Fraction 40 and 60 simplified
Introduction :
Fraction is defined as the ratio of numerator to the denominator , that is it can be written in the form of `p/q` where p is the numerator and q is the denominator. Fraction is nothing but the part of the whole. In this section we shall discuss the simplification of fraction `40/60` and `60/40` .
Methods to simplify fraction:
The following are the ways to simplify the fractions.
Method 1:
Simplify fraction `40/60` and `60/40` .
Solution:
The given fraction is `40/60` and `60/40`
We can write 40 as 20 x 2……….(1)
We can write 20 as 10 x 2……….(2)
We can write 10 as 5 x 2…………(3)
Substitute (3) in (2) we get 20 = (10 x 2) = (5 x 2) x 2………(4)
Substitute (4) in (1) we get 40 = 20 x 2 = ((5 x 2) x 2) x 2.
Therefore 40 can be written as 40 = 2 x 2 x 2 x 5.
Similarly for 60:
We can write 60 as 30 x 2……….(1)
We can write 30 as 15 x 2……….(2)
We can write 15 as 5 x 3…………(3)
Substitute (3) in (2) we get 30 = (15 x 2) = (5 x 3) x 2………(4)
Substitute (4) in (1) we get 60 = 30 x 2 = ((5 x 3) x 2) x 2.
Therefore 60 can be written as 60 = 2 x 2 x 3 x 5.
Let us simplify `40/60` :
`40/60` = `(2 xx 2 xx 2 xx 5)/( 2 xx 2 xx 3 xx 5)` .
= `((2 xx 2 xx 5 )xx(2))/((2 xx 2 xx 5 )xx(3))`
= `2/3` , where `(2 xx 2 xx 5 )` cancels each other.
The simplified fraction for `40/60` is `2/3`
Let us simplify `60/40` :
`60/40` = `(2 xx 2 xx 3 xx 5)/( 2 xx 2 xx 2 xx 5)` .
= `((2 xx 2 xx 5 )xx(3))/((2 xx 2 xx 5 )xx(2))`
= `3/2` , where `(2 xx 2 xx 5 )` cancels each other.
The simplified fraction for `60/40` is `3/2` .
Fraction is defined as the ratio of numerator to the denominator , that is it can be written in the form of `p/q` where p is the numerator and q is the denominator. Fraction is nothing but the part of the whole. In this section we shall discuss the simplification of fraction `40/60` and `60/40` .
Methods to simplify fraction:
The following are the ways to simplify the fractions.
Method 1:
- Find out a common factor of the numerator and denominator. A common factor is nothing but a number that will divide into both numbers equally. For example three is a common factor of 6 and 15.
- Then divide both the numerator and denominator by that common factor.
- Replicate this procedure until there is an end to common factors.
- The fraction is simplified when down with common factors subsist.
- Find out the Greatest Common Factor (abbreviated as G.C.F) of the numerator and denominator
- Divide the fraction ,that is both the numerator and the denominator by the Greatest Common Factor.
Simplify fraction `40/60` and `60/40` .
Solution:
The given fraction is `40/60` and `60/40`
We can write 40 as 20 x 2……….(1)
We can write 20 as 10 x 2……….(2)
We can write 10 as 5 x 2…………(3)
Substitute (3) in (2) we get 20 = (10 x 2) = (5 x 2) x 2………(4)
Substitute (4) in (1) we get 40 = 20 x 2 = ((5 x 2) x 2) x 2.
Therefore 40 can be written as 40 = 2 x 2 x 2 x 5.
Similarly for 60:
We can write 60 as 30 x 2……….(1)
We can write 30 as 15 x 2……….(2)
We can write 15 as 5 x 3…………(3)
Substitute (3) in (2) we get 30 = (15 x 2) = (5 x 3) x 2………(4)
Substitute (4) in (1) we get 60 = 30 x 2 = ((5 x 3) x 2) x 2.
Therefore 60 can be written as 60 = 2 x 2 x 3 x 5.
Let us simplify `40/60` :
`40/60` = `(2 xx 2 xx 2 xx 5)/( 2 xx 2 xx 3 xx 5)` .
= `((2 xx 2 xx 5 )xx(2))/((2 xx 2 xx 5 )xx(3))`
= `2/3` , where `(2 xx 2 xx 5 )` cancels each other.
The simplified fraction for `40/60` is `2/3`
Let us simplify `60/40` :
`60/40` = `(2 xx 2 xx 3 xx 5)/( 2 xx 2 xx 2 xx 5)` .
= `((2 xx 2 xx 5 )xx(3))/((2 xx 2 xx 5 )xx(2))`
= `3/2` , where `(2 xx 2 xx 5 )` cancels each other.
The simplified fraction for `60/40` is `3/2` .