Question

How many to fill these here buckets

Answer 1

Each bucket will be
`(1)/(2)` full

Explanation:

First add up all the different fractions to find out how many buckets of water are in all 3 buckets combined.

Adding up the fractions we get the expression:

`(5)/(12) + (3)/(4) + (1)/(3)`

To add these fractions first find the LCM(least common multiple of the denominators, 12, 4 and 3

This is the smallest number divisible by all 3 numbers without a remainder

There are several strategies for finding the LCM but here we can see that 12 is evenly divisible by12, 4 and 3

We convert each of the fractions to have the same denominator as the LCM of 12 and adjust the numerator accordingly

Multiply each of the fractions by the LCM

12 x 5/12 = 5

12 x 3/4 = 9

12 x 1/3 = 4

These will become the numerators in the addition with the common denominator of 12

`(5)/(12) + (3)/(4) + (1)/(3)\\\\= (5 + 9 + 4)/(12)\\\\= (18)/(12)\\\\`

This is how many buckets it will take to hold the water from all three buckets

Divide numerator and denominator by 6 to reduce to lowest fraction

`(18 / 6)/(12/6) = (3)/(2)`

This is 1 1/2 buckets. If this amount of water is to be evenly divided among 3 buckets then the amount of water in each bucket

`(3)/(2) / 3\\\\= (3)/(2) * (1)/(3)\\\\= (1)/(2)`

So each bucket will be half full