Percent means ‘for every 100 ’. So, when we say P% .it means P out of 100 . Thus, P%=P/100 . It is often denoted by symbol “% ”. Any percentage can be expressed as a fraction. For example, 40%=40/100=2/5 .
Percentages are used to find whether one quantity is large or small compared with another quantity. The first term usually represents a part of, or a change in the second term, which should be greater than zero.
Percentages are usually used to express numbers between zero and one, any dimensionless proportionality can be expressed as a percentage.
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Let us now express some percentages as fractions:
a. 5%=5/100=1/20 .
b. 10%=10/100=1/10 .
c. 25%=25/100=1/4 .
d. 75%=75/100=3/4 .
e. 125%=125/100=5/4 .
f. 175%=175/100=7/4 .
g. (3 1/8)%=25/800=1/32 .
h. (6 1/4)%=25/400=1/16 .
i. (8 1/3)%=25/300=1/12 .
j. (16 2/3)%=50/300=1/6 .
k. (66 2/3)%=200/300=2/3 .
l. (87 1/2)%=175/200=7/8 .
Calculation of Percentage:
Calculation of percentage:
The percent symbol can be treated as being equivalent to the pure number constant 1/100=0.01, while performing calculations with percentage.
If a number is first changed byP% and then changed by Q% , then the net change in the number =[P+Q+((PQ)/100)] . Remember that any decreasing value in the formula should be taken as ‘negative’ and increasing value should be taken as ‘positive’.
Similarly, if A’s salary is P% less than B’s salary, then the percentage by which B’s salary is more than A’s salary is(100P)/(100-P) .
If expenditure also, then percentage change in expenditure or revenue=[P+Q+((PQ)/100)] . Where ‘P’ is the percentage change in price and ‘Q’ is the percentage change in consumption.
Problems on number percentages:
Ex1 : What percentage of 1600 is 40?
Sol: Let 40 be "P% of 1600.
So, 40=P% of 1600 =(P/100)(1600)=16P .
Thus, P=40/16=2.5% .
Ex2 : Calculate 40% of 625 .
Sol: 40% of a number =2/5 of the number =2/5 of 625=(2/5)(625)=250 .
Ex :3 A number is first increased by 30% and then decreased by 20% . Find the net change in the number.
Sol: Let the original number be 100 .
Increasing by 30%, " it becomes " 130 .
Now, if 130 is decreased by 20% , it becomes 104 .
Thus, the net change =(104-100)=4% increase.
Algebra is widely used in day to day activities watch out for my forthcoming posts on Divide Fractions by Whole Numbers and sample paper of class 9 cbse sa2. I am sure they will be helpful.
Practice problems on number percentages:
Q:1 A’s salary is 25% more than B’s salary. By what percent is B’s salary less than A’s?
Sol: Let B’s salary be .
Since A’s salary is 25% more than that of B, his salary will be Rs. 125 .
Thus, B’s salary is Rs. 25 less than the A’s salary.
So, in percentage: (25125)(100)=20% . Hence, B’s salary is 20% less than A’s salary.
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