Explanation:
remember : to convert a fraction of one denominator into a fraction of another denominator, we need to multiply both (numerator and denominator) by the same factor, so that the denominator changes to the desired number, and the overall value of the fraction remains unchanged.
4 1/3 - 8
first I convert the mixed number into a full fraction :
4 1/3 = (4×3 + 1)/3 = 13/3
then, to be able to subtract 8, I need to convert 8 into a fraction with the same denominator as 13/3 :
8 = (8×3)/3 = 24/3
so, now I can do the subtraction :
13/3 - 24/3 = -11/3
-11/3 = -3 remainder 2 = -(3×3 + 2)/3 = -3 2/3
5 2/5 - (-2 4/15)
again, we convert all mixed numbers into full fractions :
5 2/5 = (5×5 + 2)/5 = 27/5
2 4/15 = (2×15 + 4)/15 = 34/15
now we need to bring both to the same denominator, and because 5 is a factor or 15, we can bring both to fractions of 1/15, for which we only need to transform the first fraction :
27/5 = 27/5 × 3/3 = 81/15
so, the subtraction is actually
81/15 - (-34/15) = 81/15 + 34/15 = 115/15 = 23/3
23/3 = 7 remainder 2 = (7×3 +2)/3 = 7 2/3