Final answer:
The number that must be subtracted from the numerator and added to the denominator of 13/8 to result in a fraction equivalent to 2/5 is 7.
Step-by-step explanation:
The question asks to find a number which, when subtracted from the numerator of 13/8 and added to the denominator, results in a fraction equivalent to 2/5. Let's denote the unknown number as 'x'. So we have the transformed fraction as (13 - x) in the numerator and (8 + x) in the denominator.
We set up the equation based on the given condition:
- (13 - x) / (8 + x) = 2/5.
To find the value of 'x', we cross-multiply:
- 5(13 - x) = 2(8 + x)
- 65 - 5x = 16 + 2x
- 7x = 49
- x = 7
Therefore, the number that must be subtracted from the numerator and added to the denominator to make 13/8 equivalent to 2/5 is 7.