How do you evaluate #18\times ( - \frac { 1} { 9} ) \times \frac { 1} { 5}#?

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Answer 1 · 2016-12-27T23:34:59

Since there is only one #-# you may as well put it in front

#=-18xx1/9xx1/5#
#=-2xxcancel9xx1/cancel9xx1/5#
#=-2/5#

Answer 2 · 2016-12-29T22:29:32

#-2/5#

Lets split the approach into 2 parts, the signs and then the numbers.

#color(blue)("Dealing with the signs ( plusses and minuses)")#

Putting the plusses and minuses into brackets so that they do not get confused with the multiply. Grouping the first two with [ ] gives:

#[color(white)(2/2)(+)xx(-)color(white)(.)]xx(+)#

Inside the [ ] the signs are different so the answer for that bit is negative giving:

#[color(white)(2/2)(-)color(white)(.)]xx(+)#

Now we have:

#(-)xx(+)#

The signs are different so the answer for that bit is negative so the final answer to the question will be negative.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Dealing with the numbers")#

#18xx1/9xx1/5#

This is the same as:

#18/9xx1xx1/5#

#(18-:9)/(9-:9)xx1xx1/5#

#2xx1xx1/5" "=" "2/5#

But the answer is to be negative so we have:

#-2/5#