Question

The denominator of a rational number is greater than its numerator by 6. If the numerator is increase
by 15 and the denominator is decreased by 2, the number obtained is 7/2. Find the rational number.​

Answer 1

Answer:

13/21

Step-by-step explanation:

let numerator be x  

Then,

Denominator = x+8

ATQ,

⇒x+17/x+8-1=3/2  

⇒x+17/x+7=3/2  

⇒2(x+17)=3(x+7)  

⇒2x+34=3x+21

⇒34-21=3x-2x    

⇒13=x  

∴x/x+8

=13/21

Answer 2

Correct Question : -

The denominator of a rational number is greater than its numerator by 8. If numerator is increased by 17 and denominator is decreased by 1 , the number obtained is 3/2 . Find the rational number ?

- : Answer : -

Given : -

The denominator of a rational number is greater than its numerator by 8.

If numerator is increased by 17 and denominator is decreased by 1 , the number obtained is 3/2 .

Required to find : -

Rational number ?

Solution : -

The denominator of a rational number is greater than its numerator by 8.

If numerator is increased by 17 and denominator is decreased by 1 , the number obtained is 3/2 .

we need to find the original fraction ?

So,

Here we need to use the basic knowledge of linear equations in 1 variable to solve this question .

Here,

Let the numerator be x

Denominator is great than the numerator by 8 = x + 8

so,

➝ Rational number = x/x + 8

According to problem ;

Consider the 2nd statement ;

If numerator is increased by 17 and denominator is decreased by 1 , the number obtained is 3/2 .

This implies ;

➝ x + 17/x + 8 - 1 = 3/2

➝ x + 17/x + 7 = 3/2

By cross multiplication ;

➝ 2 ( x + 17 ) = 3 ( x + 7 )

➝ 2x + 34 = 3x + 21

➝ 2x - 3x = 21 - 34

➝ - x = - 13

Taking - ( minus ) common on both sides

➝ - ( x ) = - ( 13 )

- ( minus ) gets cancelled on both sides

➝ x = 13

Hence,

• Value of x = 13

Numerator = x = 13

Denominator = x + 8 = 13 + 8 = 21

Therefore,

• Rational number = 13/21

Additional Information :

Question

What is a linear equation in one variable.

Answer

It is an equation which consists of only one variable in it .

The equations are bit easy to solve .

example :-

2x + 3 = 0 , 3x - 6 = 2 etc. are some linear equations in one variable .

Question

What is linear equation in 2 variables

Answer

It is an equation which consists of 2 variables in it .

These equations are little bit complicated to sole .

But, we have different methods to solve them .

Example :-

3x + 2y = 0 , 5x + 6y = 2 , etc. are some linear equations in 2 variables .

The common methods which are used to solve the linear equations in two variables are ;

• Elimination method

• Substitution method

• Cross multiplication method .

The equations can also be plotted on a graph .

Moreover,

The linear equations will further become as algebraic expressions and then the algebraic expressions will be modified in order to become polynomials.

So,

All algebraic expressions , polynomials are nothing but linear equations .