Question

Jane bought a poster that had a length of 2 1/3 feet and a width of 3/4 feet. What is the perimeter of her poster?3 1/15 feet1 3/4 feet6 1/8 feet6 1/8 square feet

Answer 1

1 1/6

Explanation:

1. We are given the length and width of the poster board. The perimeter of an object is the sum of all four sides.
2. If it helps, picture a rectangle. The length, or the long side, is 2 1/3 feet long. Since both of the rectangle's long sides would be identical, we can assume both sides are 2 1/3 feet long.
3. This also applies to the short side, or the width. Both ends of the poster board would be 3/4 feet long.
4. To find the perimeter, you need to add all four sides together. I assume this is the tricky part for you, as you are not sure how to add fractions yet.
5. First, let's add the two long sides together. 2 1/3 + 2 1/3 would equal 4 2/3. How did I get this? Well, 2 + 2 = 4 (you add the number outside of the fraction first). To add fractions, you look to see if the bottom of the fraction, or the denominator, is the same. As 1/3 and 1/3 have the same denominator, you can leave the 3 alone and only add the top, giving us 2/3.
6. Duplicate this process with the width. 3/4 + 3/4 would give us 6/4. How do we reduce this? We turn it into what is called a mixed number. This means that there will be a big number on the outside, then a fraction attached to it. How do we turn this improper fraction, or a fraction where the top is greater than the bottom, into a mixed number?
7. A fraction can also be interpreted as a division problem. You can look at 6/4 as 6 ÷ 4. Four goes into 6 one time, with 2 left over (6 - 4 = 2). We take how many times four goes into 6 (once) and use that as our big number. All we have to do now is take our leftover number (2) and turn it into a fraction. How? We use 4 as our bottom, or denominator, because it is left over from how many times 4 goes into 6. In conclusion, our mixed number is 1 2/4. Reduced, this is 1 1/2, because 2/4 cut in half is 1/2.
8. So now we have two numbers. 4 2/3 and 1 1/2. How do we add these together if their denominators are different? 2/3 and 1/2 are not compatible by themselves. Well, we need to find a number that both 3 and 2 go into. This number would be 6. But we can't just turn 2/3 into 2/6, we need to multiply the bottom by a number that would make it six, and multiply the top by the same number. 2 • 3 = 6 (from 2/3) so we multiply the top by 2 also. This gets us 4/6. Don't forget the big 4 on the outside to get us 4 4/6!
9. We do the same to the other mixed number, 1 1/2. Half of 6 is 3, so we can turn 1/2 into 3/6, then we make sure our big 1 is on the outside. Now we can add 1 3/6 to 4 4/6!
10. First, add 1 and 4 by itself to get us 5. Then, you can add the fractions 3/6 and 4/6 (don't add the bottom, just the top!) to get 7/6. To reduce this, we divide 7 by 6 to get us 1 1/6!

If I am incorrect in my reasoning, please let me know so that I can plan better for my future answers. Have an amazing day.