a)
b)
c)
d)
e)
7/8
8/12
7/9
7/10
2/3
a)
b)
c)
d)
e)
11/12
7/10
8/15
16/12 or 1 ¼
11/24
a)
b)
c)
d)
e)
1 7/12
1 5/56
29/30
29/52
1 1/10
a)
b)
c)
d)
e)
5/8
5/12
1/3
2/5
1/2
a)
b)
c)
d)
e)
7/20
8/21
23/36
9/22
71/126
Adding and Subtracting Fractions
Multiples
A.
1.
2.
3.
4.
5.
List the first 5 multiples of:
5
7
12
14
19
B.
1.
2.
3.
4.
5.
6.
What is the:
9th multiple of 8
7th multiple of 6
12th multiple of 12
11th multiple of 10
13th multiple of 5
5th multiple of 13
C.
1.
2.
3.
4.
5.
D.
1.
2.
3.
4.
5.
List 3 numbers which are
in:
a) 5,10,15,20,25
7.14.21.28.35
3 and 4 times tables b)
c) 12,24, 36, 48, 60
3 and 5 times tables d) 14,28,42,56,70
10 and 4 times tables e) 19,38,57,76,95
9 and 2 times tables a) 72
42
12 and 10 times tablesb)
c) 144
What is the lowest
5 and 6
7 and 8
4 and 8
9 and 6
10 and 6
E. What is the lowest
1. 13 and 5
2. 15 and 12
3. 16 and 10
4. 14 and 21
5. 21 and 70
d) 110
e) 65 multiple
common
f) 65
a)
b)
c)
d)
e)
12,24,36
15,30,45
20,40,60
18,36,54
60,120,180
a) 30
b) 56
common
c) 8
d) 18
e) 30
a)
b)
c)
d)
e)
of:
multiple of:
65
60
80
42
210
Factor Trees
Answers
1.
1. Draw factor trees for the following numbers:
2.
a) 20
2x5
a)2
b) 24
b)3 x 23
c) 48
d) 90
c)3 x 24
e) 81
d)2 x 32 x 5
f) 50
4
e)3
g) 75
2
f)2
x
5
h) 120
g)3 x 52
i) 200
j) 1800
h)23 x 3 x 5
2. Using your factor trees from question 1, write the numbers
products
of
2
i)23 xas 5
their prime factors .
j)23 x 32 x 52
Factors and HCF
ANSWERS
1.
1) Find all the factors of the following numbers:
1.1,2,4,5,10,20
1) 20
2) 24
2.1,2,3,4,6,8,12,24
3) 27
3.1,3,9,27
4) 32
4.1,2,4,8,16,32
5) 40
5.1,2,4,5,8,10,20,40
6) 50
7) 56
6.1,2,5,10,25,50
8) 120
7.1,2,4,6,7,8,14,28,56
9) 200
8.1,2,3,4,5,6,10,12,20,24,30,40,60,120
2) 2 only has 2 factors (1 and 2), how many numbers can you find between
1 and 30 which have exactly 2
factors? (these are called prime numbers)
9.1,2,4,5,10,20,40,50,100,200
3) Find the highest common factors of the following pairs of 2.
numbers:
2,3,5,7,11,13,17,19,23,29 (10 of them)
1) 18 and 54
3.
2) 25 and 45
1.18
3) 12 and 18
4) 27 and 108
2.5
5) 30 and 75
3.6
4) Find the HCF of these pairs of numbers:
4.27
1) 90 and 450
2) 96 and 480
5.15
3) 39 and 195
4.
1.90
2.96
3.39
HCF and LCM
Find the Highest Common Factor
of these numbers:
•18 and 30
•15 and 20
1.6
•16 and 24
2.5
•12 and 36
3.8
•20 and 30
4.12
•28 and 70
5.10
•39 and 65
6.14
•38 and 57
7.13
8.19
Find the Lowest Common
Multiple of these numbers
•6 and 7
•4 and 6
•5 and 8
1.42
•10 and 4
2.12
•16 and 5
3.40
•14 and 21
4.20
•2.2 and 5
5.80
•0.4 and 7
6.42
7.55
8.14
Equivalent Fractions
2.
a)4
b)15
c)12
d)20
e)60
f)8
g)26
h)32
i) 120
j)15
k)64
l) 154
m)125
n)400
o)615
p)9720
Ratio
1.
2.
3.
4.
5.
6.
7.
8.
ANSWERS
There are 10 girls and 15 boys in a class, what is the ratio of girls to boys in its simplest 1. 2:3
2. 7:8
form?
There are 14 cats and 16 dogs in an animal shelter, what is the ratio of cats to dogs in its 3. 2:5
4.
simplest form?
a) 4:5
There 22 caramels and 55 fudges in a bag of sweets, what is the ratio of caramels to fudges
b) 3:5
in its simplest form?
c) 7:12
Simplify these ratio to their simplest forms:
d) 5:8:16
e) 3:7:12
a) 48:60
5.
b) 45:75
a) 2 and 8
c) 63:108
b) 6 and 24
d) 25:40:80
c) 9 and 36
e) 24:56:96
6.
f) 120:180:600
a) 8 and 12
b) 12 and 18
g) 320:400:440
c) 22 and 33
Archie and Charlie share their Thomas the tank engine toys in the ratio 1:4, how many do
7.
they each get if they have:
a) 9 and 21
a. 10 toys
b.30 toys c.45 toys
b) 18 and 42
Tom and Jerry share sweets in the ratio 2:3, how many do they each get if they share:
c) 27 and 63
a. 20 sweets
b.30 sweets c.55 sweets
8.
a) 10 and 20 and 30
Sue and Linda share some money in the ratio 3:7, how many do they each get if they share:
b) 12 and 24 and 36
a. £30
b.£60
c.£90
c) 50 and 100 and
Mike, Dave and Henry share some little bits of blue tack in the ratio 1:2:3, how many do
150
they each get if they share:
a. 60 pieces
b.72 pieces c.300 pieces
Fractions, Decimals and Percentages
1.
a)
b)
c)
d)
e)
75%
10%
20%
35%
42%
a)
b)
c)
d)
e)
0.7
0.25
0.3
0.15
0.05
a)
b)
c)
d)
e)
60%
70%
8%
27%
80%
a)
b)
c)
d)
e)
¼
33/100
51/100
4/5
1/5
a)
b)
c)
d)
e)
0.4
0.9
0.74
0.03
0.05
a)
b)
c)
d)
e)
7/10
3/5
11/50
7/20
21/50
2.
3.
4.
5.
6.
Ordering Fractions
ANSWERS
1. 1/4 3/8
2. 2/5 ½
3. 1/3 5/12
4. 1/4 1/2
5. 1/4 2/5
6. 1/3 4/9
7. 2/6 1/4
8. 2/7 2/4
½ and 4/8
3/5 and 6/10
1/1
4/6
2/3
5/6
1/2
6/10
1/2
2/3
5/12
2/3
5/8
11/14
3/4
2/29
3/4
7/8
3/4
5/6
7/9
3/2
Ordering Decimals
1. For each pair of numbers say
which is bigger by adding > or <.
a) 0.2
0.7
b)0.3
0.1
c)0.7
0.9
d)0.3
0.4
e)0.6
0.3
f)0.24
0.2
g)0.3
0.39
h)0.4
0.35
i)0.9
0.85
j)0.22
0.3
2. Try these:
a) 0.04
0.05
b)0.02
0.09
c)0.12
0.02
d)0.04
0.23
e)0.4
0.04
3. These are trickier:
a) 2.34
0.09
b)4.49
4.0003
•
c)5.01
5.1
d)6.32
6.325
e)7.436
7.43
f)8.35
8.345
a)
b)
c)
d)
e)
f)
g)
h)
i)
j)
<
>
<
<
>
>
<
>
>
<
a) <
b) <
c) >
d) <
e) >
f) < (smallest to
4. Put these decimals in ascending order
•
biggest):
a) >
a. 0.2
0.3
0.15
b) >
b. 0.7
0.64
0.072
c) <
c. 0.85
0.9
0.425
d) <
d. 0.734
0.7345
0.7335
e) >
e. 6.234
6.009
6.4f) >
•
a) 0.15 0.2 0.3
b) 0.072 0.64 0.7
c) 0.425 0.85 0.9
d) 0.7335 0.734
0.7345
e) 6.009 6.234 6.4
ANSWERS
Finding Percentages
1. what single sums can I
1) Some percentages I can find easily by doing a single sum,
a) divide by 10
do to find:
b) divide by 2
a. 10%
b. 50% c.25%
c) divide by 4
2.
2) If I know 10% how can I find:
a) half the answer
b) divide by 10
a. 5%
b. 1%
c. 20 %
d. 90%
c) double
3) If I know 50% how can I find:
d) multiply by 9 or subtract
10% from original
a. 5%
b. 25%
quantity
3.
4) Find:
a) divide by 10
a. 30% of 250
b. 40% of 500 c. 15% of 220
d. 75%
b) half of
50% 84
4.
5) Find:
a) 75
b) 200of 96
a. 35% of 440
b. 65% of 450 c. 16% of 220
d. 82%
c) 33
6) Find:
d) 63
5.
a. 94% of 640
b. 8% of 520 c. 27% of 220
d. 53%
of 96
a) 154
b) 292.5
7) Compare you methods for the questions above with a partner,
where they the
c) 35.2
same ?
d) 78.72
6.
a)
b)
c)
d)
601.6
41.6
59.4
50.88
ANSWERS
1.
2.
a) 319.5
Explain how you would use ab)434.52
calculator to
c)177.5
decrease an amount by a given
percent.
d) 636.16
e)727.04
Decrease the following amounts
by 28%
3.
a) £225
a)134.40
b) £306
b)157.20
c)186
c) £125
d)195
d) £448
e)239.88
e) £512
4.
A TV costs £120, how much a)73.50
will it cost if its
b) 77.91
price is decreased by:
c)91.49
a) 19%
5.
6.
b) 32%
a)162
c) 79%
b)220.32
d) 73.5%
c)90
d) 322.56
e) 42%
e)368.64
A car bought for £6, 500
depreciates
in
7.
value by 12.5% each year, how
much will it
a)97.20
b) 81.60
be worth after:
c)25.20
a) 1 year
d)31.80
b) 2 years
e)69.60
8.
c) 5 years?
a)5687.50
b) 4976.56
c)333.91
Percentage Increase/Decrease
1. Explain how you would use a calculator to increase
an amount by a given percent.
2. Increase the following amounts by 42%
a)£225
b) £306
c)£125
d)£448
e)£512
3. A TV costs £120, how much will it cost if its price is
increased by:
a) 12%
b)31%
c)55%
d)62.5%
e)99.9%
4. Simon puts £70 in a bank, each year the money in
his bank increase by 5.5%, how much does he have
in:
a) 1 year
b)2 years
c)5 years?
5.
6.
7.
8.
Limits
1) These numbers have been rounded
to the nearest 10, write down the
largest and smallest values they
could be:
1) 50
2) 80
3) 110
2) These numbers have been rounded
to the nearest whole number, write
down the upper and lower limits:
1) 3
2) 17
3) 23
4) 100
5) -3
3) These lengths have been rounded to
the nearest 10th of a cm, write the
upper and lower limits:
1) 12.5cm
2) 21.7cm
3) 35.8cm
4) 52.1cm
5) 80.4cm
Answers
4) A field is 100m wide and 120m long, both lengths have been
1.
rounded to the nearest metre.1.45 and 54.9999999..
2.75 and 84.999....
a) Find the perimeter and area of the field if these
3.105 and 114.9999...
measurements are accurate
2.
b) Find the largest and smallest possible perimeter
1.2.5 and 3.4999...
c) Find the largest2.16.5
and smallest
possible area.
and 17.4999...
3.22.5 and 23.49999...
4.99.5 and 100.4999..
5) A rectangle has it’s area rounded
to the nearest
5.-3.499999
and whole
-2.5 number,
3.
it becomes 40cm2. One side of the rectangle is exactly 10cm; find
1.
12.45 and 12.55
the maximum and minimum lengths
theand
other21.75
length could have.
2.21.65
3.35.75 and 38.5
4.52.05 and 52.15
6) Two lengths of wood are stuck
together
and80.45
their combined
5.80.35
and
4.
length is rounded to the nearest
and itand
is 14.9cm,
length2
a) mm
p=44om
area=one
12000m
is rounded to the nearest mmb)
andlargest=
is 7.1cm. 442m
Find the smallest=438m
minimum
c) largest= 12110.25m2
and maximum length of the othersmallest=11890.25m
length.
2
5. smallest- 3.95cm
largest- 4.05cm
6. largest- 7.9cm smallest- 7.7cm
ANSWERS
a) 0.5
b) 1.2
c) 0.8
d) 1.3
e) 1.5
Adding and Subtracting Decimals
•
•
•
a)
b)
c)
d)
e)
1.47
1.28
1.66
0.97
1.68
a)
b)
c)
d)
e)
31.44
70.81
39.46
34.15
50.8
a)
b)
c)
d)
e)
0.45
0.54
0.49
0.71
0.7
a)
b)
c)
d)
e)
2.94
39.02
67.25
77.03
54.11
Directed Numbers
•ANSWERS
1) -13
2) 12
3) -5
4) 10
5) 14
6) -1
7) -11
8) -1
9) 7
10)-7
1) -17
2) -24
3) -23
4) -24
5) -9
6) -8
7) 8
8) -12
9) -14
10)-9
1) 17
2) -5
3) 1
4) 8
5) -10
6) 23
7) 26
8) 36
9) 17
10) 16
Directed Numbers 2
1) I am £250 into my overdraft () but then I get paid £535, how much
will I have in my bank account?
1.
285
my living room is 40°C warmer than that, what is the temperature in my
2. 23
living room?
I have £32 and each month for 4 months I have to pay £15 to my
3.
-28
mobile phone, if I don’t put any money into my account, how far will I
4. 66
be into my overdraft?
I jump out of a plane 125m above the ocean, I travelled 191m before I
5.
23
stop, how far am I from the surface of the water?
2) The temperature at the North Pole is -17°C; luckily the temperature in
3)
4)
5) I am playing air hockey with my friend, because I am amazing I agree
start on -9 points, we play first to 14, how many points do I need to
score?
A.
Bidmas
A)
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
(3 + 3 ) x 4
4x2–5
(5 + 7) ÷ 6
5x3+5
(9 – 4 ) + 5
1+1–1
2 x (15 – 2)
(5 x 4 ) + 2
(8 + 2 ) ÷ 10
(21 x 1 ) – 2
B)
1.(1 + 14) – (5 x 3 )
2.(10 + 6 ) ÷ (4 x 2)
3.(1 + 2 ) x (6 – 3)
4.(2 x 6 ) – (14 ÷ 2)
5.(7 x 2) ÷ ( 20 – 6)
6.(3 x 10) – (2 x 2)
7.(9 x 5) – ( 2 x 10)
C)
1.
2.
3.
4.
5.
6.
(3 x 3 – 4 ) x (2 + 2)
2 x (13 – 4) – (23 ÷ 23)
3 x (1 + 4) – (5 x 2)
4 x (3 + 2) – ( 24 – 5)
7 x ( 4 ÷ 2 ) ÷ ( 3 x 5 -1 )
((9 + 7 x 3 ) ÷ 10) – 1
B.
C.
1) 24
2) 3
3) 2
4) 20
5) 10
6) 1
7) 26
8) 22
9) 1
10) 19
1)
2)
3)
4)
5)
6)
7)
0
2
9
5
1
26
25
1)
2)
3)
4)
5)
6)
20
17
5
1
1
2