answer:If Tom divided 2 apples into 8 slices each, then he has a total of 2 * 8 = 16 apple slices. Tom gave away 3/8ths of the slices, which is 3/8 * 16 = 6 slices. So, Tom had 16 - 6 = 10 slices remaining. Tom then consumed half of the remaining slices, which is 10/2 = 5 slices. Therefore, Tom has 10 - 5 = 5 apple slices left. 5 The answer is: 5

answer:We have two cases to consider: x + 5 = 20 and x + 5 = -20. For the first case, we have x = 15. For the second case, we have x = -25. The positive difference between these two solutions is 15 - (-25) = boxed{40}. The answer is: 40

answer:We simplify the numerator first: 3 times 4 = 12. Then, we divide the numerator by the denominator: dfrac{12}{6} = boxed{2}. The answer is: 2

answer:If three builders can construct a cottage in 8 days, this means that it takes 3 builders x 8 days = 24 builder-days to complete the cottage. If six builders are working at the same rate, the number of builder-days needed to complete the cottage remains the same. Therefore, it will still take 24 builder-days to complete the cottage. Since there are now six builders, we can divide the total number of builder-days by the number of builders to find the number of days it will take to complete the cottage. 24 builder-days / 6 builders = 4 days. So, it will take six builders, working at the same rate, 4 days to build a cottage of the same size. 4 The answer is: 4