Question

How do you simplify `-1/9div(-3)`?

Answer 1

See a solution process below:

Explanation:

First, rewrite this expression as:

`(-1/9)/(-3) => (-1/9)/(-3/1) => ((-1)/9)/((-3)/1)`

We can now use this rule for dividing fractions to simplify the expression:

`(color(red)(a)/color(blue)(b))/(color(green)(c)/color(purple)(d)) = (color(red)(a) xx color(purple)(d))/(color(blue)(b) xx color(green)(c))`

`(color(red)(-1)/color(blue)(9))/(color(green)(-3)/color(purple)(1)) = (color(red)(-1) xx color(purple)(1))/(color(blue)(9) xx color(green)(-3)) = (-1)/-27 = 1/27`

Answer 2

`+1/27`

Explanation:

`color(blue)("Dealing with just the numbers")`

A quick note about the short cut approach used:

It is both correct and permissible to write 3 as `3/1`

For divide the rule is: Turn upside down what you were dividing by and then multiply.

So you turn `3/1` upside down giving `1/3` and then multiply giving:

`1/9-:3/1" "->" "1/9xx1/3`

So, ignoring the signs for the moment the numbers are:

`1/9xx1/3" "=" "(1xx1)/(9xx3)" "=" "1/27`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Dealing with the signs.")`

`color(brown)("For multiply or divide")`

`" "`If the signs are the same the answer is positive.
`" "`If the signs are different then the answer is negative

In this question the signs are the same so the answer is positive thus we have:

`+1/27`