4) The denominator of a fraction is 6 more than its numerator. If 2 is added to both the numerator and the denominator, the fraction be

Question

4) The denominator of a fraction is 6 more than its numerator. If 2 is added to both the
numerator and the denominator, the fraction becomes Find the fraction.​

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Madeline 2 weeks 2021-09-13T16:24:50+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-09-13T16:26:07+00:00

    Question:

    The denominator of a fraction is 6 more than its numerator. If 2 is added to both the numerator and the denominator, the fraction becomes Find the fraction.

    Answer:

    \underline\bold{\frac{2}{5}} \: is \: the \: fraction

    Step-by-step explanation:

    The denominator of a fraction is 6 more than its numerator.

     \implies Numerator = x

     \implies Denominator = x + 6

    Now, 2 is added to both the numerator and the denominator

     \implies Numerator = x  + 2

     \implies Denominator = x + 8

    Thus, the equation is

     \implies\frac{x + 2}{x + 8}  =  \frac{1}{2}

    \implies 2(x + 2) = 1(x + 8)

    \implies 2x + 4 = x + 8

    \implies 2x - x = 8 - 4

    \implies\boxed{x = 4}

    Also, \: given \: \boxed{y=x+6}

    Substitute the value of x = 4

    \implies y = 4 + 6

     \implies \boxed{y = 10}

    Fraction =  \frac{x}{y}

     \implies  \frac{4}{10}

     \implies  \boxed{\frac{2}{5} }

     \therefore \boxed{\frac{2}{5} } \: is \: the \: fraction.

    Hint:

    Hint given in the question :

    ★ The denominator of a fraction is 6 more than its numerator.

    ★ Fraction =  \frac{x}{y}

    0
    2021-09-13T16:26:08+00:00

    CORRECT QUESTION.

    The denominator of a fraction is 6 more than

    it’s numerator. if 2 is added to both the numerator

    and the denominator the fraction become 1/2.

    find the friction.

    EXPLANATION.

    • GIVEN

    y = x + 6 [ denominator of fraction is 6 more than

    it’s numerator ]

    According to Given question

    equation will be written as :-

    x + 2 / x + 6 + 2 = 1/2

    x + 2 / x + 8 = 1/2

    2x + 4 = x + 8

    x = 4

    put the value of x in equation

    we get,

    y = 4 + 6

    y = 10

    hence,

    fraction will be written as

    x/y = 4/10 = 2/5

    Hence,

    fraction will be = 2/5

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