Question

How do you solve `\frac { 17} { 6} - 31\frac { 31} { 15} - \frac { 306} { 5}`?

Answer 1

`-2743/30 = -91 13/30`

Explanation:

We can not DIRECTLY add or subtract fractions directly unless the bottom numbers are the same.

5 will exactly divide into 15 but 6 will not.

So we need some multiple of 15 that 6 will divide exactly into. That value is 30.

`color(blue)("Consider "31 31/15)`

Multiply by 1 and you do not change the value. However, 1 comes in many forms.

`color(green)(31 31/15 color(white)("ddd")->color(white)("ddd") [31color(red)(xx1)]color(white)("dd")+31/15)`

`color(green)( color(white)("ddddddd")->color(white)("ddd")[31color(red)(xx15/15)]+31/15 )`

`color(green)(color(white)("ddddddd")->color(white)("ddddd")[465/15]color(white)("d")+31/15 color(white)("d")=color(white)("d")496/15)`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Putting it all back together")`

`17/6-496/15-306/5`

Using the same approach as above we end up with:

`85/30-992/30-1836/30 = -2743/30 = -91 13/30`