Question

What is `3 4/9 + 3 3/4`?

Answer 1

`259/36`

Explanation:

`1`. Start by converting both mixed fractions into improper fractions.

`color(darkorange)3` `color(brown)4/color(red)9+color(teal)3` `color(violet)3/color(blue)4`

`=(color(red)9xxcolor(darkorange)3+color(brown)4)/color(red)9+(color(blue)4xxcolor(teal)3+color(violet)3)/color(blue)4`

`=(27+4)/9+(12+3)/4`

`=31/9+15/4`

`2`. Determine the L.C.M. of the denominators of the fractions, `9` and `4`. Use the long division method.

`|ul(9color(white)(X)4)`

Determine a prime number that can divide either `9` or `4` without producing a decimal. Try the number, `color(red)2`.

`color(red)2|ul(9color(white)(X)4)`
`color(white)(Xx)color(darkorange)9color(white)(X)color(blue)2`

Since `color(darkorange)9` can be broken down further, divide by `color(brown)3`. Since `color(blue)2` can't be divided by `color(brown)3` without producing a decimal, you skip that part and drop the `color(blue)2` down.

`color(red)2|ul(9color(white)(X)4)`
`color(brown)3|ul(color(darkorange)9color(white)(X)color(blue)2)`
`color(white)(Xx)color(violet)3color(white)(X)color(purple)2`

Since `color(violet)3` and `color(purple)2` can't be divided by any other prime number except for `1`, multiply `color(red)2`, `color(brown)3`, `color(violet)3`, and `color(purple)2` together to determine the L.C.M.

L.C.M.`=color(red)2xxcolor(brown)3xxcolor(violet)3xxcolor(purple)2`

L.C.M.`=36`

`3`. In `31/9` and `15/4`," multiply the numerator and denominator by the same number so that the denominator of each fraction is `36`.

`=31/9+15/4`

`=(31color(teal)(xx4))/(9color(teal)(xx4))+(15color(teal)(xx9))/(4color(teal)(xx9))`

`=124/36+135/36`

`4`. Add the fractions together.

`=(124+135)/36`

`=color(green)(|bar(ul(color(white)(a/a)259/36color(white)(a/a)|)))`