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

Given that:

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

To Find:

• The fraction.

We know that:

• Fraction = Numerator / Denominator

Let us assume:

• Numerator be x.
• Denominator = x + 7
• Fraction = x / (x + 7)

When 1 is added to the numerator and 6 is added the denominator.

• Numerator = x + 1
• Denominator = x + 7 + 6

Finding the value of x:

According to the question.

⟶ (x + 1) / (x + 7 + 6) = 1 / 2

⟶ (x + 1) / (x + 13) = 1 / 2

Cross multiplication.

⟶ 2 (x + 1) = 1 (x + 13)

⟶ 2x + 2 = x + 13

⟶ 2x - x = 13 - 2

⟶ x = 11

∴ The value of x = 11

Finding the fraction:

• Fraction = x / (x + 7)
• Fraction = 11 /(11 + 7)
• Fraction = 11 / 18

Hence,

• The required fraction is 11/18.

Answer 2

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$\red{\bigstar}\underline{\underline{\textsf{\textbf{ Question\::- }}}}$

• 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.

$\red{\bigstar}\underline{\underline{\textsf{\textbf{ To\:Find\::- }}}}$

• Fraction = ?

$\red{\bigstar}\underline{\underline{\textsf{\textbf{ Answer\::- }}}}$

• Fraction = 11/18

$\red{\bigstar}\underline{\underline{\textsf{\textbf{ Step\:by\:step\:explanation\::- }}}}$

• Let numerator be n. So, denominator is (n + 7), we know that numerator is the number at the top of a fraction and denominator is the number at the bottom of a fraction. So, fraction is n/(n + 7).

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$\red{\bigstar}\underline{\underline{\textsf{\textbf{ Atq, }}}}$

• If 1 is added to the numerator and 6 is added to the denominator, then the value of fraction will be 1/2.

$\red{\bigstar}\underline{\underline{\textsf{\textbf{ Therefore, }}}}$

$\leadsto\qquad\tt \dfrac{n + 1}{n + 7 + 6} = \dfrac{1}{2}$

$\leadsto\qquad\tt \dfrac{n + 1}{n + 13} = \dfrac{1}{2}$

$\red{\bigstar}\underline{\underline{\textsf{\textbf{ By \:cross\:multiplication\::- }}}}$

$\leadsto\qquad\tt 2(n + 1) = 1(n + 13)$

$\leadsto\qquad\tt 2n + 2 = n + 13$

$\leadsto\qquad\tt 2n - n = 13 - 2$

$\leadsto\qquad{\boxed{\frak{\pink{n = 11}}}}\:\purple{\bigstar}$

$\red{\bigstar}\underline{\underline{\textsf{\textbf{ Hence, }}}}$

• Numerator = n = 11. So, denominator = n + 7 = 11 + 7 = 18.

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$\small\therefore\:{\underline{\sf{Hence,\:fraction\:=\:\bf{\frac{Numerator}{Denominator}}\:=\:\frac{11}{18}\:\sf{respectively.}}}}$

$\red{\bigstar}\underline{\underline{\textsf{\textbf{ More\:to\:know\::- }}}}$

$\quad$$\boxed{\begin{minipage}{6 cm}\bf{\dag}\:\:\underline{\textsf{Fraction Rules :}}\\\\\bigstar\:\:\sf\dfrac{A}{C} + \dfrac{B}{C} = \dfrac{A+B}{C} \\\\\bigstar\:\:\sf{\dfrac{A}{C} - \dfrac{B}{C} = \dfrac{A-B}{C}}\\\\\bigstar\:\:\sf\dfrac{A}{B} \times \dfrac{C}{D} = \dfrac{AC}{BD}\\\\\bigstar\:\:\sf\dfrac{A}{B} + \dfrac{C}{D} = \dfrac{AD}{BD} + \dfrac{BC}{BD} = \dfrac{AD+BC}{BD} \\\\\bigstar\:\:\sf\dfrac{A}{B} - \dfrac{C}{D} = \dfrac{AD}{BD} - \dfrac{BC}{BD} = \dfrac{AD-BC}{BD}\\\\\bigstar \:\:\sf \dfrac{A}{B} \div \dfrac{C}{D} = \dfrac{A}{B} \times \dfrac{D}{C} = \dfrac{AD}{BC}\end{minipage}}$

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