Intro to Remainders in a Division Problem

32 &#247 4 = 8. There are 8 books on each shelf.

45 &#247 9 = 5. I have 5 rows.

1 &#247 4 = [ggfrac]1/4[/ggfrac], so each person gets [ggfrac]1/4[/ggfrac] of the pizza.

2 &#247 4 = [ggfrac]2/4[/ggfrac] = [ggfrac]1/2[/ggfrac], so each person gets [ggfrac]1/2[/ggfrac] of a pizza.

I cannot divide evenly.

15 &#247 3 = 5. There is no remainder. 15 &#247 4 = 3 R 3.

I want to ask, 5 times what is equal to 34? 5 × 6 = 30 and 5 × 7 = 35, so I know that I have a remainder when I divide 34 &#247 5. If I want to distribute 34 objects evenly into 5 groups, I now know that I can put 6 objects into each group, and then I have 4 left that cannot be distributed. The answer is 6 with a remainder of 4.

30 &#247 4 = 7 R 2. I can make 7 dresses, and I have 2 meters of fabric leftover. Maybe I can make a shirt!

46 &#247 10 = 4 R 6. I can fill 4 boxes and then I have 6 apples leftover. I still need a box for those apples, although it will not be full. I need 5 boxes in total.

7 &#247 3 = 2 R 1. Each person gets 2 bowls of soup, and then there is one bowl left to be shared. The contents of one bowl can be divided by 3, and 1 &#247 3 = [ggfrac]1/3[/ggfrac]. So in total, each person gets 2[ggfrac]1/3[/ggfrac] bowls of soup. Then there is no remainder left!