Four friends shared a candy bar. The first friend ate 1/4 of the candy bar, the second friend ate 1/3 of the candy bar, and the third friend ate 1/6 of the candy bar. How much of the candy bar did the fourth friend eat? (Leave your answer as a fraction in lowest terms.)
1/4 + 1/3 + 1/6 = 3/12 + 4/12 + 2/12 = 9/12 = 3/4
that's how much the three ate.
To find out how much of the candy bar the fourth friend ate, we need to subtract the portions eaten by the first three friends from the whole candy bar.
Let's calculate the sum of the portions eaten by the first three friends:
1/4 + 1/3 + 1/6
To add fractions, we need a common denominator. The least common multiple of 4, 3, and 6 is 12.
For the first fraction (1/4), to get a denominator of 12, we have to multiply the numerator by 3:
(1/4) * (3/3) = 3/12
For the second fraction (1/3), to get a denominator of 12, we have to multiply the numerator by 4:
(1/3) * (4/4) = 4/12
The third fraction (1/6) already has a denominator of 12.
Now we can add the fractions:
3/12 + 4/12 + 1/6 = 8/12 + 2/12 + 2/12 = 12/12 = 1
So, the first three friends ate a total of 1 whole candy bar.
To find out how much the fourth friend ate, we subtract this total from the whole candy bar:
1 - 1 = 0
Therefore, the fourth friend did not eat any of the candy bar, which means the answer is 0/1 or simply 0.