CHANGING PERCENTAGES TO FRACTIONS AND DECIMALS.
To change a percentage to fraction express the percentage amount as a numerator and 100 as a denominator then simplify the fraction if needed to. The obtained fraction divide it to get its decimal.
Example: Change 50% to fraction
Solution
Express the percentage amount as a numerator and 100 as a denominator hence from the question we are given 50% as the percentage amount hence we express it as follows:
50%=50/100
We simplify the fraction
50/100=1/2
We divide the obtained fraction to get its decimal value
1/2= 0.5
Hence,50%=1/2.
Exercise
Change to fractions
a) 60%
Solution
60/100 = 6/10 = 3/5
b) 24%
Solution
24/100 = 6/25
Try these
c) 35%
d) 2%
Change to percentages
a) 1/4
Solution
1/4×100%=25%
b) 0.72
Solution
0.72×100%=72%
c) 7/8
Solution
7/8×100%= 87.5%
Try these
d) 1/3
e) 1/20
f) 0.31
Change to decimals
a) 36%
Solution
36%= 36/100 = 9/25=0.36
b) 28%
28%= 28/100 =7/25=0.28
Try these
c) 7%
d) 13.4%
Finding a percentage.
To find a percentage of an amount, change the percentage into a decimal then multiply by the amount.
Example
Find 60% of 150
Solution
1) Change 60% into a decimal
60%= 60/100 =0.6
2) Multiply 0.6 by the amount 150
0.6×150=90
Hence, 60% of 150=90
Exercise
1) Find each of the following
a) 68% of 320
Solution
68%= 68/100 =0.68
0.68×320=217.6
Hence,68% of 320=217.6
b) 52.2% of 801
Solution
52.2%= 52.2/100 = 0.522
0.522×801= 418.122
Hence,52.2% of 801=418.122
c) 221% of 370
Solution
221%= 221/100 =2.21
2.21×370=817.7
Hence, 221% of 370=817.7
Try these
d) 109%
e) 96%
f) 77.7% of 120
2) What is 12% of 68kg?
Solution
12%= 12/100
12% of 68kg= 12/100×68kg
=0.12×68kg
=8.16kg
Hence, 12% of 68%=8.16kg
3) Jeff is on a journey of 385km. So far, he has completed 31% of his journey. How far has he traveled?
Solution
31%=31/100 =0.31
31% of 385km=0.31×385km
=119.35km
Hence, Jeff has traveled 119.35km.
4) A jug can hold 2.4 liters of water. It is 34% full. How much more water will fit the jug.
Solution
34%= 34/100 =0.34
34% of 2.4 liters =0.34×2.4litres
=0.816litres
The remaining amount of water= (2.4-0.816) litres
=1.584 litres
Hence, 1.584 litres of water will fit the jug.
5) Which is larger 22% of £57 or 46% of £28. By how much?
Solution
22% of £57=22/100×57=0.22×£57= £12.54
46% of £28=46/100×28=0.46×£28= £12.88
£12.88-£12.54=£0.34
Since £12.88 is greater than £12.54. Hence 46% of £28 is greater than 22% of £57 by £0.34.
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