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 1

Find the fraction.​

Answer 1

Answer :-

$\: \large{\boxed{\boxed{\sf{Firstly,\;let's\;understand\;the\;concept\;used\;:-}}}}$

Here the concept of Linear Equations has been used. We are given two unknown values of numerator and denominator of a fraction. We can find it using constant terms.

Let's do it !!

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★ Correct 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 1/2.

Find the fraction.

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★ Solution :-

Given,

» The Denominator = 6 + The Numerator

» 2 + Numerator and Denominator = ½

• Let the numerator of the fraction be x

• Let the denominator of the fraction be y

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~ Case I :-

$\: \large{\sf{:\Longrightarrow\;\;\; y \; = \; \bf{6\;+ \; x}}}$

Let this be equation (i).

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~ Case II :-

$\: \large{\sf{:\Longrightarrow\;\;\; \dfrac{x\;+\;2}{y\;+\;2}\;\; = \;\; \bf{\dfrac{1}{2}}}}$

By cross - multiplication, we get,

$\: \large{\sf{:\Longrightarrow\;\;\; 2x\;+\;4 \; = \; \bf{y\;+\;2}}}$

Let this be equation (ii).

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From equation (i) and (ii), we get,

✏ 2x + 4 = 6 + x + 2

✏ 2x - x = 6 + 2 - 4

✏ x = 4

$\: \large{\boxed{\boxed{\sf{Hence,\;value\;of\;x\;is\;=\;\bf{4}}}}}$

Now using the value of x and equation (i), we get,

✏ y = 6 + 4

✏ y = 6 + 4

✏ y = 10

$\: \large{\boxed{\boxed{\sf{Hence,\;value\;of\;y\;is\;=\;\bf{10}}}}}$

• So the fraction is = x/y = 4/10

$\: \large{\underline{\underline{\rm{Thus,\;the\;fraction\;is\;\;\boxed{\bf{\dfrac{4}{10}}}}}}}$

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★ More to know :-

• Polynomials are the mathematical expressions which are formed using constant and variable terms and where the variable term can be of any degree.

• Linear Equations are the equations formed using constant and variable terms but the variable terms are of single degrees.

Answer 2

Correct 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 1/2. Find the fraction.​

Given,

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 1 /2

To find :

Find the fraction.

Solution :

Let the numerator be m and denominator be (m + 6)

If 2 is added to both numerator and denominator fraction = 1/2

So atq,

⇒ (m + 2)/(m + 6 + 2) = 1/2

⇒ (m + 2)/(m + 8) = 1/2

⇒ 2m + 4 = m + 8

⇒ 2m - m = 8 - 4

⇒ m = 4

So,

⇒ Numerator , m = 4

⇒ Denominator, m + 6 = 4 + 6 = 10

So fraction = 4/10

∴ Required fraction = 4/10