Quantitative Aptitude – Fractions
Fractions represents as the part of a whole number. It shows, how many equal parts are there in that whole number. We use two numbers to write a fraction. One line separate these two numbers, like 1/4. The upper number or top number represents the number of parts and lower number or bottom number represents the total number of parts.
So, in examination you will get two to three questions from fraction chapter. Therefore, prepare this chapter very well. Now, we will discuss few types of fractions –
Types of Fractions
-
Decimal Fraction:
In Decimal Fraction, numbers are written like 0.50, 0.25, 0.70 etc. These numbers are not separated by any separator, but you can convert these fraction as simple fraction. A decimal number 0.50 can be written in decimal fraction as 1/2.
-
Proper Fraction:
A fraction is said to be a Proper Fraction if numerator is less than denominator. For example, 1/2, 5/7, 13/20 etc.
-
Improper Fraction:
A fraction is said to be a Improper Fraction if numerator is bigger than denominator. For example, 4/3, 9/7, 31/23 etc.
-
Mixed Fraction:
A mixed fraction is a combination of two numbers. One of them is an integer number (non zero) and another one is a proper fraction. And, we write a mixed fraction as 31/2 . It’s actually the sum of two different numbers. When we write mixed fraction numbers, we do not add ‘+’ operator. So, 31/2 is actually 3 + 1/2.
Few Examples to Test your Fractions learnings:
Example #1
How much more is
compared to 1?
A. 1/3
B. 1/4
C. 1/6
D. 1/12
Correct Answer is: 1/4 [Option B].
How to Solve:In this example we need to analyze the question and put everything in an equation.
So, in the question it mentioned that sum of
and
is more than 1.
Therefore, the value of sum is bigger than 1.
So, by subtracting 1 from the sum we get, how much more the sum from 1.
Like,
or,
or,
so,
or,
or,
So, the sum is
1/4 more than 1.
Rough Workspace:
Example #2
Between
and
which equation is greater?
A. First Equation
B. Second Equation
C. Both are Equal
D. Can't Determine
Correct Answer is: Both are Equal [Option C].
How to Solve:In this example we need to find out value of both the equations.
So, from the first equation we get,
or,
or,
And, from the first equation we get,
or,
or,
So, no one is greater. Both equations are equal.
Rough Workspace:
Example #3
Arrange the fractions in their descending order:
3/11, 2/15, 7/18, 4/13
A. 4/13 > 7/18 > 2/15 > 3/11
B. 3/11 > 2/15 >7/18 > 4/13
C. 2/15 > 3/11 > 4/13 > 7/18
D. 7/18 > 4/13 > 3/11 > 2/15
Correct Answer is: 7/18 > 4/13 > 3/11 > 2/15 [Option D].
How to Solve:
3/11, 2/15, 7/18, 4/13
So, in this example we need to find out the decimal fraction of every value. And, then compare the decimal value with every other fraction.
So, Decimal fraction of these fractions are:
3/11 = 0.272
2/15 = 0.133
7/18 = 0.388
4/13 = 0.307
Therefore, from the decimal value we can clearly arrange these fractions into their descending order-
7/18 > 4/13 > 3/11 > 2/15
Rough Workspace:
Example #4
Arrange the fractions in their ascending order:
3/5, 2/9, 5/8, 1/3
A. 3/5 < 5/8 < 2/9 < 1/3
B. 5/8 < 2/9 < 3/5 < 1/3
C. 2/9 < 1/3 < 3/5 < 5/8
D. 5/8 < 3/5 < 1/3 < 2/9
Correct Answer is: 2/9 < 1/3 < 3/5 < 5/8 [Option C].
How to Solve:
3/5, 2/9, 5/8, 1/3
So, in this example we need to find out the decimal fraction of every value. And, then compare the decimal value with every other fraction.
So, Decimal fraction of these fractions are:
3/5 = 0.600
2/9 = 0.222
5/8 = 0.625
1/3 = 0.333
Therefore, from the decimal value we can clearly arrange these fractions into their ascending order-
2/9 < 1/3 < 3/5 < 5/8
Rough Workspace:
Example #5
If a fraction is divided by it's reciprocal and then it multiplied by the original fraction, we get the result
. Find out the fraction.
A. 8/3
B. 11/3
C. 11/5
D. 11/9
Correct Answer is: 11/3 [Option B].
How to Solve:So, in this example we need to form the equation and find out the value of that equation.
Let, the resulting fraction is X.
So, according to the question we get,
so,
or,
or,
So, the original fraction here is
11/3.
Rough Workspace:
Example #6
A. 49/113
B. 53/136
C. 68/157
D. 77/169
Correct Answer is: 68/157 [Option C].
How to Solve: In this example we need to simplify the expression to get the result.
So, by evaluating the expression we get,
or,
or,
so,
or,
or,
so,
or,
or,
so,
Therefore, the answer is,
68/157.
Rough Workspace:
Example #7
A. 1.34
B. 1.83
C. 3.17
D. 5
Correct Answer is: 5 [Option D].
How to Solve: So, in this example we need to evaluate the expression and find the value.
And, here we need to apply some basic formula to get the value. You can also use the conventional way of evaluating the value. But, it will be very quick if you use basic math formula.
Let,
is
a and
is
b.
So,
or,
or,
so,
or,
or,
so,
or,
5 Rough Workspace:
Example #8
What is the fraction form of decimal value 87.00013
Correct Answer is: [Option B]. How to Solve:Fraction form of 87.00013
So, in this example we need to find out the fraction form of this decimal value.
So, from the given decimal value we can say that:
or,
or,
or,
Therefore, the fraction form of decimal value 87.00013 is:
Rough Workspace:
Example #9
Which fraction here is equivalent to 35%?
A. 3/14
B. 5/17
C. 7/20
D. 9/22
Correct Answer is: 7/20 [Option C].
How to Solve:So, in this example we need to find out the fraction value of 35%.
And, this is so simple to find out. For instance, we need to write 35% as fraction.
Like,
35%
so,
or,
5 is the HCF of 35 and 100 or,
So, the fraction value of
35% is
7/20.
Rough Workspace:
Example #10
An integer number is 15 more than it's 3/4th part. Find out the integer number.
A. 15
B. 30
C. 45
D. 60
Correct Answer is: 60 [Option D].
How to Solve:So, in this example we need to form the equation and find out the value of that equation.
Let, the integer number be X.
So, according to the question we get,
or,
or,
so,
or,
or,
So, the integer number is
60.
Rough Workspace:
So, if you need any farther help on Fractions, then please let us know. And, definitely we will discuss on those problems here in www.AptitudeTricks.com.