Sample Material of Online Coaching For SSC CGL (Tier - 2) - Fraction
Sample Material SSC CGL TIER-2 Online Coaching
Numerical Aptitude (Chapter - Fraction)
A fraction is a part of the whole (object, thing, region). It forms the part of basic aptitude of a person to have and idea of the parts of a population, group or territory. Aspirants must have a feel of ‘fractional’ thinking. eg, 5/12, here ‘12’ is the number of equal part into which the whole has been divided, is called denominator and ‘5’ is the number of equal parts which have been taken out, is called numerator.
Example1 : Name the numerator of 3/7 and denominator of 5/13.
Solution : Numerator of 3/7 is 3.
Denominator of 5/13 is 13.
Lowest Term of a Fraction
Dividing the numerator and denominator by the highest common element (or number) in them, we get the fraction in its lowest form. eg, To find the fraction 6/14 in lowest form Since ‘2’ is highest common element in numerator 6 and denominator 14 so dividing them by 2, we get 3/7. Which is the lowest form of 6/14.
Equivalent Fractions
If numerator and denominator of any fraction are multiplied by the same number then all resulting fractions are called equivalent fractions. eg, 1/2 ,2/4,3/6,4/8 all are equivalent fractions but 1/2 is the lowest form.
Example 2 : Find the equivalent fractions of 2/5 having numerator 6.
Solution: We know that 2 × 3 = 6. This means we need to multiply both the numerator and denominator by 3 to get the equivalent fraction.
Hence, required equivalent fraction =2/5=(2 x3) / (5x3)=6/15
Addition and Subtraction of Fractions
Here two cases arise as denominators of the fraction are same or not.
Case I: When denominators of the two fractions are same then we write denominator once and add (or subtract) the numerators.
eg, (2/7+3/7)=5/7
Case II: If denominators are different, we need to find a common denominator that both denominators will divide into.
eg, 1/6+3/8
We can write, 1/6=2/12,3/18 =4/24
3/8=6/16 =9/24
(1/6+3/8) =(4/24 +9/24)=13/24
Example 3: Calculate 1/2-3/7
Solution. 1/2=(1x7)/(2x7)=7/14 and 3/7=(3x2)/(7x2)=6/14
1/2-3/7 =7/14-6/14 =1/14
Multiplication and Division of Fractions
To multiply fractions, the numerators are multiplied together and denominators are multiplied together.
eg, 1/6x3/8=(1x3)/(6x8) =3/48=1/16
In division of fraction, the numerator of first fraction is multiplied by the denominator of second fraction and gives the numerators. Also denominator of first fraction is multiplied by the numerator of second fraction and gives the denominator.
eg, (1/6)/(3/8) becomes1/6x8/3 =8/18=4/9
Proper and Improper Fractions
The fractions in which the number in numerator is less than that of denominator, are called proper fractions. Also if the number in numerator is greater than that of denominator, then the fractions are called improper fractions.
eg, 4/3 is an improper fraction while 3/4 is a proper fraction.
Mixed Numbers
A mixed number is that, which contains both a whole number and a fraction.
eg, 55/12,13/4,53/8 are mixed numbers.
Example 4: Which of the following are proper and improper fractions?
(a)7/9
(b)6/5
(c)12/7
(d)5/13
Solution. (a) and (d) are proper fractions as numerator is less than denominator.
Also, (b) and (c) are improper fractions as numerator is greater than denominator.
Example 5: Are7/13 and 29/6 mixed number?
Solution. 7/13 is only a proper fraction as it does not contain any whole number, while 29/6 is a mixed number as it contains ‘4’ as a whole number and 5/6 as a fraction.
Decimal Fractions
The fractions in which denominators has the power of 10 are called decimal fractions.
eg, 0.25
=25/100 =1/4= one quarter
0.1 = nought point one =1/10 = one-tenth.
For converting a decimal fraction into simple fraction, we write the numerator without point and in the denominator, we write ‘1’ and put the number of zeros as many times as number of digits after the point in the given decimal fraction
eg, 0.037 =37/1000,0.1257 =1257/10000
Example 6: Convert the each of the following decimal fractions into simple fractions.
(a) 5.76 (b) 0.023 (c) 257.5
Solution.
(a) 5.76 =576/100 =288/50=144/25
(b) 0.023 =23/1000
(c) 257.5 = = 2575/10=515/2
Addition or Subtraction of Decimal Fractions
In the addition or subtraction of decimal fractions, we write the decimal fractions in such a way that all the decimal points are in the same straight line then these numbers can be add or subtract in simple manner.
Multiplication of Decimal Fractions
To multiply by multiplies (powers) of 10 the decimal point is moved to the right by the respective number of zero.
Example 8: 0.75 × 10 = ?
Solution. 0.75 × 10 = 7.5 (The decimal point is shifted to right by one place)
To multiply decimals by number other than 10. We ignore the decimal point and multiply them in simple manner and at last put the points after the number of digits (from right) corresponding to the given problem.
Example 9: Multiply 8 and 10.24
Solution. First we multiply 8 and 1024
8 × 1024 = 8192
Now, 8 × 10.24 = 81.92 (We put decimal points after two digits from right as in given question).
Example 10: 12.4 × 1.62
Solution. We know that
124 × 162 = 20088
12.4 × 1.62 = 20.088
Division of Decimal Fractions
Division of decimal numbers is the reverse of the multiplication case ie, we move the decimal point to the left while dividing by multiplies of 10.
Example 11: 25.75 ÷ 10 = ?
Solution. 25.75 ÷ 10 = 2.575
When a decimal number is divided by an integer, then at first divide the number ignoring the decimal point and at last put the decimal after the number of digits (from right) according to the given problem.
Example 12: Divide 0.0221 by 17
Solution. First we divide 221 by 17 ie, without decimal 221 ÷ 17 = 13
Now, we put decimal according as in the given problem
0.0221 ÷ 17 = 0.0013
If divisor and dividend both are decimal numbers then first we convert them in simple fraction by putting number of zero in the denominator of both. Then divide by the above manner.
Example 13: Divide by 0.0256 by 0.016
Solution.0.0256/0.016 =(256x1000)/(16x10000) =256/160=25.6/16=1.6
:: Home Assignment for Practice ::
1. If Ö15 = 3.88, then the value of Ö5/3 is:
(a) 1.39
(b) 1.29
(c) 1.89
(d) 1.63
2. If 2805 ÷ 2.55 = 1100, then 280.5 ÷ 25.5 is:
(a) 111
(b) 1.1
(c) 0.11
(d) 11
3. The value of 213 + 2.013 + 0.213 + 2.0013 is:
(a) 217.2273
(b) 21.8893
(c) 217.32
(d) 3.217.32
4. What approximate value should come in place of z in the following question?
2422 + 2.422 + 0.2422 + 0.02422 = z
(a) 670
(b) 575
(c) 580
(d) 680
5. Find a fraction such that if 1 is added to the denominator it reduces to ½ and reduces to 3/5 on adding 2 to the numerator.
(a) 12/25
(b) 13/25
(c) 11/13
(d) 11/25