Question

9.) Jenny refinished a wooden table. She used 1/3 can of varnish for a first coat, 1/4 can for a second coat, and 1/6 can for a third coat. What fraction of the can did she use in all?​

Answer 1

9/12 or simplified as 3/4

Explanation:

We are given 3 fractions that we have to add because the question says "What fraction of the can did she use in all?​"

First: Write down
`(1)/(3) + (1)/(4) +(1)/(6)`

Then: We can't just add up all these fractions, we need a LCM. The LCM (Least Common Multiple) We need all the denominators (3, 4, and 6) to be the same. To do that we need to find a number that they can multiply to get. Let's find out all the multiples of each number: (just write the first 5 down because most of the time we can find it easily from this list)

3: 3, 6, 9, 12, 15

4: 4, 8, 12, 16, 20

6: 6, 12, 18, 24, 30

After: just change all the fractions one at a time by whatever you multiply the bottom number to get 12, do it to the top:

`(1)/(3) -- > (4)/(12)`

`(1)/(4) -- > (3)/(12)`

`(1)/(6) -- > (2)/(12)`

Finally we get to add everything up to get:

`(4)/(12) +(3)/(12) +(2)/(12) =(9)/(12)`

(simplified as 3/4)