Question

How do you simplify `\frac { \frac { 7} { 3} + \frac { 8} { 6} } { \frac { 3} { 11} - \frac { 1} { 22} }`?

Answer 1

Please see the explanation.

Explanation:

Multiply by 1 in the form of `2/2`

`(2(7/3+8/6))/(2(3/11-1/22) )= (14/3+8/3)/(6/11-1/11)`

Now that there are common denominators, we can combine the fractions:

`(14/3+8/3)/(6/11-1/11) = (22/3)/(5/11)`

We know that dividing by a fraction is the same thing as inverting (flipping) the divisor and multiplying:

`(22/3)/(5/11) = (22/3)(11/5)`

When you multiply two fractions, multiply the numerators and the denominators.

`(22/3)(11/5) = 242/15`

Answer 2

`242/15= 16 2/15`

Explanation:

Although it is possible to work with this fraction in this form, it is pretty daunting, so let's work with it in a simpler form:

`(7/3+8/6)" " div" " (3/11-1/22)" "larr` simplify each bracket

`((14+8)/6)" " div" "((6-1)/22)" "larr` change each bracket to LCD

`22/6color(white)(......) divcolor(white)(......) 5/22`

To divide fractions, multiply by the reciprocal of the second fraction

`22/6color(white)(......) xx color(white)(......) 22/5" "larr` cancel if possible (cancel by `2`)

`22/cancel6_3color(white)(......) xx color(white)(......) cancel22^11/5`

`=242/15`

`= 16 2/15`

Answer 3

`color(red)(16 2/15`

Explanation:

`(7/3+8/6)/(3/11-1/22)`

`:.=((14+8)/6)/((6-1)/22)`

`:.=(22/6)/(5/22)`

`:.=cancel22^color(red)11/cancel6^color(red)3 xx 22/5`

`:.=(11 xx22)/(3 xx 5)`

`:.=242/15`

`:.color(red)(=16 2/15`