Question

How do you add `1/3+1/9`?

Answer 1

Take the larger of the two numbers in the denominator and then use addition for each term.

Explanation:

`1/3 + 1/9 = (3+1)/9 = 4/9.`

You add the multiples for the numerator.

Answer 2

`4/9`

A fuller explanation about method given.

Explanation:

`color(blue)("2 very important facts about fraction")`

`color(red)("Fact 1")`

You can not `ul("directly")` add or subtract fractions top numbers (numerators) unless the bottom numbers (denominators) are the same.

Consider:

`("numerator")/("denominator")->("count")/("size indicator of what you are counting")`

`1/2` you have a count of 1 but it takes 2 of what you are counting
`color(white)(....)`to make a whole of something (all of it).

`2/5` you have a count of 2 but it takes 5 of what you are counting
`color(white)(....)`to make a whole of something (all of it).

'...........................................................................................................
`color(white)(.)`

`color(red)("Fact 2")`

Multiply by 1 and you do not change the intrinsic value.

Multiply by 1 in another form and you can change the way a fraction looks without changing its intrinsic value.
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Answering your question")`

Given:`" "1/3+1/9`

Multiply `1/3` by 1 but in the form of `1=3/3`

`color(brown)( (1/3xx1)+1/9 color(blue)(" "=" "(1/3xx3/3)+ 1/9`
`color(white)(.)`

`(1xx3)/(3xx3)+1/9" "=" "3/9+1/9" " =" " 4/9`