I'll just write some definitions first:
* Mixed numbers are composed a whole number and a fraction, for example, 4 4/5
* Improper fractions are fractions whose numerator is greater than the denominator, for instance, 8/3.
* Numerator is the number above the bar line of a fraction.
* Denominator is the number below the bar line of a fraction.
What we'll do here is to first, change the mixed numbers to improper fractions. To convert them, we multiply the constant by the denominator, then add the product with the numerator, while the denominator stays the same. In the problem, we change both 4 4/5 and 1 7/8 to improper:
4 4/5 = (4*5 + 4)/5 = (20 + 4)/5 = 24/5
1 7/8 = (1*8 + 7)/8 = (8 + 7)/8 = 15/8
We rewrite the expression:
24/5 - 15/8
Now, to perform addition or subtraction of fractions, they should have the same denominator, but looking at them, they don't. So we find the LCD (Least Common Denominator) or the smallest number where it is both divisible by 5 and 8. The LCD is 40 (sometimes they're just equal to their product).
Then we'll change both fractions such that their denominators are 40. We divide the LCD by the denominator, and multiply this by the numerator, with the denominator now equal to 40:
40/5 = 8, thus 8*24/40 = 192/40
40/8 = 5, thus 5*15/40 = 75/40
Finally, to subtract, we just subtract the numerators and retain the denominators:
192/40 - 75/40 = (192 - 75)/40 = 117/40
Sorry, I think I made my solution very long.
Hope this helps~ :3