Question

the numerator of a fraction is 4 less than its denominator. if the number is decreased by 2 and the denominator is increased by 1 then the fraction become 1/8 find the fraction​

Answer 1

Answer:

The fraction is (3/7).

Step-by-step explanation:

Let the denominator be x, then numerator will be (x - 4)

Thus,

The fraction is (x - 4)/x

Now, according to the Question,

(N - 2)/(D + 1) = (1/8)

Here N and D is nothing but numerator and denominator.

So,

((x - 4) - 2)/(x + 1) = (1/8)

(x - 4 - 2)/(x + 1) = (1/8)

(x - 6)/(x + 1) = (1/8)

Corss multiplying we get,

8(x - 6) = 1(x + 1)

8x - 48 = x + 1

8x - x = 48 + 1

7x = 49

x = 49/7

x = 7

Thus,

The fraction is ((7 - 4)/7) = (3/7)

Hence,

The fraction is (3/7).

Hope it helped and believing you understood it........All the best

Answer 2

$\large{\boxed{\boxed{\sf Let's \: Understand \: Question \: F1^{st}}}}$

Here, we have said that the numerator of a fraction is 4less than its denomiator. an if the numerator is decreased by 2 and the denominator is increased by 1 then the fraction becomes 1/8. Then what will be the real fraction.

$\large{\boxed{\boxed{\sf How \: To \: Do \: It?}}}$

Here, f1st we let the numerator 'x' and denominator 'y'. The going according to the Question numerator is 4less than denominator marking this eq.(1) Now, according to 2nd case After 1 is added to denomiator and 2 is removed from the numerator the fraction becomes 1/8 Now, substituting eq(1) into it. And then solving it we will get the value of 'y' Now, substituting this value in eq(1) we get the value of y also Now, placing this like x/y we will get our required answer.

Let's Do It ⚡

$\huge{\underline{\boxed{\sf AnSwer}}}$

____________________________

Given:-

• Numerator is 4 less than the denominator.
• If numerator is decreased by 2 and numerator is increased by 1 then the fraction becomes = $\sf\dfrac{1}{8}$

Find:-

• What will be the fraction.

Solution:-

Let, the numerator be 'x'

and denominator be 'y'

$\underline{\red{\textsf{Note:}}}$ Here, I m letting numerator as x and denominator as y but you can let According To ur wish.

⌬ Case: 1

Numerator of the fraction is 4 less than the denominator.

$\sf \implies x = y - 4 \quad \big\lgroup Equation\: ..\boxed{ \frak1} \big\rgroup$

Now,

⌬ Case: 2

If numerator is decreased by 2 and the denominator is increased by 1 then the fraction becomes 1/8.

$\sf \implies \dfrac{x - 2}{y + 1} = \dfrac{1}{8}$

$\red\bigstar$ Cross-multiplication

$\sf \implies 8(x - 2) = 1(y + 1)$

$\sf \implies 8x - 16= y + 1$

$\pink\bigstar$ Collect like terms

$\sf \implies 8x= y + 1 + 16$

$\sf \implies 8x= y +17$

$\blue\bigstar$ Using eq.$\bf{\boxed{\frak 1}}$

$\sf \implies 8x= y +17$

$\sf \implies 8(y - 4)= y + 17\quad \footnotesize{\big\lgroup Equation\: \boxed{ \frak1}....\big\{ x = y - 4 \big \}\big\rgroup}$

$\sf \implies 8y - 32= y + 17$

$\purple\bigstar$ Collect like terms

$\sf \implies 8y -y=17 + 32$

$\sf \implies 7y=49$

$\sf \implies y= \dfrac{49}{7}$

$\sf \implies y= 7$

⌾Using value of y in eq.(1)

$\sf \Longrightarrow x = y - 4$

$\sf \implies x = 7 - 4\quad \big\lgroup.... y = 7\big\rgroup$

$\sf \implies x = 3$

$\qquad$__________________________

☃ Fraction = $\bf{\dfrac{x}{y}}$

☃ Fraction = $\bf{\dfrac{3}{7}}$

$\underline{\boxed{ \sf\therefore The \: Fraction \: will \: be \: \dfrac{3}{7}}}$