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Fractions or percentages are simply used to compare the quantities. For example with the help of percentages, a student can be ranked in his class. The % sign is used to represent percentages. On the other hand, a fraction consists of a numerator and a denominator. For example, ¾ is a fractional number in which 3 lying above the line represents the numerator and 4 lying below the line represents the numerator. Percentages are simple ratios hence it can be represented in the form of fractions and further this fraction can be expressed in decimals by dividing its numerator by its denominator.
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Key Takeaways: Fraction, decimal percent, numerator, denominator, fractional number
Conversion of Fractions into Percentage
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To understand conversions of percentage into fractions let us consider this example- the number of female students in a class is 50 and the total strength is 100. So in order to find the total percentage share of female students, we need to keep the total number of female students in the numerator and the total strength as the denominator followed by simplifying it. After simplification, the decimal value is to be multiplied by a hundred.
[50/ 100] x100 = 50%
To get some more clarity in the concept of fractions let us take one example of one pizza having 6 slices, a mother distributes one slice each to her two sons and one daughter and at last, she herself ate one. In the above example, the total no. of pizza slices were 6 out of which 4 were consumed or we can simply write it in a fraction as 4/6.
Fraction and Percentage
Let us take the fractional number as x/y and carefully look at the steps given below:
Step-1: Multiply x/y with 100 i.e.,( x/y)*100 and place a %age sign.
Step-2: Multiply the Numerator with 100 and later on divide it with the denominator.
I.e., (X*100/y)%.
Examples
- 3/4 = (3/4) * 100 % = 300/4 % = 75 %
- 5/40 = (5/40) * 100 % = 500/40 % = 15/2 % = 7.5 %
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Conversion of Decimals into a Percentage
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Step-1: For converting decimal numbers into percentages, Multiply the decimal number by a hundred.
Step-2: Add a percentage% sign to the final answer.
Examples
- 0.11 becomes 0.11 x 100 = 11%
- 0.675 becomes 0.625 x 100 = 62.5%
Also Check: Ratio to Percentage
Conversion of Percentages into Fractions or Decimals
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Let us take the fractional number as x% and carefully look at the steps given below:
Step-1: Divide the given x% by 100 i.e.,( x/100)%
Step-2: Simplify it up to a point where the numerator is no longer divisible by the denominator and get the fractional value.
Step-3: This fractional value can be expressed into decimals by further dividing the numerator by its denominator value.
Examples
- 60% = 60/100 = 6/10 = 0.6
- 25% = 25/100 = 5/20 = ¼ = 0.25
Things to Remember
- The term percent means parts per hundred and is derived from the Latin word centum which again meant hundred or by hundred.
- For converting percentage into fraction Divide the given x% by 100 i.e.,( x/100)%.
- For converting a fraction into percentage, multiply x/y with 100 i.e.,( x/y)*100 and place a % sign.
- For converting decimal into percentage, multiply the number with 100.
Also Read:
Sample Questions
Ques 1. The number of female students in class VII A is 24 and the number of male students in the same class is 32. Find the percentage of female students in the class? [2 marks]
Ans. Given:
No. of female students-24
No. of male students-32
To find:
Percentage of female students
Total no. of students = no.of female students+no.of male students
= 24+32
= 56
Therefore, Percentage of female students = no.of female students/total no. of students in class
=24/56 * 100
= 0.42*100
=42%
Ques 2. Mr Khan along with his wife and 2 daughters went to a cafe to celebrate their weekend. Mr Khan ordered one large-sized pizza having 6 slices and distributed it among four people equally, one piece each. Write the fractional number representing the ratio of the total number of slices consumed vs the total number of slices left. [2 marks]
Ans. Step-1 total no. of slices in pizza=6
Therefore, the denominator of the fraction =6
Step-2 total no. of family members.=4
Total no. of pizza consumed = 4
Therefore, the numerator of the fraction=4
So,the fraction becomes= 4/6 = ?
Ques 3. If the total number of books in a library is 96000, out of which 50% books are of science,25% books are of literature and 25% are of social science. Find the number of books for each subject mentioned in the question? [2 marks]
Ans. Total number of books = 96000
i) 50% of books are science,
Therefore,
50/100*96,000
= 48000
ii) 25% of books are literature,
Therefore,
25/100*9600 = 24000
iii) 25%of books are social science,
Therefore,
25/100*9600 = 24000
Ques 4. There are 55 staff in the railway food kitchen. The number of staff was reduced to 22 due to the covid pandemic for the month of January. What percent of staff was active in the month of January? [2 marks]
Ans. Percentage of staff in the month of January = (22/55)*100
= 2200/55
= 40%
Therefore, 40% of staff was active in the month of January.
Ques 5. A man having a company worth of $500000. 25% of his company’s equity is with his son. What is the total percentage of shares the son has in his name? [2 marks]
Ans. Total company worth = $50,0 000
equity his son got = 25% of 500000
= 25/100*500000
= 125,000
Therefore, the son got $1, 25, 000.
Ques 6. Prisha obtained 300 marks in her exam. If she obtained 75 % marks on her report card, find the maximum marks? [2 marks]
Ans. Prisha obtained 300 marks
Let the Maximum Marks be x
75% of x = 300
(75/100)*x = 300
x = (300*100)/75
= 400
Ques 7. 25% of silver is present in an alloy . How much quantity of alloy is required to obtain 250 g of silver? [2 marks]
Ans. Let the quantity of silver needed = x
25% of x = 250g
25/100*x = 250
x = (250*100)/25
= 1000 gms
Therefore, Quantity of Alloy Required to get 250g of Silver is 1000 gms.
Ques 8. Convert the following decimals & fractions into percentage given below: [2 marks]
Ans.
- 7/4 = (7/4) * 100 % = 700/4 % = 175%
- 70/40 = (70/40) * 100 % = 7000/40 % = 175%
- 0.111 = 0.111 x 100 = 110%
- 0.62 = 0.62 x 100 = 62%
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