In Mathematics, sometimes you get complicated sums and long calculations, which is very common in fraction questions. Some students find it more difficult and take a long time to solve. But don’t worry, this article on simplification in Mathematics has a resolution for you. It will help you to simplify the fractions in easy ways. In this article, you'll learn what simplification is, how to simplify fractions, and the steps involved in simplifying fractions. You'll also find out how to do it step by step.
What is Simplification?
As you know, simplification of mathematical problems helps increase scores in exams and is also used in daily life like in malls you get 35% discount, flat discount or 20% discount up to Rs 100. You only need to use fundamental simplification rules to solve equations in this part.
’BODMAS’ Rule:
This rule depicts the correct sequence in which the operations are to be executed, so as to find out the value of a given expression.
Here,
‘B’ stands for ’bracket’,
’O’ for ‘of’,
‘D’ for’ division’
‘M’ for ‘multiplication’,
‘A’ for ‘addition’ and
‘S’ for ‘subtraction’.
Thus, in simplifying an expression, first of all the brackets must be removed, strictly in the order (...), {...} and [...].
After removing the brackets, we must use the following operations strictly in the order:
-
of
-
division
-
multiplication
-
addition
-
subtraction.
​
Modulus of a real number:
Modulus of a real number a is defined as |a| = {a, if a>0 - a, if a<0
Thus, |5|=5 and |-5|=-(-5) =5.
Vinculum (or bar):
When an expression contains Vinculum, before applying the ‘BODMAS’ rule, we simplify the expression under the Vinculum.
How to Simplify Fractions Stepwise
​
Following is the process of how to simplify fractions step by step -
Step 1: Write the denominator and numerator's factors in step one. The ratio between 8 and 24 is 1 through 8 factors: 2; 4; and 8.1, 2, 3, 4, 6, 8, 12, and 24 are the 24 factors.
Step 2: Verify the shared factors between the denominator and the numerator. 1, 2, 4, and 8 are the common factors of the numbers 8 and 24.
Step 3: Subtract the common components from the numerator and denominator until there is only one remaining.
The fraction that is so obtained is in its most basic form. Starting with a division of 2, ----- becomes
------
------ = -----.
------
------
Up until the point where we can no longer divide by 2, we will keep doing so. Thus, ------- = --------,
------
------
which is equal to ------- = -------
------
The fraction ----- is thus represented by its simplest form, -------
​
Let's return to the original issue of how to make the fraction ------ simpler. Between 8 and 24, 8 is their largest-
common factor. The simplest form of the fraction, which is ------, can be obtained by immediately dividing the numerator, 8, by the denominator, 24, and vice versa.
8
24
8
2
242
4 12
4 2
122
2 6
2 2
6 2
1 3
8
24
8
24
1 3
1 3
SOLVED EXAMPLES
Ex. 1. Simplify: (I) 5005 - 5000 + 10
(ii) 18800 + 470 + 20
Sol. (i) 5005 - 5000 + 10 = 5005 - (5000/10)
= 5005 - 500
= 4505.
(ii) 18800 + 470 + 20 = (18800/470) + 20
= 40/20
= 2.
Ex. 2. Simplify: b - [b - (a + b) - {b - (b - a - b)} + 2a]
Sol. Given expression= b - [b - (a + b) - {b - (b - a + b)} +2a]
= b - [b - a - b - {b - 2b + a} +2a]
= b - [- a - {b - 2b + a + 2a}]
= b - [- a - {- b + 3a}]
= b - [- a + b - 3a]
= b - [- 4a + b]
= b + 4a - b
= 4a.
Ex. 3. What value will replace the question mark in the following equation?
4 ----- + 3 ----- + ? + 2 ----- = 13 ------.
Sol. Let 9/2 + 19/6 + x + 7/3 = 67/5
Then x= (67/5) - (9/2 + 19/6 + 7/3)
= (67/5) - ((27 + 19 + 14) /6)
= ((67/5) - (60/6)
= ((67/5) - 10)
= 17/5
=3 ------
Hence, missing fractions =3 ------
1 3
1 2
1 6
1 3
2 5
2 5