26
Aug
Percentages
26.08.2013 16:57

Percent comes from the Latin word “Per Centum”. Centum means 100, so percent means for every hundred. For example, the passing percentage in an exam is 65% means 65 out of 100 students have passed the exam. Percent can be expressed as ratio and also in decimal. For example 65%=65/100=0.65. If we want to find percentage of 70 books out of 350 books, then we have to find ratio of 70/350=0.2 and then 0.2 is multiplied by 100 to get 20%, so 20% represents 70 books out of 350 books. So decimals, fractions and percentages are inter-related and can be converted to each other. Percentages are used in everyday life. When we go to shops, we see the discount sales put in the form of percent. For example, discount of 25% , discount of 50% and so on. Percentages are used in various fields like in commission, mark up, sales tax, rate of interest, and so on. Let us now see how the percentages, fractions and decimals are inter-related.
1)    Converting a fraction to a percent- To do this divide numerator by denominator and then multiply by 100. The answer with the % sign gives the percentage. For example: ¼ =0.25*100 =25%
2)    Converting a percentage to a fraction- To do this eliminate the % sign and now the given number divided by 100 gives the desired fraction. The fraction can be simplified if possible. For example: 25% = 25/100 = ¼
3)    Converting decimals to percentages- To do this multiply the given decimal by 100 and keep the percent sign. For example: 0.25 = 0.25 * 100 = 25%
4)    Converting percentages to decimals- To do this eliminate the % sign and divide the number by 100 using long division process. The quotient is the desired answer. For example: 35% = 35/100 = 0.35

Examples:

1)Find 14% of 850.
Solution:
14% of 850 = 0.14 times 850 = 119.

2) What percent of 900 is 30?
Solution: 
Let the percent be x.
X% of 900 = 30
(x/100) * 900 = 30
x/100 =30/900
x = ( 30/900) x 100 = 3.33
so 3.33% of 900 is 30.

Let us now understand how to find perimeter of a triangle. A triangle is the smallest polygon which is composed of 3 sides. Perimeter of a triangle is the sum of all 3 sides. So perimeter is found only when all 3 sides are known. In general, if a, b and c are side lengths of a triangle, then perimeter is given by a+ b+ c. For example: the perimeter of a triangle with sides 5cm, 6cm, 7cm is 5+6+7=18cm.
In case of right triangle, perimeter can be found even if we only two sides are known. This is because we can find the third side of the right triangle using Pythagorean Theorem. Pythagorean Theorem states that sum of square of legs is equal to the square of the hypotenuse. The formula is a2+b2=c2, where c is the hypotenuse, a and b are the legs of the right triangle.

Problem 1: Find the perimeter of right triangle whose legs are 3 cms and 4cms.
Solution: we know that a = 3 cms and b= 4 cms. We have to find c using the Pythagorean theorem formula a2+b2=c2 .
32 +42= c2
9+16= c2
25= c2
C= 5.
So perimeter = a+ b+ c= 3+4+5 = 12 cms.

Inflection Point
Right Triangle

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