Q16. The denominator of a rational number is greater than its numerator by 5. If the numerator is increased by 8 and the denominator is decreased by 1, the new number becomes 5/3.Find the original number:
Answers
Given:
• The denominator of a rational number is greater than its numerator by 5.
• If the numerator is increased by 8 and the denominator is decreased by 1, the new number becomes 5/3.
To calculate:
• The original number.
Calculation:
Let us assume the numerator as 'x'. So, the denominator becomes :
- Denominator → x + 5
- Numerator → x
According to the question:
» If the numerator is increased by 8 and the denominator is decreased by 1, the new number becomes 5/3. So,
Here, an equation has been formed. So, at first we'll calculate the value of x and then we'll substitute the value of x in the original number expression in order to find the original number.
[Removing brackets.]
[Performing addition.]
Now, by cross multiplication :
[Performing multiplication.]
Now, substituting the value of x in original fraction.
Therefore, original number is 2/7.
Verification:
As the question states that,
» If the numerator is increased by 8 and the denominator is decreased by 1, the new number becomes 5/3.
So, here :
- LHS =
- RHS =
Solving LHS :
[Dividing denominator & numerator by 2.]
RHS :
Hence,
LHS= RHS
Hence, verified!
Question
The denominator of a rational number is greater than its numerator by 5. If the numerator is increased by 8 and the denominator is decreased by 1, the new number becomes 5/3.Find the original number.
Given
- The denominator of a rational number is greater than its numerator by 5.
- If the numerator is increased by 8 and the denominator is decreased by 1, the new number becomes 5/3.
To Find
- The original number.
Solution
Let the Numerator be x and denominator be ( x + 5)
According to the Question
When numerator is increased by 8 and the denominator by 1,So the fraction 5/3.
So,
Now,
→ 3 (x + 8) = 5 (x + 4)
→ 3x + 24 = 5x + 20
→ 5x - 3x = 24 - 20
→ 2x = 4
→ x = 4/2
→ x = 2
Now,substituting the value of x.
→ x + 5
→ 2 + 5
→ 7