The denominator of a rational number is greater than its numerator by 8. If the numerator is increased by 17 and the denominator is decreased by 1, the number obtained is 3/2. Find the rational number.
The fraction is a part of a whole expressed as N/D.
Answer: The required rational number is 13/21.
Let's find out the rational number with the given conditions.
Assume the numerator of the fraction as a variable.
- Use the first condition to express the denominator in the form of a variable
- Use the second condition to form the equation.
Let the numerator of the rational number be x.
Given that, the denominator of the rational number is 8 more than the numerator.
Then, denominator = (x + 8)
x / (x + 8) is the rational number.
Given that, (N + 17) / (D - 1) = 3/2
[(x) + 17] / [ (x + 8) - 1] = 3/2
[x + 17 ] / [ x + 7] = 3/2
By cross-multiplication, we get:
2(x + 17) = 3(x + 7)
2x + 34 = 3x + 21
34 - 21 = 3x - 2x
13 = x
Numerator of the rational number: x = 13
Denominator of the rational number: x + 8 = 13 + 8 = 21
Rational number = 13/21