If the numerator of a fraction is increased by 2 and the denominator by 1, it becomes 5/8 and if the numerator and denominator of the same fraction are each increased by 1, the fraction becomes 1/2.
Hence, the fraction whose numerator is [tex]2[/tex] less than the denominator and becomes [tex]\frac{1}{2}[/tex] if the denominator is increased by [tex]1[/tex] is [tex]\frac{3}{5}[/tex].
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Answer:
If the numerator of a fraction is increased by 2 and the denominator by 1, it becomes 5/8 and if the numerator and denominator of the same fraction are each increased by 1, the fraction becomes 1/2.
The fraction is [tex]\frac{3}{5}[/tex].
Given,
Numerator is [tex]2[/tex] less than denominator.
Fraction is [tex]\frac{1}{2}[/tex] if the denominator is increased by [tex]1[/tex].
To find,
The fraction.
Solution,
Let the denominator be [tex]x[/tex].
Then Numerator will be [tex]x-2[/tex].
According to the question,
[tex]\frac{x-2}{x+1} =\frac{1}{2}\\ 2(x-2)=x+1\\ 2x-4=x+1\\ x=5[/tex]
and the fraction will be:
[tex]=\frac{5-2}{5} \\ =\frac{3}{5}[/tex]
Hence, the fraction whose numerator is [tex]2[/tex] less than the denominator and becomes [tex]\frac{1}{2}[/tex] if the denominator is increased by [tex]1[/tex] is [tex]\frac{3}{5}[/tex].