest
(b) the sum of the even numbers from the sum of the odd numbers
(c) each of the numbers from 10 000.
4 794
999
7 843
8 005
5 076
Number (2) Multiplication 1. Work out each of the following multiplication:
(a) 143 x 7 (b) 645 x 5 (c) 1024 x 4 (d) 294 x 9
(e) 345 x 23 (f) 174 x 52 (g) 803 x 64 (h) 358 x 17
(i) 927 x 42 (j) 257 x 78 (k) 3217 x 36 (l) 793 x 98
2. The chairs in the assembly hall are arranged so that there are 32 seats per row. If there are 24
rows, how many seats are there in the hall?
3. In a soccer tournament there are thirty-eight teams, and each team has a total of eighteen
players. How many players are there in the tournament?
4. Calculate each of the following:
a) 15 x 15
b) 18 x 26
c) 19 x 33
d) 45 x 21
e) 61 x 43
f) 47 x 58
g) 92 x 36
h) 107 x 25
i) 341 x 28
j) 25 x 25
k) 162
l) 312
5. A local shop has a delivery of 42 cases of cola. If each case contains 24 cans of cola, how
many cans were delivered?
6. Multiply eight hundred and twenty five by thirty seven.
7. Multiply three hundred and seven by forty six.
8. The average number of pupils in each form at Castlerock High School is 27. If there are 13
forms in each of the five year groups how many pupils are there in
(a) each year (b) the whole school ?
9. The mathematics department buys 164 pens at 23p each, 287 pencils at 16p each and 54
protractors at 37p each.
(a) What is the total cost for (i) pens (ii) pencil (iii) protractors?
(b) What is the total cost for all these items together?
Number (3) Division 1. Work out each of the following:
(a) 390 5
(b) 119 7
(c) 144 3
(d) 268 4
(e) 216 9
(f) 756 7
(g) 992 8
(h) 2562 6
(i) 1084 4
(j) 3480 4
(k) 3054 6
(l) 1620 5
2. Calculate each of the following, leaving your answer with a remainder:
(a) 283 4 (b) 847 3 (c) 1024 7 (d) 2938 6
(e) 134 5 (f) 407 8 (g) 10245 9 (h) 1383 12
(i) 2078 8 (j) 3467 9 (k) 8171 6 (l) 10724 7
3. Divide three thousand four hundred and sixty four by six.
4. Calculate each of the following, leaving your answer with a remainder.
(a) 125 12
(b) 1820 14
(c) 210 18
(d) 3510 23
(e) 5424 22
(f) 7266 32
(g) 867 25
(h) 9076 38
(i) 12427 47
(j) 17500 54
5. Divide eight thousand six hundred and twenty nine by thirty-one.
6. The school bought 9 textbooks for £117. What was the price for each textbook?
7. If a coach can hold 54 pupils, how many coaches are required to
take 741 pupils to Alton Towers for the day?
8. At Coalclough High school there are 46 classes with the same number of students in each
class. If there is a total of 1656 students in the school, how many students are there in each
class?
9. Asda has 1896 eggs, which are to be placed into cartons
containing 24 eggs each. How many cartons will he
require?
Number (4) Estimations 1. By rounding off each number below to a suitable degree of accuracy find an approximate
answer to the following:
a) 3824
b) 4178
c) 13102
d) 33271
e) 47549
f) 98314
g) 9811
h) 4.316.27
i) 8.759.82
j) 1027718
2. By rounding off each number below to a suitable degree of accuracy find an approximate
answer to the following:
a) 17544
b) 461334
c) 783666
d) 981176
e) 53477
f) 371036
g) 641792
h) 11473
i) 413157
j) 1026632
3. By rounding off each number below to a suitable degree of accuracy find an approximate
answer to the following:
a)
23
6573
b)
17
5448
c)
49
17164
d)
68
51403
e)
9
1672
f)
66
34106
g) 41
2319
h) 59
4891
i) 147
2614
j) 449
8751
4. Abdul is asked to estimate 42.4 x 57.1. He gives the answer 2400.
Explain how Abdul arrived at his answer.
5. Sara gave 1500 as her estimate to the calculation 52.1 x 28.7.
Explain how Sara arrived at her answer.
6. In calculating 381 47, Kamran gave the answer as approximately 8. Show how Kamran
arrived at his answer.
7. Give the approximate solution to the calculation 8145 91.
8. In the year 2001 the population of the United Kingdom was 59.3 million. If approximately one
third travelled abroad for their summer holidays approximately how many people stayed in the
United Kingdom for the summer.
9. Jackie estimated her checkout bill at the local supermarket by rounding off to the nearest £1.
(a) Copy and complete the table below giving her approximate total for the bill.
Shopping Item Actual cost Estimated cost
to nearest £1
Bread 76p
Washing powder £4.76
Milk £2.38
CD £11.99
Biscuits 89p
(b) Work out what her total estimated bill would have been if she had rounded off to the
nearest 50 pence instead.
Number (5) Index notation 1. Work out the value for each of the following:
a) 27
b) 35
c) 38
d) 46
e) 49
f) 55
g) 83
h) 62
i) 82
2. Express each of the following in index notation:
a) 9 9 9
b) 7 7 7 7 7
c) 3 3 3 3 3 3
d) 8 8 8 8 8 8 8
e) 5 5
f) 7 7 7 7 7
g) 2 2 2 2 2
h) 4 4 4 4 4 4 4
i) 10 10 10 10
3. Express each of the following in index notation:
a) 4 43 5
b) 5 57 3
c) 2 28 7
d) 6 65 3
e) 9 97 7
f) 3 33 4
g) 7 7 710 6
h) 10 10 102 3 8
i) 5 5 55 3 3
4. Express each of the following in index form:
a) 743 5858
b) 5324 6262
c) 5623 4343
d) 2565 7272
e) 8762 5335
f) 5837 810810
g) 4244 339
h) 6436 9797
i) 6868 885
5. Express each of the following in index form:
a) 4
4
6
2
b) 8
8
9
7
c) 6
6
12
5
d) 10
10
7
6
e) 5
5
10
4
f) 7 6
7 6
6 8
4 6
g) 3 4
4 3
13 8
3 9
h) 2 9
9 2
21 11
5 15
6. Find the value of each lettered index to make the statement correct:
a) 466
6
a
b) 3
52
2
2
b
a) 7
77
83
c
b) 5
55
158
d
a) 6 6
66
3
4
7e
b) 3 3
33
7
6
2
f
7. Find the value of each lettered index to make the following statements correct:
a) 94 333 a
b) 76 444 b
c) 6 6 611c
d) 5 5 5 54 8d d
e) 8 8 8 83 11 e e
f) 2 2 2 24 f f f
g) 7 7 7 7 73 10 g g
h) 8 8 82 12h h
i) 3 3 34 3 7i
Number (6) Multiples & factors 1. Write down the first five multiples of
(a) 7 (b) 5 (c) 8 (d) 12 (e) 9 (f) 15
2. From the set of numbers {2, 3, 5, 6, 8, 10, 12, 15, 16, 18, 20, 21} write down those numbers
which are:
(a) multiples of 2 (b) multiples of 4 (c) multiples of 3
(d) multiples of 6 (e) multiples of 8
3. What is the smallest number which divides exactly by both
(a) 2 and 3?
(b) 4 and 6?
(c) 2 and 5?
4. What is the largest number which will divide into both
(a) 10 and 15?
(b) 24 and 32?
(c) 18 and 42?
5. Find the lowest common multiple of:
(a) 3 and 4
(b) 4 and 8
(c) 2 and 5
(d) 6 and 8
(e) 6 and 9
(f) 7 and 10
(g) 12 and 20
(h) 4 and 6
(i) 3 and 15
(j) 2, 4 and 10
6. Is 2 a factor of:
(a) 4 (b) 7 (c) 16 (d) 31 (e) 134?
7. How do you know that two is a factor of the number 15574358?
8. Is 5 a factor of:
(a) 4 (b) 25 (c) 40 (d) 21 (e) 190?
9. How do you know that five is a factor of the number 187455?
10. List the factors of:
(a) 8 (b) 14 (c) 36 (d) 16 (e) 26 (f) 28 (g) 120
11. (i) Is three a factor of:
(a) 51 (b) 38 (c) 75 (d) 102 (e) 154 (f) 471?
(ii) In each of the above add the digits together and test whether your answers are also divisible
by 3.
Number (7) Prime Numbers 1. Write down the first six prime numbers.
2. Write down a list of all prime numbers between 10 and 30.
3. In the set of numbers {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}, which members are prime numbers?
4. In the set {30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41}, which numbers are prime?
5. Express the following numbers as products of their prime factors, using index form where
possible.
(a) 12
(b) 36
(c) 24
(d) 34
(e) 32
(f) 60
(g) 108
(h) 40
(i) 110
(j) 200
(k) 324
(l) 1225
(m) 2000
(n) 432
(o) 968
Number (8) Directed Number 1. Every morning Gerald notes the temperature on the
thermometer attached to his shed. These are shown in the
diagram drawn opposite.
What is the difference between the temperatures on
a) Monday and Friday
b) Tuesday and Wednesday
c) Monday and Thursday
d) Thursday and Friday
e) Tuesday and Saturday?
2. When I got up this morning the temperature was – 4 C. By midday the temperature had risen
by 7C. What was the temperature at midday?
3. For each of the following fill in the missing spaces
Original Temperature Change New Temperature
4C
8C
3C
5C
–9C
–3C
–6C
2C
–6C
–11C
–7C
+3C
+6C
–7C
–4C
–3C
+2C
–1C
2C
–3C
4C
–5C
4. On Tuesday morning the temperature was – 2C and by 11 o’clock the temperature had risen
to 4C. By how many degrees had the temperature risen?
0
–1
–2
–3
–4
1
2
3
4
5
C
Monday
Thursday
Tuesday
Friday
Wednesday
Saturday
5. The temperature outside the classroom is given as – 3C and yet inside the classroom it is
said to be 15C. What is the difference in the temperatures?
6. Outside Gerald’s shed the temperature was recorded as –3 C yet inside the temperature is
8 C. What is the difference in the temperature from outside to inside?
7. The temperature this morning is 3 C but the weather forecast has predicted that by midnight
the temperature will have fallen by 12C. What is the predicted temperature for midnight?
8. Mr Robinson had £50 in his bank account on the 15th of August yet on the 16
th of August he
withdrew £200.
What is Mr Robinson’s balance on the 16th of August?
9. Before my pay cheque was paid in this week the balance of my account read as –£25. (i.e. £25
overdrawn). If my pay packet for the week was £100, how much will I now have in my bank
account?
10. When the temperature in Britain is –2 C the temperature in Canada was –14 C.
What is the difference in these temperatures?
Number (9) Directed Number
1. Work out the following
a) 2 – 6
b) 1 – 4
c) 4 – 5
d) 5 –3
e) 4 – 2
f) 4 – 7
g) 3 – 12
h) 4 – 4
i) 8 + 2
j) –1 + 5
k) –2 + 7
l) –4 + 2
m) –7 + 6
n) –3 + 3
o) –1 + 9
p) –9 + 7
q) –1 – 3
r) –6 – 4
s) –3 – 8
t) –1 – 5
u) 2 + 7
v) –2 – 7
w) – 5 – 5
x) –12 + 4
y) –20 + 13
z) –16 – 4
2. Work out each of the following:
a) 7 minus 4
b) 12 take away 20
c) 3 minus 8
d) 4 minus –2
e) 6 take away –8
f) –8 minus 6
g) –5 take away –7
h) –1 minus –3
i) –15 take away 13
j) –9 minus –4
3. Work out the following:
a) 12 x 5
b) 8 x 8
c) –6 x –3
d) 5 x –4
e) 7 x –9
f) –6 x 4
g) –12 x –11
h) –7 x 3
i) –8 x –2
j) 9 x –5
k) –12 x 4
l) –12 x –9
m) 15 x –5
n) –13 x –13
o) 14 x –33
p) –25 x 22
q) 42 x –36
4. Work out the following:
a) 24 4
b) 15 3
c) –12 4
d) –28 –4
e) 64 –8
f) –48 –6
g) –60 12
h) 36 –3
i) 72 –9
j) –70 –5
k) –54 2
l) –42 3
m) 56 –7
n) –21 –3
o) 102 6
p) –120 –5
q) 432 –9
Number (10) Expressing as a fraction 1. Express the following in their simplest form:
a 8
16
b 9
27
c 14
16
d 24
36
e 17
50
f 34
36
g 15
65
h 6
51
i 27
54
j 15
20
k 48
108
l 45
144
m 40
64
n 76
92
2. What fraction of the title “The wind in the willows” is made up of W’s?
3. My mother buys some fruit, of which 8 are apples, 7 are oranges and 5 are bananas. What
fraction of the fruit is made up of (a) oranges (b) apples ?
4. Janet spent £104 on Saturday, of which £24 went on food, £16 on a CD and the rest on clothes.
What fraction of her money did she spend on (a) food (b) clothes?
5. A farmer has 20 cows, 35 sheep, 12 pigs and 8 geese.
What fraction of his animals are (a) sheep (b) geese?
6. The time Alan spent on his homework last week was as follows:
2h on science 2 12
h on English 1 12
h on geography 1h on Religious Studies
3h on Maths 12
h on German 1 12
h on History
What fraction of his time was spent on (a) Maths (b) Science (c) German?
7. On a plane to Spain there are 216 men, 144 women and 120 children.
What fraction of the total number of passengers are (a) children (b) men?
8. The BBC viewing on one day spent 3 hours on news programmes, 6 hours on films, 4 hours on
documentaries, 9 hours on entertainment and 2 hours on other programmes.
What fraction of the day’s viewing was on (a) films (b) documentaries?
9. At a school disco 12 students drank lemonade, 26 drank coke, 6 drank orange-squash and 4
drank water. What fraction of the students drank (a) coke (b) water?
10. On a journey to London, a distance of 240 miles, 160 miles is by motorway and the rest is by
ordinary roads. What fraction do motorways take up?
Number (11) Fractions of a quantity [Without a calculator]
1. Find
a 1
3 of 18 b
1
3 of 24 c
1
4 of 24 d
1
5 of 30 e
1
6 of 30
f 1
7 of 21 g
1
8 of 64 h
1
9 of 54 i
1
10 of 120 j
1
12 of 48
2. Work out each of the following
a. 5
2 of 45
b. 7
4 of 63
c. 12
5 of 108
d. 7
3 of 98
e. 9
4 of 180
f. 11
6 of 88
g. 3
2 of 171
h. 5
2 of 325
i. 8
7 of 392
j. 13
6 of 364
3. Find
a 3
5 of 20 metres b
2
3 of 18 metres c
5
9 of £45 d
7
8 of 56 cm
e 7
16 of 48 litres f
3
7 of 84 miles g
2
7 of 1 week h
3
5 of £1
i 5
8 of 1 day j
4
5 of one year. [note: 1 day = 24 hours. 1 year = 365 days]
4. James bought a roll of paper 36 metres long and used 2
9 of it to rap his brother birthday
present.
(a) What length of paper did James use for his brothers present?
(b) What length of paper did James have left?
5. The P.T.F.A raised £1340 at the Christmas fair, of which one tenth went on expenses. A charity
was given four fifths and the rest went in the bank. What amount went
(a) On expenses (b) to charity (c) in the bank account?
6. Over a period of time a car industry manufactured 1080 cars. 7
15 of the cars were saloons,
4
9
were hatchbacks and the rest were estates.
How many were (a) Hatchbacks (b) estates?
7. In a small village there are 756 children.4
7 of these are girls, and of these girls
1
6 go to school.
Of the girls who go to school, 5
9 go to secondary school.
(a) How many girls are there? (b) How many girls go to school?
(c) How many girls go to secondary school?
8. A house agent receives commission of 1
250 of the sale of a house. Find his commission on a
sale of £ 75 000
9. A box of chocolates has a mass of 250 grams. 3
20 of this mass is packaging.
What mass is (a) packaging (b) chocolates?
10.A farmer grows potatoes on 3
7 of his land and silage on
2
5 of his land.
If he has 315 hectares, on how much of the land does he grow (a) potato (b) silage?
11.A carpet covers 2
3 of the lounge floor, which has a total area of 15 square metres. Find
(a) The area covered by carpet (b) the area uncovered?
12. 3250 candidates sat a Mathematics examination. 17
25 of them passes with distinction and
3
10
of them failed. How many (a) failed (b) obtained a distinction?
13. 2
9 of the computer chips made by a certain machine are found to be faulty. If a total of 243
chips are made in one hour, how many are likely to be faulty?
14. Paula earns £28 from a Saturday job. If her wage is increased by 1
4 how much will she earn
now?
15. The Adams family bought a car for £8100 and sold it three years later losing 4
9 the original
price. How much did they lose?
16. An airline gives a reduction of 2
7 on fares for children aged 2 to 12. Find the child fare when
an adult fare is £343.
Number (12) Addition of fractions
1. Workout each of the following
a) 16
3
4
3
b) 5
3
3
2
c) 8
3
24
5
d) 30
7
6
1
e) 4
3
9
4
f) 9
5
36
7
g) 8
52
4
31
h) 7
4
2
13
i) 3
12
12
56
j) 3
21
7
32
k) 3
12
11
3
l) 9
41
27
4
m) 5
14
4
15
n) 15
11
5
3
o) 4
33
3
22
p) 3
2
8
1
q) 5
41
9
23
r) 35
17
7
5
s) 9
43
8
52
t) 4
3
3
2
2
1
2. On Saturday Andrew spent 5
3 of his pocket money and on Sunday he spent
12
1
What fraction of his pocket money did Andrew (a) spend (b) have left over ?
3. Work out the perimeters for each of the following shapes.
(a) (b)
4. On a recent shopping trip Mrs Smith bought 4
15 kg of potatoes,
6
51 kg of carrots and
3
22 kg of
cabbage. What is the total weight of these items ?
5
23
7
31
12
51
6
52
8
33
Number (13) Subtraction of fractions
1. Workout each of the following
a) 16
3
4
3
b) 5
3
3
2
c) 14
3
7
4
d) 5
43
3
27
e) 9
5
8
7
f) 3
22
8
75
g) 12
7
2
11
h) 5
34
4
18
i) 6
53
10
76
j) 5
21
3
13
k) 18
7
6
5
l) 15
4
9
8
m) 24
171
8
32
n) 7
52
2
14
o) 15
73
10
18
p) 5
41
13
64
q) 5
45
4
311
r) 11
72
9
27
s) 14
11
7
13
t) 18
51
6
59
2. A cake has an initial weight of 8
37 kg. Sarah eats a piece which weighs
6
51 kg. Work out the
weight of the cake remaining.
3. A piece of ribbon has a length of 5
33 metre. If
8
31 metres is cut off, what is the length of ribbon
left over ?
4. A garden has a lawn of area 12
1115 square metres. If a vegatable patch of area
4
36 square
metres is to be cut out of this lawn, what area of lawn left ?
Number (14) Multiplication & Division 1. Work out each of the following:
a) 5
2
3
2
b) 6
5
7
1
c) 7
3
4
3
d) 5
3
9
4
e) 14
3
11
6
f) 20
7
9
8
g) 20
11
22
5
h) 13
6
10
7
i) 2
11
9
51
j) 5
44
8
13
k) 4
15
7
22
l) 5
22
6
14
m) 9
82
4
3
n) 13
91
11
42
o) 8
71
9
4
p) 15
61
5
41
q) 21
51
4
36
r) 33
151
64
63
s) 15
113
7
33
t) 9
7
9
7
2. Simplify each of the following:
a) 4
3
5
2
b) 8
5
11
6
c) 5
3
9
7
d) 13
9
7
3
e) 12
7
8
5
f) 25
16
15
8
g) 21
20
9
4
h) 5
4
45
32
i) 24
16
39
32
j) 44
21
33
28
k) 21
15
9
41
l) 14
31
21
131
m) 3
11
26
9
n) 36
35
14
33
o) 29
18
2
11
p) 8
14
2
17
q) 25
31
7
57
r) 7
13
3
22
s) 3
26
9
62
t) 14
111
6
55
Number (15) Addition & Subtraction of decimals
1. Work out the following:
a) 24.7 + 18.27 + 5.4
b) 13.78 + 24.3 + 6.98
c) 19.78 – 4.37
d) 54.19 – 32.81
e) 45.09 + 13.185
f) 109.3 – 45.99
g) 37.66 –15.67
h) 254.3 – 113.98
i) 58.4 +78 + 19.77
j) 97.203 – 45.73
2. What is the difference between 67.4 and 42.27?
3. What is the sum of the numbers 6.56, 7.14 and 12.8?
4. Joanne buys four items costing £3.98, £4.15 , £6.59 and £11.98. What is the total cost for
these four items?
5. Three buildings have heights of 324.13 metres, 471.3 metres and 354.5
metres. What is the difference in height between the tallest building and
the shortest building?
6. The heights of three boys are 1.54 m, 1.6 m and 1.78 m. What is their total
combined height?
7. A plant bought at B&Q had a height of 9.4 cm. During the summer months the plant flourished
and increased its height to 24.65 cm. By how much did the plant increase its height over the
summer months?
8. During the first eight weeks a new born child, Chloe, increased her weight
from
3.19 kg to 5.72 kg.
By how much has Chloe’s weight increased?
9. Four weights are laid on a table. The weights are individually labelled as 3.88 kg , 0.75 kg , 0.6
kg and 3.142 kg. What is the total weight on the table?
10. The capacities of two containers are 2.76 litres and 5.4 litres. What is the
Difference in capacity between the two containers?
Number (16) Multiplication of Decimal 1. Work out each of the following:
(a) (b) (c) (d) (e)
(f) (g) (h) (i) (j)
2. Work out each of the following:
(a) (b) (c) (d) (e)
(f) (g) (h) (i) (j)
3. Multiply together each of the following:
a) 4.51 by 23
b) 8.44 by 96
c) 12.4 by 15
d) 6.03 by 97
e) 4.102 by 18
f) 12.77 by 33
g) 11.7 by 25
h) 6.05 by 51
i) 12.46 by 43
j) 105.3 by 82
4. The price of a CD is £11.49 if bought through the Internet.
What is the price of thirteen CD’s bought through the Internet?
5. Work out each of the following:
a) 5.06 x 10
b) 4.65 x 100
c) 1.37 x 1000
d) 0.204 x 10
e) 7.98 x 1000
f) 25.3 x 1000
g) 6.7 x 100
h) 0.098 x 10
i) 0.998 x 100
j) 4.108 x 10
6. Given that 1cm = 10mm convert the following cm into mm.
a) 5cm b) 7.6cm c) 0.07cm d) 12.7cm e) 56.16cm
7.38
x 5
15.3
x 7
2.14
x 2
30.7
x 3
21.03
x 4
3.142
x 9
0.761
x 4
3.67
x 7
109.5
x 9
10.607
x 5
3.88
x 17
8.2
x 24
7.14
x 43
6.34
x 71
62.3
x 62
3.142
x 72
0.354
x 18
50.8
x 38
0.106
x 59
9.087
x 33
7. Given that 1m = 100cm convert the following m into cm.
a) 4m b) 1.7m c) 0.37m d) 42.01m e) 8.569m
8. Given that 1km = 1000m convert the following km into m.
a) 7km b) 3.74km c) 0.47km d) 8.735 km e) 0.0575km
Number (17) Division of decimals 1. Work out each of the following:
(a) 44.73 (b) 34.15 (c) 94.237 (d) 04.354 (e) 72.369
(f) 4.1748 (g) 9.365 (h) 72.906 (i) 04.304 (j) 824.163
2. Work out each of the following:
(a) 36.4512 (b) 26.4717 (c) 01.4323 (d) 9.28827 (e) 554.9434
3. Divide 24.72 by 3
4. Divide 46.8 by 4
5. Divide 55.62 by 6
6. Divide 321.3 by 7
7. Divide 38.04 by 12
8. Divide 1572.9 by 15
9. Divide 16.88 by 16
10. Divide 499.38 by 21
11. If thirteen albums cost £175.37 What is the cost of each album?
12. If 24 loafs of bread cost £12.96 what is the price of one loaf?
13. If a box of nine apples weighs 2.43 kg what is the approximate
weight of each apple?
14. Work out each of the following:
a) 9.426 10
b) 18 10
c) 13.75 100
d) 182.7 1000
e) 342.7 100
f) 8.2 100
g) 91.6 10
h) 120.78 1000
i) 0.78 100
j) 0.0274 1000
1. Given that 1cm = 10mm convert the following mm into cm.
a) 5mm b) 21.7mm c) 6.1mm d) 0.7mm e) 5.46mm
2. Given that 1m = 100cm convert the following cm into m.
a) 209.1cm b) 6.4cm c) 0.45cm d) 54.7cm e) 8205.3cm
3. Given that 1km = 1000m convert the following m into km.
a) 5m b) 314.7m c) 1140.6m d) 0.5m e) 6331.2
Number (18) Rounding off
1. Round off £3487.29 correct to
i) the nearest pound
ii) the nearest ten pound
iii) the nearest hundred pound
iv) the nearest thousand pound.
2. Given the amount banked by a local charity fair was £2098.81 write down this amount
i) correct to the nearest £1
ii) correct to the nearest £10
iii) correct to the nearest £50
iv) correct to the nearest £100
v) correct to the nearest £200
vi) correct to the nearest £1000
3. The weight of a box of potatoes is given as 67.3 kg. What is this weight correct to the nearest
a) kilogram b) 10 kg
4. The number of pupils attending Castlerock High School is 1056. Give this number correct to
the nearest (a) 10 (b) 20 (c) 50 (d) 100
5. For each of the following numbers write down the number correct to 1 decimal place
a) 3.142
b) 12.88
c) 6.319
d) 23.31
e) 91.7656
f) 4.86430
g) 45.509
h) 109.99
i) 32.019
j) 5.554
6. Write down each of the following numbers correct to 2 decimal places
a) 6.245
b) 8.2493
c) 34.584
d) 55.492
e) 9.08713
f) 37.19187
g) 0.98512
h) 13.09972
i) 45.5482
j) 109.9984
7. Express each of the following numbers to the number of places given in the brackets.
a) 3.141592654 [4]
b) 65.48755 [3]
c) 12.67487 [2]
d) 103.7845 [1]
e) 3.98445 [3]
£
8. For each of the following numbers write down the number correct to 1 significant figure
a) 3.87
b) 92
c) 648
d) 3944
e) 0.56
f) 0.0498
g) 684.98
h) 1024
i) 6.198
j) 0.000795
9. Write down each of the following numbers correct to 2 significant figures
a) 325
b) 6894
c) 34.77
d) 15.3795
e) 0.4548
f) 0.00688
g) 6792.55
h) 10657
i) 34953
j) 264984
10. Express each of the following numbers to the number of places given in the brackets.
a) 3.141592654 [4]
b) 2918.547 [3]
c) 4157.734 [2]
d) 9079.6 [1]
e) 8817.99 [3]
Number (19) Conversions
1. Convert the following decimals into fractions, simplifying where possible.
a) 0.3
b) 0.8
c) 0.03
d) 0.08
e) 0.007
f) 0.006
g) 0.15
h) 0.47
i) 0.68
j) 0.95
k) 0.088
l) 0.254
m) 1.2
n) 1.5
o) 3.56
p) 5.34
q) 6.045
r) 9.9
s) 12.7
t) 3.142
2. Convert the following fractions into decimals.
a) 5
3
b) 10
9
c) 20
17
d) 25
9
e) 25
13
f) 50
33
g) 20
11
h) 25
22
i) 4
3
j) 10
7
3. Convert the following fraction into decimals (care where required!)
a) 8
3
b) 3
2
c) 7
4
d) 6
5
e) 11
6
f) 9
4
g) 12
7
h) 15
4
i) 13
5
j) 5
17
Number (20) Conversions II 1. Write each of the following percentages as fractions, giving your answers in their simplest form.
(a) 20%
(b) 45%
(c) 24%
(d) 35%
(e) 82%
(f) 98%
(g) 52%
(h)19%
(i) 28%
(j) 64%
2. Write each of the following percentages into decimals.
(a) 14%
(b) 33%
(c) 81%
(d) 17 12%
(e) 56%
(f) 2.4%
(g) 1%
(h) 150%
(i) 8%
(j) 13.14%
3. Which is the larger value 54% or 0.499?
4. Which is the larger 2
5 or 39%?
5. Which is the larger 0.299 or 1
3?
6. Place the following qualities in order of size starting with the smallest value.
3
10, 24% , 0.34 ,
1
4, 0.17, 31%
7. Place the following qualities in order of size starting with the smallest value.
56%, 3
5, 0.056,
17
20, 47%, 0.475
Number (21) Expressing as a Percentages 1. Express each of the following fractions as percentages
(i) 5
2
(ii) 10
7
(iii) 50
3
(iv) 25
12
(v) 5
3
(vi) 20
7
(vii) 50
39
(viii) 4
3
(ix) 20
13
(x) 25
16
(xi) 10
9
(xii) 8
3
(xiii) 9
5
(xiv) 7
4
(xv) 15
7
2. Express each of the following decimals as percentages
(i) 0.21
(ii) 0.45
(iii) 0.94
(iv) 0.23
(v) 0.6
(vi) 0.06
(vii) 0.71
(viii) 0.1
(ix) 0.18
(x) 0.09
(xi) 1.47
(xii) 1.6
(xiii) 1.02
(xiv) 0.96
(xv) 1.175
3. For each of the following diagrams, what percentage is unshaded?
(a) (b) (c) (d)
(e) (f) (g)
4. Shade in 25% for each of the following diagrams
(a) (b) (c)
5. A box contains 16 homework books out of a class of 40. Express the number of homework
books in the box as a percentage of those in the class.
6. Asif obtained 33 out of 60 in a recent Science test. What percentage of the marks did she
(a) answer correctly? (b) answer incorrectly?
7. Last week I purchased a Television for £1200 but only left a deposit of
£360. What percentage of the total purchase price did I leave for a
deposit?
8. Nasir obtained 32 out of 40 in a Science test and 18 out of 30 in an English test. Which test did
he perform the best in? Explain your answer.
9. The tickets to a holiday in France should have been £350 but were reduced to £280.
(a) By what amount was the holiday reduced?
(b) What percentage was the holiday reduced by?
10. When travelling to France the weight of a suitcase, when full,
must not exceed 25 kg or else you must pay an extra £13 for
each kilogram over this weight.
Travelling home from France Louise was charged £52.
(a) What was the weight of Louise’s suitcase?
(b) By what percentage did Louise exceed the allowed
weight?
Number (22) Percentage of a quantity 1. Calculate each of the following without a calculator
(a) 20% of 80
(b) 25% of 52
(c) 30% of 150
(d) 40% of 200
(e) 65% of 160
(f) 80% of 350
(g) 55% of 300
(h) 70% of 130
(i) 45% of 220
(j) 95% of 340
2. Work out each of the following
(a) 40% of £130
(b) 90% of 180 cm
(c) 35% of 260 kg
(d) 44% of 175 pupils
(e) 60% of £205
(f) 17% of 1 million
(g) 12% of 225 cm
(h) 56% of $175
(i) 62% of 150 euros
(j) 4% of 50 metres
3. 45% of students at Beecon High School study German in year 7. If there are 160 pupils in year
7, how many study German?
4. In a recent NEXT sale Janet received a discount of 35% for this jacket. If the
jacket was originally priced at £140, how much did Janet actually pay?
5. A bank offers interest at 4% per annum (i.e. per year). If Mr Khan
deposited £150 into his account on the 1st of January what interest
will he receive on the 1st of January the following year?
6. In Texton approximately 64% voted in the last general election. If Texton consists of 850
people, how many turned out to vote?
7. A box contains 60 crayons. If 45% are red, 20% are blue and the rest green. What quantity of
the box are (a) red crayons? (b) green crayons?
8. At the local cinema the opening weekend for the film “Toy Story 3”
took £8245 and had an audience of 3450 people. If 58% of the
audience were boys
(a) How many boys saw the film in the opening weekend?
(b) What percentage of the audience were girls?
9. 52% of pupils at Castlerock High School travel to school by bus where each bus can hold up to
32 pupils. If there are 175 pupils at this school
(a) How many travel by bus?
(b) How many buses are needed each morning for these pupils?
Number (23) Percentage Change
1. James works at a local garage for £8 per hour. If his pay is increased to £9.60, then what is his
percentage increase in pay?
2. The teaching staff at Thomas Whitham has fallen from 30 to 24 employees over the last twelve
months. What is the percentage decrease?
3. At a certain supermarket the price of a loaf of bread has increased from 70
pence to 91 pence. What is the percentage increase in the cost of this
bread?
4. In another supermarket there is a price war and so they have dropped
the price of six eggs from £1.50 to £1.05. What is the percentage
decrease in the cost of these eggs?
5. The price of a television increases from £340 to £391. Work out this
increase as a percentage of the original price.
6. Ali works 30 hours a week, however for one week in December he worked 39 hours. By what
percentage did his hours of work increase for this particular week?
7. Sam has a jar contianing 90 sweets. His sister eats 27 sweets. What is the percentage
decrease in the jar of sweets?
8. Coalville primary school had a new intake of 25 students last year. This year they have moved
to a new building and as such have a new intake of 31. What is the percentage increase in
intake?
9. A holiday to Florida for a family of four is calculated at £7900. However
when shopping around the same holiday is found for £6715. What is the
percentage difference from the original cost?
10. In a sale a pair of Jeans is reduced from £45 to £27. What is the percentage reduction in this
price?
Number (24) Ratio 1. Express each of the following ratios in their simplest form:
a. 6 : 8
b. 3 : 27
c. 18 : 6
d. 14 : 8
e. 21 : 12
f. 15 : 20
g. 16 : 12
h. 24 : 42
i. 30 : 80
j. 144 : 48
k. £20 : £12
l. 30p : £3
m. £2.40 : £1.80
n. 800g : 1.5 kg
o. 54m : 27m
p. 1.2m : 40cm
q. 9 : 3 : 12
r. 8 : 6 : 20
s. 21 : 42 : 14
t. 24cm : 64cm : 42cm
2. A couple have 10 children of which 4 are girls.
(a) Write down in its simplest form the ratio number of boys to number of girls.
(b) Write down the ratio of number of boys to number of children, giving your answer in its
simplest form.
3. Asif has 16 sweets in a bag while Brian has only 12.
(a) Write in its simplest form the ratio of sweets Asif has to sweets Brian has.
Both students eat 6 sweets from their bags
(b) Write in its simplest form the new ratio of sweets Asif has to sweets Brian has.
4. Two rectangles are drawn below.
Find the ratio of
(a) the length of rectangle A to the length of rectangle B.
(b) the area of rectangle A to the area of rectangle B.
(c) the perimeter of rectangle A to the perimeter of rectangle B.
5. In travelling to school John can walk 1.5 km in 45 minutes, whilst his teacher can travel 6km in
20 minutes. Express in its simplest form the ratio of
a) John’s distance travelled to his teachers distance travelled,
b) John’s time taken to that of his teachers.
8cm
3cm
24cm
9cm
A B
Number (25) Dividing into a given ratio
1. Divide £85 in the ratio of 2 : 3
2. Divide 49 cm in the ratio of 4 : 3
3. Divide 60pence in the ratio of 3 : 7
4. Divide £420 in the ratio 7 : 5
5. Divide 325km in the ratio 1 : 5 : 7
6. In a class of 33 pupils the ration of boys to girls is 6 : 5. How many girls are there?
7. Josh and Mary win £1050 on the lottery and decide to divide the money in the ratio of their ages. If
Josh is 32 years old and Mary 24. How much does Josh receive?
8. A box contains both blue and black pens such that the ratio of blue pens to black pens is 5 : 3. If
there are 120 pens in the box how many blue pens are there?
9. The perimeter of a rectangle is 45cm. If the lengths of its sides are in the ratio 5 : 4, find the length
of this rectangle.
10. The land surrounding a house in the lake district consists of
water and a garden in the ratio of 13 : 7. If the total area of
land covers 4000 km2 find the area covered by
(i) water (ii) the garden.
Number (26) Calculator work Using your calculator work out each of the following writing down exactly what is on your
calculator.
1. 32.232.5
2. 45
14580
3. 224
4. 34
5. 5
6. 6.3
2.831.5
7. 3.82.4
6.431.8
8. 46.13
1.862.9
9. 31.82.6
3.587.2
10. 58.642.9(
11. 25.6
5
12. 7.53.11
3.196.13
13. (a) Workout using your calculator the value of 6.03.0
3.841.9
.
(b) Give this answer correct to 2 decimal places.
14. (a) Use your calculator to find the value of 35.689.5
(b) Write this answer correct to three significant figures.
15. (a) what is the value of 87.11.4
7.3 2
?
(b) Give this answer correct to two significant figures.
Number (27) Fractions of a quantity 1. Find the following fractions
a) 3
2 of £4.41
b) 7
3 of £315
c) 10
7 of 8350km
d) 8
5 of 50 litres
e) 5
2 of £2275
f) 12
7 of £101.40
g) 9
4 of £25.92
h) 25
19 of £107
2. Mr Hussein earns £486.50 in one week. After tax is deducted, he receives only three fifths of
this amount. How much does he receive?
3. A farmer increased his stock of potatoes this year by 7
2 if
last year his entire stock of potatoes was 23.8 tonnes,
(a) How much has he increased his stock by?
(b) what is his stock od potatoes this year?
4. Mr Moorhouse had a mass of 73.5 kg before he went on a diet. After a month on a diet he lost
5
2 of this mass.
(a) How much did he lose? (b) What is his mass now?
5. In recent months with the shortage of good joiners Alan
has increased his hourly rate by three eighths. If his rate
was £15 per hour, work out
a) the increase in his hourly rate,
b) his new hourly rate.
6. If a total of 12870 hours are spent at school over the eleven
years and 6
1 of this time spent on the study of mathematics.
How many hours are spent studying mathematics in
a) the eleven years, b) one year?
Number (28) Percentage of a quantity 1. A bank account earns interest at 8%. What interest is earned if there is £225 in the account?
2. In a recent sale 15% was deducted of the price of all electrical equipment.
A DVD player usually costs £299
a) what is the reduction in its price?
b) What is the new price of the DVD player?
3. If a television at the same shop usually costs £1050, what is its new price in
the sale?
4. The population of the village Buckley has 42% men
and 35% women. If the population of the village is 1800, find
the number of
a) men, b) women, c) children.
5. A boy spends 36% of his savings on a new football top. If he had saved £70,
a) How much did he spend? b) how much is left over?
6. When Jim bought his new car in December the price was £11900.
Yet in January the price was reduced by 9%.
a) How much would Jim have saved if he waited a month?
b) What was the price of the car in January?
7. A box of chocolates has a mass of 325 grams. 24% of this mass is through packaging. What is the
mass of a) the packaging? b) the chocolates?
8. A restaurant adds a service charge of 14% to its bill. For a party
of ten people the total bill was £76 plus the service charge. What was
the total price paid by the ten people?
Number (29) Average speed
Distance travelled
Work out the distance travelled for each of the following journeys. Remember to state the units.
1. A car travelling for 3 hours at 30 mph
2. A train travelling for 2 hours at 55 km/h
3. A boy jogging at 2m/s for 25 seconds
4. A boy running at 4m/s for 15 seconds
5. A girl walking to school at 1m/s for 20 minutes
6. A car travelling at 45mph for ½ an hour
7. A cyclist travelling at 9mph for 45 minutes
8. A bus travelling at 35 km/h for 50 minutes.
9. A formula one car travelling for 2½ hours at 180 mph
10. An aeroplane travelling at 400 mph for 5 hours.
Average speed
Work out the average speed for each of the following journeys. Remember to state the units.
11. A girl swims 10 miles in 2 hours
12. A car travels 162 miles in 3 hours
13. A train takes 4 hours to travel 220 miles
14. A cyclist takes 3 minutes to travel 720 metres
15. A bus takes ½ an hour to travel 14 miles
16. A coach takes ¾ of an hour to travel 42 miles
17. A car travels 136 miles with stops taking a total of 4 hours
18. A boy walks the 2km to school taking 20 minutes
19. A sprinter takes 14 seconds to cover a distance of 168 metres
20. A car can travel without stopping 224 miles in 3½ hours
Number (30) Direct proportion 1. In six hours Joan can earn £42. How much does she earn in five hours?
2. If three pints of milk cost £1.38, what is the cost of seven pints of milk?
3. In 5 seconds a train can travel 55 metres. How far can it travel in
a) 12 seconds? b) 1 minute?
4. If a box of six colouring pencils cost 96 pence, how much will it cost for
a) 4 pencils, b) 15 pencils?
5. If I can buy 12 large envelopes for £2.88, how much would I pay for 17 large envelopes?
6. 500 paper clips cost £1.25. What would be the cost for (a) 300?
(b) 700?
7. On a hospital ward eight nurses can look after 56 children. How
many children can seven nurses look after?
8. If six bananas cost £1.35, how much will a dozen bananas cost?
9. A wholesaler can by Christmas cards at 24 pence for 10. How much will it cost for a gross of
Christmas cards {NB a gross means 144}
10. Adrian can spend 20 hours on the internet and it will cost him £10.80.
a) How much will it cost him for just 3 hours on the internet?
b) How many hours will he have on the internet for £4.86?
11. If seven peaches cost £2.52
a) what is the cost of ten peaches?
b) How many peaches can you buy with £10?
Number (31) Inverse Proportion 1. Six men can paint a fence in four days. How long would it take eight men?
2. If three lumberjacks can fell six trees in an hour, how many lumberjacks would
it take to fell nine trees in one hour?
3. If it takes seven police offices to walk the beats on 24 streets on a given morning,
how many streets could ten police officers walk on a given morning?
4. Twelve tarmackers take four hours to lay a road. How long would it have taken
eight tarmackers to lay the same road?
5. If ten bricklayers take six days to build a wall, how long would it have taken
four bricklayers?
6. Eight diner ladies can prepare food for thirty children in fifty minutes. How long would it take ten
diner ladies?
7. Alice has enough food to feed six horses for twelve days. How many days would the food last if she
had sixteen horses?
8. If Sarah paid £150 a month of her credit card it would take twenty five
months to pay of the balance. How many months would it take if she paid of
£250 a month?
9. The express train can travel at 80 km/h and take three hours to
complete its journey. How long would it take if the train had been travelling
at 60 km/h?
10. A fish pond can be filled in 4½ hours using four taps. How long would it take if one tap was broken?