This document provides instructions for working with percentages, including:
- Converting percentages to fractions and decimals by writing the percentage over 100 and dividing by 100 respectively
- Converting fractions to decimals by dividing the numerator by the denominator
- Converting decimals to percentages by multiplying the decimal by 100
- Calculating percentages of quantities by writing quantities as fractions, converting to decimals, and multiplying
- Worked examples are provided for each type of percentage calculation.
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2. How to change percentages, into
fractions and decimals
A percentage is a special
fraction.
The % says, “per hundred.”
For example, 47%, is simply another
way of writing the fraction 47/100
3. You can almost see the 100 in the
percentage sign
The 1
The
noughts
Percentage Fraction
7% 7/100
19% 19/100
83% 83/100
Etc.
4. 24% = 24/100 12/50 6/25
So to write a percentage as a
fraction, you simply put it
over 100 like this:
24% = 24/100
Yes, but remember to try
to write the fraction in its
simplest terms
6. To change a fraction into a decimal, you divide the
bottom number (the denominator) into the top number
(numerator). For example, to change ¾ into a
decimal, you would divide the 3 by the 4.
¾
3 ÷ 4 = 0.75
Remember that a percentage is a
fraction always has 100 as its
denominator
7. So, to change a percentage into a
decimal, you always divide by
100
For example, 35% as a fraction is 35/100 so to
change this into a decimal, you divide 35 by
100
35% 0.35
÷ 100
8. To change decimal into a
percentage
Decimal Percentage
To change a decimal into a
percentage, you X by 100
0.23 23%
X 100
9. You Should Know
A a percentage is a
special fraction.
23% = 23/100
Percentage
to a
decimal
÷ 100
Decimal
to a
percentag
e
X 100
12. Finding one quantity as a percentage of
another quantity
Jill obtained a
score of 23 out
of 32 in a
science test.
She wants to
know what this
will be as a
percentage?
To do this, you
• Write the result as a fraction
23/32
• 4. 72%
• Change the fraction into a
decimal (23 ÷ 32 = 0.71875)
• Change the decimal into a %
(0.71875 X 100 = 71.9%)
13. There are lots of similar problems and all of
these can be tackled in the same way
1. Write the quantities as a fraction
23/32
2. Change the fraction into a decimal (23 ÷ 32 =
0.71875). It’s probably a good idea to round off to
2 decimal places.
3. Change the decimal into a % (0.72 X 100 =72%)
4. So, 23 is 72% of 32
The total
quantity
The quantity that
you want as a %
14. Car Par Survey
Colour Frequency
Green 2
Silver 4
Black 5
What percentage of the
cars are green?
Total is 11 Want 2/11 as a percentage
Change 2/11 into a decimal = 0.1818
(round off to 2 d,p. Change 0.18 into a %
(0.18 X 100 = 18%) Answer 18%
15. Try these:
1 Work out your percentage if you got 12 out of 25
2 Work out your percentage if you got 15 out of 25
3 Work out your percentage if you got 17 out of 20
4 Work out your percentage if you got 19 out of 24
5 Work out your percentage if you got 17 out of 31
6 A player scores 3 times out of 6 shots.What is their score percentage
7 A player scores 4 times out of 10 shots. What is their score percentage
8 A player scores 44 times out of 69 shots. What is their score percentage
9 Work out 12.5 out of 26 as a percentage
10 Calculate the score percentage if out of 15 shots 12 are successful
16. The ‘percentage of’ problem
What is
12% 0f
34?
What is 13%
of 56?
What is
78% of
57?
17. To answer these questions
First: Change the percentage into a decimal
Second: Change the word ‘of’ into a X sign
Third: Workout
Example: What is 23% of 45
23% = 0.23 and ‘of’ X
0.23 X 45 = 10.35
18. Finding Percentages of Different Numbers
Problem:
In a survey of 120 pupils it was found that 20% had
personal stereos. How many pupils had personal
stereos?
Change the percentage to a decimal, then multiply by the
number of children.
20% = 0.20
0.20 times 120 = 24
19. 1. 25% of 32
2. 75% of 36
3. 80% of 35
4. 10% of 142
5. 20% of 60
6. 35% of 70
7. 6% of 220
8. 15% of 150
9. 12% of 20
10. 27% of 30
Try these
