Question

if 1 is subtracted from numerator of a fraction the result is 3/4 and 6 is added to the denominator the result is 1/2. find the fraction by using substitution method​

Answer 1

Answer:

• The original fraction is 7/8.

Step-by-step explanation:

Given that:

• 1 is subtracted from numerator of a fraction the result is 3/4.
• 6 is added to the denominator the result is 1/2.

To Find:

• The fraction by using substitution method.

Let us assume:

• The fraction be x/y.

Where,

• x is numerator of the fraction.
• y is the denominator of the fraction.

When 1 is subtracted from numerator of a fraction:

⇢ (x - 1)/y = 3/4

Cross multiplication.

⇢ 4(x - 1) = 3y

⇢ 4x - 4 = 3y ______(i)

When 6 is added to the denominator:

⇢ x/(y + 6) = 1/2

Cross multiplication.

⇢ 2x = y + 6

⇢ y = 2x - 6 ______(ii)

In equation (i).

⇢ 4x - 4 = 3y

Substituting the value of y from eqⁿ(ii).

⇢ 4x - 4 = 3(2x - 6)

⇢ 4x - 4 = 6x - 18

⇢ - 4 + 18 = 6x - 4x

⇢ 14 = 2x

⇢ x = 14/2

⇢ x = 7

Now in equation (ii).

⇢ y = 2x - 6

Substituting x.

⇢ y = (2 × 7) - 6

⇢ y = 14 - 6

⇢ y = 8

Therefore,

• Fraction = x/y = 7/8

Answer 2

Answer:

Given :-

• If 1 is subtracted from numerator of a fraction the result is 3/4 and 6 is added to the denominator then the result is 1/2.

To Find :-

• What is the fraction.

Method Used :-

• Substitution Method.

Solution :-

Let, the numerator be x

And, the denominator will be y

Then,

$\mapsto$ $\sf\bold{The\: fraction\: be\: =\: \dfrac{x}{y}}$

$\leadsto$ 1 is subtracted from the numerator of a fraction the result is 3/4 :

$\implies \sf \dfrac{x - 1}{y} =\: \dfrac{3}{4}$

By doing cross multiplication we get,

$\implies \sf 4(x - 1) =\: 3(y)$

$\implies \sf 4x - 4 =\: 3y$

$\implies \sf\bold{\purple{4x - 4 =\: 3y\: ------\: (Equation\: No\: 1)}}$

Again,

$\leadsto$ 6 is added to the denominator then the result is 1/2 :

$\implies \sf \dfrac{x}{y + 6} =\: \dfrac{1}{2}$

By doing cross multiplication we get,

$\implies \sf y + 6 =\: 2(x)$

$\implies \sf y =\: 2x - 6$

$\implies \sf\bold{\purple{y =\: 2x - 6\: ------\: (Equation\: No\: 2)}}$

Now, by putting the value of y in the equation no 1 we get,

$\implies \sf 4x - 4 =\: 3y$

$\implies \sf 4x - 4 =\: 3(2x - 6)$

$\implies \sf 4x - 4 =\: 6x - 18$

$\implies \sf 4x - 6x =\: - 18 + 4$

$\implies \sf {\cancel{-}} 2x =\: {\cancel{-}} 14$

$\implies \sf 2x =\: 14$

$\implies\sf x =\: \dfrac{\cancel{14}}{\cancel{2}}$

$\implies \sf\bold{\green{x =\: 7}}$

Again, by putting x = 7 in the equation no 1 we get,

$\implies \sf 4x - 4 =\: 3y$

$\implies \sf 4(7) - 4 =\: 3y$

$\implies \sf 28 - 4 =\: 3y$

$\implies \sf 24 =\: 3y$

$\implies \sf \dfrac{\cancel{24}}{\cancel{3}} =\: y$

$\implies \sf 8 =\: y$

$\implies \sf\bold{\green{y =\: 8}}$

Hence, the required fraction will be :

$\dashrightarrow \sf \dfrac{x}{y}$

• x = 7
• y = 8

$\dashrightarrow \sf\bold{\red{\dfrac{7}{8}}}$

$\therefore$ The fraction is 7/8 .