1. What is 20% of 40?
‘Per cent’ is the same as saying ‘out of a
hundred’ or ‘per hundred’ or by using the
symbol ‘%’.
In this case the question is what are 20
hundredths of 40. 20% is one fifth. Then,
to find one fifth of 40, divide by 5.
A quick way to do percentages is to use
10 per cent. Thus, 10% is one tenth of
100%. Therefore, in this case, 10% or one
tenth of 40 is 4. 20% would be twice this
figure, which is 8. Answer: 8
22 Test your numerical aptitude
What is 53 ÷ 21?
What is 4 41 ÷ 2 41?
Answer: 11
5
Answer: 18
9
20% = 20 = 1
100 5
40/5
41 ÷ 21
4 4
=17 ÷ 9 = 17 × 4
4 4 4 9
=68 = 34 = 17
36 18 9
3 ÷ 1
5 2
= 3 × 2
5 1
= 6
5
2. What is 24% as a fraction?
Simply place the percentage over a
hundred. Then reduce both the
denominator and the numerator equally
until you cannot break it down any further.
In this case, both parts were divided (or
cancelled) by 2 and then 2 again. No other
number can be divided into both 6 and
25, so this fraction has reached the lowest
common denominator.
3. What is 12½% as a fraction?
Fractions in the numerator are eliminated
by multiplying by the denominator and
adding the part of the numerator. In this
case, 2 by 12 is 24, add 1 is 25.
As the numerator has been multiplied by
2, so the denominator has to be multiplied
by 2.
The fraction can now be reduced (or
cancelled) using 5.
4. Change 5 to a percentage
16
To change a fraction to a percentage you
multiply by 100%.
The resulting fraction can be cancelled
by 4. Dividing the numerator by the
denominator results in a decimal
percentage or another, correct answer,
31¼%. Answer: 31.25%
5. What is a 40% reduction on an item
costing £240.00?
Another way is to say that 10%, that is,
one tenth, of £240 is £24. So, 40% is 24
by 4, which is £96. Answer: £96
Number tutor 23
24% = 24 = 12 = 6
100 50 25
Answer: 6
25
Answer: 1
8
40% = 40 = 0.4
100
0.4 × 240
121% = 121/2 = 25 = 1
2 100 200 8
5 × 100
16 1
= 500
16
= 125
4
1. What is the average of 4, 7, 8 and 9?
To find the average add all the quantities 4 +7 + 8 + 9 = 28
and divide by the number of the quantities. 28 ÷ 4
There are four numbers. The total is
divided by the number of quantities. Answer: 7
2. What is the average time to complete a
journey if recorded times were 1 hour
50 minutes, 2 hours 10 minutes, 2 hours
40 minutes, 2 hours 15 minutes and 1 hour
5 minutes? Total hours = 10
Journeys = 5
Answer: 2 hours
3. If there are 8 boys in a class and 12
girls, what is the ratio of boys to girls?
A ratio compares one quantity with 8 to 12
another. It is common to reduce or 8 : 12
(simplify) ratios to the smallest possible or 2 : 3
whole numbers.
Answer: 2 : 3
4. What is the ratio of the following articles
to each other: 15 books, 25 newspapers 15 : 25 : 10
and 10 magazines? or 3 : 5 : 2
Answer: 3 : 5 : 2
5. What proportion of the number of
articles are newspapers?
Proportion is another word for ratio. It is
a part of the whole or total number. In
this case, the total is 3 + 5 + 2 = 10.
Newspapers are 5 parts out of 10. Answer: 1 : 2 (or ½)
1. What is the average of 4, 7, 8 and 9?
To find the average add all the quantities 4 +7 + 8 + 9 = 28
and divide by the number of the quantities. 28 ÷ 4
There are four numbers. The total is
divided by the number of quantities. Answer: 7
2. What is the average time to complete a
journey if recorded times were 1 hour
50 minutes, 2 hours 10 minutes, 2 hours
40 minutes, 2 hours 15 minutes and 1 hour
5 minutes? Total hours = 10
Journeys = 5
Answer: 2 hours
3. If there are 8 boys in a class and 12
girls, what is the ratio of boys to girls?
A ratio compares one quantity with 8 to 12
another. It is common to reduce or 8 : 12
(simplify) ratios to the smallest possible or 2 : 3
whole numbers.
Answer: 2 : 3
4. What is the ratio of the following articles
to each other: 15 books, 25 newspapers 15 : 25 : 10
and 10 magazines? or 3 : 5 : 2
Answer: 3 : 5 : 2
5. What proportion of the number of
articles are newspapers?
Proportion is another word for ratio. It is
a part of the whole or total number. In
this case, the total is 3 + 5 + 2 = 10.
Newspapers are 5 parts out of 10. Answer: 1 : 2 (or ½)
1. What is the average of 4, 7, 8 and 9?
To find the average add all the quantities 4 +7 + 8 + 9 = 28
and divide by the number of the quantities. 28 ÷ 4
There are four numbers. The total is
divided by the number of quantities. Answer: 7
2. What is the average time to complete a
journey if recorded times were 1 hour
50 minutes, 2 hours 10 minutes, 2 hours
40 minutes, 2 hours 15 minutes and 1 hour
5 minutes? Total hours = 10
Journeys = 5
Answer: 2 hours
3. If there are 8 boys in a class and 12
girls, what is the ratio of boys to girls?
A ratio compares one quantity with 8 to 12
another. It is common to reduce or 8 : 12
(simplify) ratios to the smallest possible or 2 : 3
whole numbers.
Answer: 2 : 3
4. What is the ratio of the following articles
to each other: 15 books, 25 newspapers 15 : 25 : 10
and 10 magazines? or 3 : 5 : 2
Answer: 3 : 5 : 2
5. What proportion of the number of
articles are newspapers?
Proportion is another word for ratio. It is
a part of the whole or total number. In
this case, the total is 3 + 5 + 2 = 10.
Newspapers are 5 parts out of 10. Answer: 1 : 2 (or ½)
1. What number comes next?
12 10 8 6 ?
The numbers reduce from left to right. 2 is
taken away each time. Answer: 4
2. What number comes next?
2 5 11 23 47 95 ?
The numbers increase from left to right.
Each number is double the previous
number plus 1. Answer: 191
3. What is the missing number?
2 3 4 6 6 9 8 ? 10 15 12
There are two sequences, which have been
put together.
2, 4, 6, 8, 10, 12 and 3, 6, 9, 12, 15. Answer: 12
