How do you simplify #3/5+(-6)#?

1 Answer
Nov 7, 2016

Answer:

#-27/5#

Explanation:

When you multiply two signs that are different the result is a minus (negative value)

Think of #+(-6)" "# as #" "(+1)xx(-6)#

Giving:#" "-(1xx6)=-6#

Putting it all together we have:

#3/5-6#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Multiply by 1 and you do not change the value. However, if you multiplied by #1=5/5# you would not change the value but you would change the way it looks.

#color(green)(" "3/5-[6color(magenta)(xx1)]" "->" "3/5-[6color(magenta)(xx5/5)])#

#color(brown)("You can now do direct subtraction as denominators are the same"#

#" "3/5-30/5" "->" "(3-30)/5#

#" " = " "-27/5#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Foot note")#

A fraction consist of #" "("count")/("size indicator of what you are counting")#

The difference in the function between the top number and the bottom number is very important.

#" "("count")/("size indicator")" "->" "("numerator")/("denominator")#

#color(white)(.)#

#color(green)(bar(|color(white)(2/2)"You can not "color(red)(ul("directly"))" add or subtract the counts"color(white)(2/2)"|))# #color(green)(ul(|color(white)(2/2)"unless the size indicators are the same."color(white)(" "2/2)|))#

Consider this example:

You can directly add #3+2# because their size indicators are the same. Really they are : #3/1+2/1#. It is just that people do not normally show them this way.