Three groups of students are sharing leftover pizza (all the same size originally)
Which group gets the most pizza?
6 students share 3/4?
3 students share 1/3?
4 students share 2/3?
3/4 * 1/6 = 3/24 = 1/8
1/3 * 1/3 = 1/9
2/3 * 1/4 = 2/12 = 1/6
Well, let's break it down and see.
First, the group of 6 students sharing 3/4 of a pizza. This means each student gets 3/4 divided by 6, which is 1/8 of the pizza.
Next, we have the group of 3 students sharing 1/3 of a pizza. This means each student gets 1/3 divided by 3, which is 1/9 of the pizza.
Finally, the group of 4 students sharing 2/3 of a pizza. This means each student gets 2/3 divided by 4, which is 1/6 of the pizza.
So, after all the fancy math, it turns out that the group of 6 students gets the most pizza, with each student getting 1/8 of a pizza. But hey, don't be too disappointed if you're in one of the other groups. Pizza is pizza, and any pizza is good pizza, right?
To determine which group gets the most pizza, we need to compare the fractions representing the amount of pizza each group receives.
First, let's find the common denominator for all the fractions: 3/4, 1/3, and 2/3. The least common multiple (LCM) of 4, 3, and 3 is 12.
To convert 3/4 to the equivalent fraction with a denominator of 12:
(3/4) * (3/3) = 9/12.
To convert 1/3 to the equivalent fraction with a denominator of 12:
(1/3) * (4/4) = 4/12.
To convert 2/3 to the equivalent fraction with a denominator of 12:
(2/3) * (4/4) = 8/12.
Now let's compare the fractions:
9/12, 4/12, and 8/12.
The group that gets the most pizza is the one with the fraction 9/12. Therefore, the group that shares among 6 students gets the most pizza.
To determine which group gets the most pizza, we need to compare the fractions of pizza that each group receives.
1. 6 students share 3/4:
To calculate how much pizza each student would get, we divide 3/4 by 6. So we would do: 3/4 ÷ 6 = 1/8. This means each student would get 1/8 of the pizza.
2. 3 students share 1/3:
To calculate how much pizza each student would get, we divide 1/3 by 3. So we would do: 1/3 ÷ 3 = 1/9. This means each student would get 1/9 of the pizza.
3. 4 students share 2/3:
To calculate how much pizza each student would get, we divide 2/3 by 4. So we would do: 2/3 ÷ 4 = 1/6. This means each student would get 1/6 of the pizza.
Comparing the fractions, we can see that 1/6 is more than 1/9 and 1/8. Therefore, the group of 4 students sharing 2/3 of the pizza would get the most pizza.