Question

the denominator of a fraction is 7 cm more than the numerator if 1 is added to the numerator and 6 is added the denominator the value of the fraction will be ,1/2 in the numerator and denominator​

Answer 1

$\bf \underline{ \underline{\maltese\:Given} }$

The denominator of a fraction is 7 cm more than the numerator.

If 1 is added to the numerator and 6 is added to the denominator, the value of the fraction becomes 1/2.

$\bf \underline{ \underline{\maltese\:To \: find } }$

$\sf \implies Original \: fraction = \: ?$

$\bf \underline{ \underline{\maltese\:Solution } }$

$\sf Let \: us \: assume \: that,$

$\sf \implies Numerator \: of \: the \: fraction \: be \: x.$

$\bf \implies Then, \sf\: the \: denominator \: will \: be \: x+7.$

$\sf According \: to \: question,$

$\sf Equation : \bf \red{ \dfrac{x + 1}{(x + 7) + 6} = \dfrac{1}{2} }$

$\sf \implies \dfrac{x + 1}{x + 13} = \dfrac{1}{2}$

$\sf Doing \: cross \: multiplication,$

$\sf \implies (x + 1) \times 2 = (x + 13) \times 1$

$\sf \implies 2x + 1 = x + 13$

$\sf \implies 2x + 1 - x = 13$

$\sf \implies x + 2 = 13$

$\sf \implies x = 13 - 2$

$\sf \implies x = 11$

$\bf \underline{Now},$

$\sf \implies Numerator \: (x) = \bf 11$

$\sf \implies Denominator \: (x+7) = \bf (11+7) = 18$

$\bf \underline{Therefore},$

$\implies \underline{\boxed{ \sf Original \: fraction = \dfrac{11}{18} }}$

━━━━━━━━━━━━━━━━━━━━━━━━━━

$\bf \underline{ \underline{\maltese\:Varification } }$

To verify the answer just write 11 in place of x.

$\sf \implies \dfrac{x + 1}{(x + 7) + 6} = \dfrac{1}{2}$

$\sf \implies \dfrac{11+ 1}{(11+ 7) + 6} = \dfrac{1}{2}$

$\sf \implies \dfrac{12}{11+13} = \dfrac{1}{2}$

$\sf \implies \cancel\dfrac{12}{24} = \dfrac{1}{2}$

$\sf \implies \dfrac{1}{2} = \dfrac{1}{2}$

$\bold{\longrightarrow} \:\large{\tt \red{Hence\:Verified\:!}}$

Answer 2

Answer:

• The numerator and the denominator are 11 and 13 respectively

Step-by-step explanation:

Given:

• The denominator of a fraction is 7 more than the numerator
• if 1 is added to the numerator and 6 is added the denominator the value of the fraction will be 1/2

To Find:

• The numerator of the original fraction
• The denominator of the original fraction

Assumptions:

• Let the numerator be x
• Let the denominator be x + 7

Solution:

The original fraction will be,

$\rightarrow \tt \qquad \dfrac{x}{x + 7}$

According to the question,

$\rightarrow \tt \qquad \dfrac{x+ 1}{x+ 7 + 6} = \dfrac{1}{2}$

$\rightarrow \tt \qquad 2(x+ 1 ) = 1(x + 7 + 6)$

$\rightarrow \tt \qquad 2(x+1) = 1(x + 13)$

$\rightarrow \tt \qquad 2x + 2 = x + 13$

$\rightarrow \tt \qquad 2x-x = 13 - 2$

$\rightarrow \tt \qquad {\pink{\boxed{\frak{x = 11}}}\purple\bigstar}$

The numerator and the denominator will be,

$\nrightarrow \sf \qquad Numerator = x = 11$

$\nrightarrow \sf \qquad Denominator = x + 7 = 18$

Therefore:

• ${\pink{\boxed{\tt{Original \; fraction = \dfrac{11}{13} }}}}$