(4) To add or subtract fractions with different denominators, you need to express each fraction using the same denominator. In other words, you need to find a common denominator first. The smallest one is the best and in this case 24 has been chosen because 4, 6, 8 all divide exactly into it.
4 goes into 24 6 times; 6 goes 4 times; 8 goes 3 times. These numbers are important because you need to multiply the numerators by then to get new numerators. Take 3/4 for example. We use the 6 (24÷4=6 remember?) and multiply by 3=18. So 3/4=18/24. Similarly with the other fractions. That explains where 18, 4 and 3 come from. Because the new fractions now have the same denominator 24, we can write them as 18+4+3 all over 24. That gives you 25.
So we have the improper fraction 25/24. We could write that as 24/24+1/24.
Well, 24/24=1 and so the mixed number becomes 1⅟₂₄.
(12) This needs more of an explanation.
The mixed numbers could be written:
8 + 1/12 - (3 + 1/4).
Then rearranged:
(8 - 3) + (1/12 - 1/4).
8-3=5, so that’s easy for whole numbers.
We need a common denominator for the fraction part, and since 4 goes into 12 3 times, we can use 12 as the common denominator. We write 1/4=3/12, so we have 1/12-3/12=-2/12. Whoops! It’s negative! This is where we need to borrow from the whole number 5. Borrow 1: 5-1=4; and add the borrowed 1 to -2/12 (which cancels down to -1/6). 1-1/6=(6-1)/6=5/6. So the final mixed number answer is 4+⅚=4⅚.