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In this class, we will learn how to subtract two simple fractions of the form a/b and c/d in a step by step solution, with well detailed examples.
Subtraction of Two Simple Fractions
Consider two fractions of form a/b and c/d.
We have to find their difference: (a/b) - (c/d).
First, we will learn how to find the denominator of the subtraction operation, and then we will learn how to find the numerator of the subtraction operation.
Denominator
The denominator is the product of the denominators of the two given fractions.
Denominator = b*d
Numerator
The numerator is the difference of { product of first numerator (a) with second denominator (d), and the product of second numerator (c) with first denominator (b) }.
Numerator = a*d - b*c
Result
Therefore, the subtraction of the two fractions is
(a/b) - (c/d) == (a*d - b*c)/(b*d)
Examples
1. Find the subtraction of the fractions (2/3) - (4/5).
Answer
Given:
First fraction a/b is 2/3.
Second fraction c/d is 4/5.
Find:
We have to find (2/3) - (4/5).
Formula:
Let us use the formula to find the difference of two fractions.
(a/b) - (c/d) == (a*d - b*c)/(b*d)
Calculation:
Substitute the values: a=2, b=3, c=4, d=5.
(2/3) - (4/5) == (2*5 - 3*4)/(3*5)
Simplify the right hand side expression.
(2/3) - (4/5) == (10 - 12)/15
(2/3) - (4/5) == -2/15
Therefore,
(2/3) - (4/5) == -2/15
2. Find the subtraction of the fractions (3/4) - (7/10).
Answer
Given:
First fraction a/b is 3/4.
Second fraction c/d is 7/10.
Find:
We have to find (3/4) - (7/10).
Formula:
Let us use the formula to find the difference of two fractions.
(a/b) - (c/d) == (a*d - b*c)/(b*d)
Calculation:
Substitute the values: a=3, b=4, c=7, d=10.
(3/4) - (7/10) == (3*10 - 7*4)/(4*10)
Simplify the right hand side expression.
(3/4) - (7/10) == (30 - 28)/40
(3/4) - (7/10) == 2/40
There is a common factor of 2 between the numerator and denominator.
(3/4) - (7/10) == (1*2)/(20*2)
The 2 can be cancelled from the numerator and denominator.
(3/4) - (7/10) == 1/20
Therefore,
(3/4) + (7/10) == 1/20