How do you evaluate #\frac { - 1} { 10} \div \frac { 1} { 4}#?

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Answer 1 · 2017-01-30T21:46:30

#-2/5#

Divide a negative by a positive is the same as multiply a negative by a positive. In that the answer is negative.

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

#" "(-1)/10# is the same as #-1/10# so we have

Dealing with just the signs:

#" "-1/10-:1/4->" negative answer"#

Dealing with the numbers:

#" "1/10-:1/4" "=" "1/10xx4/1#

#" "= 4/10-=(4-:2)/(10-:2) = 2/5#

This gives a final answer of #-2/5#

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#color(blue)("Foot note")#

SUPPOSE that instead of #(-1)/10# we had #(-1)/(-10)# In this case the two signs are the same giving# ->+1/10#

However. in this question the signs are different in that we have:
#(-1)/10# which is the same as # (-1)/(+10) = -1/10#