The numerator of a fraction is 4 less than its denominator. If 2 is added to
Page 3 of 3
the numerator , then the fraction becomes 5
7
. Find the fraction.
Answers
Answer:
The numerator of a fraction is 4 less than its denominator. If 2 is added to
Page 3 of 3
the numerator , then the fraction becomes 5
7
. Find the fraction.
Answer:
Answer:−
The Fraction is \tt{\dfrac{3}{7}}
7
3
\mathfrak{\large{\underline{\underline{\pink{Explanation :-}}}}}
Explanation:−
Given :
Numerator = 4 less than the denominator
If 2 added to the numerator = Fraction turns \tt{\dfrac{5}{7}}
7
5
To Find :
The Fraction
Solution :
Consider the Denominator as x
Numerator = x - 4
★ \boxed{\sf{\purple{\frac{(x - 4) + 2}{x} = \frac{5}{7}}}}
x
(x−4)+2
=
7
5
\sf{\implies} \: \dfrac{(x - 4) + 2}{x} = \dfrac{5}{7}⟹
x
(x−4)+2
=
7
5
\sf{\implies} \: 7(x - 4 + 2) = 5(x)⟹7(x−4+2)=5(x)
\sf{\implies} \: 7x - 28+ 14= 5x⟹7x−28+14=5x
\sf{\implies} \: - 28+ 14= 5x - 7x⟹−28+14=5x−7x
\sf{\implies} \: \cancel- 14= \cancel - 2x⟹
−
14=
−
2x
\sf{\implies} \:x = \dfrac{14}{2}⟹x=
2
14
\sf{\implies}\red{ \: x = 7}⟹x=7
\rule{300}{1.5}
★ Value of x - 4
\sf{\implies} \: 7 - 4⟹7−4
\sf{\implies} \: 3⟹3
Numerator = 3
Denominator = 7
\therefore∴ The Fraction is \tt{\dfrac{3}{7}}
7
3
\rule{300}{1.5}
\mathfrak{\large{\underline{\underline{\pink{Verification :-}}}}}
Verification:−
As it is given in the Question, the Fraction should be \tt{\dfrac{5}{7}}
7
5
when 2 is added to the numerator.
\sf{\implies} \: \dfrac{3 + 2}{7} = \dfrac{5}{7}⟹
7
3+2
=
7
5
\sf{\implies} \: \dfrac{5}{7} = \dfrac{5}{7}⟹
7
5
=
7
5
\therefore∴ The Fraction is \tt{\dfrac{3}{7}}
7
3
Step-by-step explanation:
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