Aptitude Made Simple Fraction
Fraction
Real time example of Fraction
Let us assume you bought 10 chocolates out of which you ate 7
chocolates.
Now if someone ask you how many chocolates you ate and how many are
remaining, it is straight forward you count as natural number and say I ate
7. How many remaining 10-7 = 3
This is very simple and anyone can tell it.
Now assume you bought 1 pizza which has 7 equal parts. Now you ate 4
parts out of it. Now can you say how many pizzas you ate??? You cant say
4 as original pizza was 1 only and how you can ate 4????
Here fraction comes into picture
How many parts were there originally?
7
How many you ate out of them??
4
So you can say you ate 4 parts out of 7 which we represent as 4/7
How many parts remaining??
3
Out of 7 parts, 3 parts are remaining.
So 3/7 is remaining.
If you buy pizza and explain this concept, I believe anyone will understand
concept of Fraction very easily.
Aptitude Made Simple Fraction
Comparing Fractions
Most of us can easily compare Integers but face challenge to compare
fractions
1)Which number is bigger 3 or 5???
Obviously 5 as we know 3 < 5. This is very simple.
Reason for this is when denominator not mentioned it is 1
<
As denominator same we compare numerator only and decide
< (As 5<8)
2)When denominator is not same we should just do cross multiplication
1 5
---- ----
2 3
1 X3 5X2
3 < 10
1 5
---- < ----
2 3
Aptitude Made Simple Fraction
5 3
---- ----
7 8
5X8 3X7
40 > 21
5 3
---- > ----
7 8
Comparing more than 2 Fractions
1 2 3
---- , ---- , -----
2 3 4
As denominator not same comparing numerator wont work
How denominator can be equal??
Take LCm of all denominators
Also find by which number you should multiply each denominator you get
12, multiply respective numerator by same number
1X6 2X4 3X3
-------- , --------- , -----
2X6 3X4 4X3
6 8 9
--- < ---- < -----
12 12 12
1 2 3
---- < ---- < -----
2 3 4
Aptitude Made Simple Fraction
Addition of 2 fractions:
1)When denominator is same. Keep denominator as is and add
numerators
5 3 5+3 8
---- + ---- = ------- = ---
7 7 7 7
8 5 8+5 13
---- + ---- = ------- = ---
3 3 3 3
2) When denominator not same, cross multiply
1 5
---- + ----
2 3
1 + 5 (1 X 3) +(5 X 2) 3 + 10
---- ---- = ------------------------- = ----------
2 3 (2 X 3) 6
= 13
-----
6
Aptitude Made Simple Fraction
Addition of more than 2 fractions
1 2 3
---- + ---- + -----
2 3 4
As denominator not same addition of numerator wont work
How denominator can be equal??
Take LCm of all denominators
Also find by which number you should multiply each denominator you get
12, multiply respective numerator by same number
1X6 2X4 3X3
-------- , --------- , -----
2X6 3X4 4X3
6 8 9 23
--- + ---- + ----- = ----
12 12 12 12
Subtraction of 2 fractions:
1)When denominator is same. Keep denominator as is and add
numerators
5 3 5-3 2
---- - ---- = ------- = ---
7 7 7 7
8 5 8-5 3
---- - ---- = ------- = --- = 1
3 3 3 3
Aptitude Made Simple Fraction
2) When denominator not same, cross multiply
5 1
---- - ----
3 2
5 - 1 (5 X 2) - (1 X 3) 10 - 3
---- ---- = ------------------------- = ----------
3 2 (3 X 2) 6
= 7
-----
6
Anay X 100 = 78%
Multiplication of Fractions
Multiplication is simplest operations for fractions
5 1 Multiply all numerators 5X1 5
---- X ---- = -------------------------------- = -------- = ---
3 2 Multiply all denominators 3 X2 6
3 7 3X7 21
---- X ---- = -------- = -------
5 8 5 X8 40
10 7 9 10 X 7 X 9 630 21 3
---- X ---- X ---- = ----------------- = ------ = ---- = -----
3 20 14 3 X 20 X 14 840 28 4
This causes big number. Instead simplify first and then solve
Aptitude Made Simple Fraction
10 7 9 1 1 3 [Simplified 7 and 14.
---- X ---- X ---- = ---- X ---- X ------ 10 and 20, 3 and 9]
3 20 14 3 2 2
3
----
4
Reciprocal:
How do you stand normally?
Head Upwards
Leg Downwards
Now imagine you are standing on your head
Leg Upwards
Head Downwards
This is nothing but reciprocal. If we interchange numerator and
denominator we get reciprocal (sign need not to be changed)
Find Reciprocals
1 7
1) ---- -> ---- = 7
7 1
2) -4 -11
------ -> -----
11 4
Aptitude Made Simple Fraction
Fractions Division:
7/2
-----
1/3
Keep first fraction as is
Get reciprocal of 2nd fraction
Multiply both of them
Keep 7/2 as is
Reciprocal of 1/3 is 3
Multiply them
7 3 21
---- X = ----
2 2
Finding Equivalent fractions
Equivalent means equal (=)
If we multiply any number by 1 we get same number. So we say it is
equivalent number
2 -> 2 X 1 = 2 , 10 -> 10 X 1 = 10
Can you imagie different ways of showing 1 as fraction???
2 3 5 10
----- , --- , ----, ----- etc.
2 3 5 10
Aptitude Made Simple Fraction
Find 3 equivalent fraction of 3
---
5
3 2 6
------ X ---- = ----
5 2 10
3 10 30
------ X ---- = ----
5 10 50
3 5 15
------ X ---- = ----
5 5 25
Finding fractions between given range
1) Find fractions between 2/7 and 9/7
It is veery simple as denominator is same
3 4 5 6 7 8
---- , --- , --- , --- , ----, ---
7 7 7 7 7 7
2)Find 20 fractions between 2/7 and 4/7
Denominator same but we can see only 1 fraction that is 3/7
If we want more fractions between given range, we should have big
difference in numerator and so big denominator
Get equivalent fraction by multiplying by big number like 50
2 X 50 100 4 X 50 200
--------- = ------ ----------- = ------
7 X 50 350 5 X 50 350
Aptitude Made Simple Fraction
Everything from 101 199
------ to ----- will come between 2/7 and 4/7
350 350
Converting to Simplest form
Simplest form means keep dividing numerator and denominator by
common factor till largest common factor is 1
32 16 8 4 2
----- when divided by 2 ---- -> ----- -> --- -> -----
48 24 12 6 3
Instead you can find HCF of Numerator and denominator and divide both of
them by it
HCF of 32 and 48 is 16
32 / 16 2
---------- = ----
48 / 16 3
