Final answer:
To obtain a fraction equal to 5/4 from 7/4, you need to add the same number to both the numerator and the denominator. Therefore, the number that must be added is 8.
Step-by-step explanation:
To obtain a fraction equal to 5/4 from 7/4, we need to add the same number to both the numerator and the denominator. Let's call this number 'x'. So, the new fraction would be (7 + x) / (4 + x). We want this fraction to be equal to 5/4, so we can set up an equation:
(7 + x) / (4 + x) = 5/4
To solve this equation, we can cross-multiply:
4(7 + x) = 5(4 + x)
Simplifying the equation gives us:
28 + 4x = 20 + 5x
Subtracting 4x from both sides:
28 = 20 + x
Subtracting 20 from both sides:
8 = x
Therefore, the number that must be added to both the numerator and the denominator of 7/4 to obtain a fraction equal to 5/4 is 8.