(a) show that 3/10 + 2/15 = 13/30 (b) show that 2 5/8 ÷ 1 1/6 = 2 1/4

(a) In order to add or subtract any fractions, they must first have a common denominator. For this example, I will take this to be 30. Looking at 3/10: in order to change the denomintor to 30, we must multiply by 3, therefore we must also do the same for the numerator ie 3/10=(33)/(103)=9/30. Similarly for 2/15, we must multiply top and bottom by 2 ie 2/15=(22)/(152)=4/30. Finally, we add the two together: 9/30 + 4/30 = 13/30, which is what we needed to show.

(b) The first step to solve this is changing the mixed numbers into top heavy fractions. Taking 2 5/8: 2 is equivalent to 16/8, meaning that 2 5/8 = 16/8 + 5/8 = 21/8. Similarly for 1 1/6: 1 = 6/6 so 1 1/6 = 6/6 + 1/6 = 7/6. Now we have 21/8 ÷ 7/6. To divide fractions, we take the reciprocal of the second fraction and multiply the resulting fractions. 21/8 ÷ 7/6 = 21/8 * 6/7 = 126/56. Both top and bottom are divisable by 14, so the fraction simplifies to 9/4. Finally, we must convert this back to a mixed number: 4 goes into 9 twice, remainder 1 so 9/4 = 2 1/4 as required.