A fraction becomes 1/2, when 1 is subtracted from the numerator and it becomes 1/4 ,when 8 is added to its denominator.Find the fraction About the author Lydia
Answer: The value of Fraction is [tex]\frac{3}{4}[/tex]. Step-by-step explanation: Let us assume Numerator as= x Let us assume Denominator as= y According to the question the first equation is ⇒[tex]\frac{x-1}{y} =\frac{1}{2}[/tex] ⇒[tex]2(x-1)=y(1)[/tex] ⇒[tex]2x-2=y[/tex] ⇒[tex]2x-y=2[/tex] —1st equation According to the question the Second equation is ⇒[tex]\frac{x}{y+8} =\frac{1}{4}[/tex] ⇒[tex]4(x)=(y+8)1[/tex] ⇒[tex]4x=y+8[/tex] ⇒[tex]4x-y=8[/tex]—2nd equation Solve equation one and two [tex](4x-y=8)-(2x-y=2)[/tex] The result is [tex]2x=6[/tex] ⇒[tex]x=\frac{6}{2}[/tex] ⇒[tex]x=3[/tex] Substitute x value in 1st equation ⇒[tex]2(3)-y=2[/tex] ⇒-[tex]y=2-6[/tex] ⇒[tex]y=4[/tex] The value of Numerator is 3. The value of denominator is 4. The value of Fraction is [tex]\frac{3}{4}[/tex]. Reply
Let the fraction be, [tex]\frac{x}{y}\\\\\\[/tex] Now, [tex]{{\frac{x-1}{y} =\frac{1}{2}} \\\\\ \: \: and \: \: {\frac{x}{y+8}=\frac{1}{4} }} \right. \\\\\frac{x-1}{y} = \frac{1}{2}\\\\2x – 2=y \: \: \: \: \\2x-y =2 .. (1)\\\\\frac{x}{y+8}=\frac{1}{4}\\\\4x= y+8\: \: \: \: \\4x-y=8 .. (2)\\\\\\\\\\Subtracting\: (1) from (2)\\\\(1)\: \: 2x – y=2 \\-\:\: \: 4x-y=8\\= -2x=-6\\x=\frac{-6}{-2} \\x=3\\\\and,\: 4x= y+8\\\:\:\:\:\: 4\times 3=y+8\\y=12-8=4\\\\[/tex] [tex]Hence, \: \frac{x}{y} =\frac{3}{4}[/tex] Reply
Answer:
The value of Fraction is [tex]\frac{3}{4}[/tex].
Step-by-step explanation:
Let us assume Numerator as= x
Let us assume Denominator as= y
According to the question the first equation is
⇒[tex]\frac{x-1}{y} =\frac{1}{2}[/tex]
⇒[tex]2(x-1)=y(1)[/tex]
⇒[tex]2x-2=y[/tex]
⇒[tex]2x-y=2[/tex] —1st equation
According to the question the Second equation is
⇒[tex]\frac{x}{y+8} =\frac{1}{4}[/tex]
⇒[tex]4(x)=(y+8)1[/tex]
⇒[tex]4x=y+8[/tex]
⇒[tex]4x-y=8[/tex]—2nd equation
Solve equation one and two
[tex](4x-y=8)-(2x-y=2)[/tex]
The result is [tex]2x=6[/tex]
⇒[tex]x=\frac{6}{2}[/tex]
⇒[tex]x=3[/tex]
Substitute x value in 1st equation
⇒[tex]2(3)-y=2[/tex]
⇒-[tex]y=2-6[/tex]
⇒[tex]y=4[/tex]
The value of Numerator is 3.
The value of denominator is 4.
The value of Fraction is [tex]\frac{3}{4}[/tex].
Let the fraction be,
[tex]\frac{x}{y}\\\\\\[/tex]
Now,
[tex]{{\frac{x-1}{y} =\frac{1}{2}} \\\\\ \: \: and \: \: {\frac{x}{y+8}=\frac{1}{4} }} \right. \\\\\frac{x-1}{y} = \frac{1}{2}\\\\2x – 2=y \: \: \: \: \\2x-y =2 .. (1)\\\\\frac{x}{y+8}=\frac{1}{4}\\\\4x= y+8\: \: \: \: \\4x-y=8 .. (2)\\\\\\\\\\Subtracting\: (1) from (2)\\\\(1)\: \: 2x – y=2 \\-\:\: \: 4x-y=8\\= -2x=-6\\x=\frac{-6}{-2} \\x=3\\\\and,\: 4x= y+8\\\:\:\:\:\: 4\times 3=y+8\\y=12-8=4\\\\[/tex]
[tex]Hence, \: \frac{x}{y} =\frac{3}{4}[/tex]