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

2 Answers
Jun 12, 2017

Answer:

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#

Jun 12, 2017

Answer:

#+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#