Percentage tricks and shortcuts | Percentage made easy, formulas and questions.

Percentage tricks and shortcuts:

We read newspaper every  morning and watch news on TV and also use Radio, social media like whats app etc. to watch/read/ listen news.

There has been a 10 percent increase rain fall in current year.

The cost of petrol has been fall by 4 percent.

Banks reduced interest rates by 2 percent.

etc.

We use the word percent often in everyday affairs.

Look at the ratios 92/100, 84/100, 65/100, 58/100

The denominator of each of the ratio is 100, such a ratio is called a percentage.

The percentage is written using the word percent or the symbol %.

The ratio 92/100 is written as 92% or 92 percent.

Similarly, 84/100 means 84% or 84 percent.

Conversion of a fraction into percentage :

We know that if the numerator and the denominator of a simple fraction are multiplied or divided by the same number we get an equivalent fraction.

For example,

1. 4 / 5 = 4 × 2 / 5 × 2 = 8 / 10.

2. 2 / 7 = 2 × 3 / 7 × 3 = 6 / 21.

3. 20 / 50 = 20 ÷ 10 / 50 ÷ 10 = 2 / 5

etc.

You use same above things to convert a simple fraction into a percentage.

For example,

Q. Convert the following fractions into percentages.

1. 2 / 5

Ans.

We have to convert 2 / 5 into a percentage, that is into a fraction with denominator 100.

Above fraction if multiply by denominator is 20 then we get denominator is 100 therefore also multiply numerator by 20.

= 2 / 5 = 2 × 20 / 5 × 20 = 40 / 100.

That is 40% or 40 percent.

Similarly,

2. 4 / 25

= 4 × 4 / 25 × 4 = 16 / 100.

That is 16%.

3. 3 / 10

= 3 × 10 / 10 × 10 = 30 / 100.

That is 30%.

3. 21 / 300

= 21 ÷ 3 /  300 ÷ 3 = 7 / 100.

That is 7%.

etc.

Question :

Convert the following decimal fractions into percentages :

1) 0.22    2) 0.07   3) 0.8

Ans.

1) 0.22

We know that 0.22 means 22 / 100.

Therefore 0.22 = 22 / 100 ( 22 percent = 22% )

2) 0.07 = 7 / 100 ( 7 percent = 7 % )

3) 0.8 = 0.80 = 80 / 100 ( 80 percent = 80 % )

Finding out a given percentage of a given number :

We know that ' 1 / 3 of 30 ' means ' 30 × 1 / 3 '

Therefore 1 / 3 of 30 = 30 × 1 / 3 = 10.

Similarly, ' 20% of 60 ' means ' 60 × 20 / 100 '

Therefore 20% of 60 = 60 × 20 / 100 = 12.

Examples :

1) 25% of 120

Ans.

25% of 120 = 120 × 25 / 100 = 30.

2) 30% of 300

Ans.

30% of 300 = 300 × 30 / 100 = 90.

3) There are 60% boys in a certain college. If the total number of students in the college is 1250, what is the number of boys in the college ?

Ans.

60% of 1250 = 1250 × 60 / 100 = 750.

Therefore number of boys 750

Finding out what percentage a given number forms of another number :

For example :

1) In the annual exam, Sachin scored 360 out of 600 marks. What is the percentage of the marks he scored ?

Ans.

360 out of 600 is expressed as 360 / 600.

Finding out the percentage of marks means making 100 the denominator of 360 / 600.

To get a denominator of 100, we divide the numerator and denominator by 6.

Thus, 360 / 600 = 360 ÷ 6 / 600 ÷ 6

= 60 / 100 = 60 percent.

Therefore Sachin 60 %  marks.

2) What percentage of 70 is the number 35 ?

Ans.

We have to convert 35 / 70 into a fraction with denominator 100.

Here, the denominator is 70. The number 100 is not a multiple of 70. Hence, we will find the reduced from of 35 / 70.

35 / 70 = 1 / 2

Since 100 is 50 times of 2,

35 / 70 = 1 / 2 = 1 × 50 / 2 × 50 = 50 / 100

= 50%.

Thus, the number 35 is 50% of 70.

Q. Find out the value of x.

1) x% of 36 = 144

Ans.

36 of x / 100 = 144

X = 144 × 100 / 36

X = 400.

2) x% of 64 = 8

Ans.

64 × x / 100 = 8

X = 8 × 100 / 64

X = 12.5

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