A fence is built around a rectangular garden that is 8 1/2 feet by 6 1/3 feet Fencing comes in panels. Each panel is 2/3 of a foot wide. How many panels are needed? Explain or show your reasoning

46

Step-by-step explanation:

It's probably easiest to break this into four parts, specifically each side of the rectangle. In a rectangle, unless they are the same size, so a square, each non square rectangle has two long sides and two short sides. Here the long sides are 8 1/2 feet and the short sides are 6 1/3 feet.

Now, we want to see how many panels it takes to measure each side. For instance, let's say you want to lay a panel along a wall that is 2/3 of a foot wide, well it would just take one panel since each panel is just as long. If the wall was 4/3 or 1 and 1/3 feet long you would need two panels because 2/3 + 2/3 = 4/3. This is the kind of thinking you want to use.

So, first let's handle the longer side. Keep in mind there are two of course, but let's solve for one and then double it. So the longer side is 8 1/2 feet. There are two ways to do this. you can keep counting 2/3 until you get to 8 1/2 or you could just divide. If you are not good with fraction division then just counting will work here. I will show both ways. First counting.

2/3

4/3 = 3 1/3

6/3 = 2

8/3 = 2 2/3

10/3 = 3 1/3

12/3 = 4

14/3 = 4 2/3

16/3 = 5 1/3

18/3 = 6

20/3 = 6 2/3

22/3 = 7 1/3

24/3 = 8

26/3 = 8 2/3

You could keep going but 8 2/3 is more than 8 1/2, so this where we stop, because the one before it, 8 is less than 8 1/2. So unless you are allowed to cut the panels, you are going to wind up using 13 panels which will total a length of 8 2/3 feet.

If you want to use division, you would use the same way you would think of splitting say 100 marbles into groups of 5, you would do 100/5 = 20. here you have a total length of 8 1/2 and divide it by 2/3. If you need an explanation how to do it let me knwo but you get to 12.75, which again, unless you can cut the panels you will need 13 n both sides. so 13 on both long sides means 26

Now the two short sides. Since we already counted let's use it again. How many does it take to get to at least 6 1/3? Well, 9 gets to 6 and 10 is 6 2/3, so that means we need 10 to get above 6 1/3. Using division again we would do 6 1/3 divided by 2/3, you get 9.5, which again shows we need more than 9 panels, so unless you can cut them that means 10. two short sides means we multiply it by 2 to get 20

So total number fo panels is 26 + 20 = 46

if there was anything you don't understand let e know so I can explain. And again, that goes for fraction division too.