Jim bought 3 1/2 pounds of apples, 2 3/4 pounds of oranges, 1 1/4 pounds of grapes, and 2 5/8 pounds of bananas. If Jim gives Bill 1/5 of the fruit, how many pounds of fruit will Bill receive?
This is a word problem for multiplication of fractions, and I don't even know where to begin with it.
Well, first you would add up the fruits.
You will have to convert all the fractions to improper fractions, get a common denominator, and simplify to one fraction.
Then multiply that by 1/5
Get common denominator. Add them all up. Give Bill 1/5 by getting common denominator
To solve this problem, we need to find the total weight of the fruits Jim bought and then calculate 1/5 of that weight.
1. First, let's convert all the mixed numbers to improper fractions.
3 1/2 pounds of apples = (2 * 3) + 1/2 = 7/2
2 3/4 pounds of oranges = (4 * 2) + 3/4 = 11/4
1 1/4 pounds of grapes = (4 * 1) + 1/4 = 5/4
2 5/8 pounds of bananas = (8 * 2) + 5/8 = 21/8
2. Next, add up the weights of all the fruits.
Total weight = 7/2 + 11/4 + 5/4 + 21/8
= 28/8 + 22/8 + 10/8 + 21/8
= 81/8
3. Now, multiply the total weight by 1/5 to find how much fruit Bill will receive.
Bill's share = 81/8 * 1/5
= (81 * 1) / (8 * 5)
= 81/40
Therefore, Bill will receive 81/40 pounds of fruit.
To solve this word problem, we need to find out how many pounds of fruit Jim will give to Bill. We will start by adding up the total amount of fruit that Jim bought.
Jim bought:
- 3 1/2 pounds of apples (which can be written as the improper fraction 7/2)
- 2 3/4 pounds of oranges (which can be written as the improper fraction 11/4)
- 1 1/4 pounds of grapes (which can be written as the improper fraction 5/4)
- 2 5/8 pounds of bananas (which can be written as the improper fraction 21/8)
To find the total amount of fruit, we need to add these fractions together. However, since the denominators are not the same, we need to find the least common denominator (LCD) of these fractions, which in this case is 8.
Converting the fractions to have a denominator of 8:
- 7/2 * (4/4) = 28/8
- 11/4 * (2/2) = 22/8
- 5/4 * (2/2) = 10/8
- 21/8
Adding the fractions: 28/8 + 22/8 + 10/8 + 21/8 = 81/8
So, Jim bought a total of 81/8 pounds of fruit.
Next, we need to find 1/5 of this amount to determine how much fruit Jim will give to Bill. To find this, we'll multiply 81/8 by 1/5.
(81/8) * (1/5) = (81 * 1) / (8 * 5) = 81/40
Therefore, Jim will give Bill 81/40 pounds of fruit.