How do you add #-9/8+7/4#?

2 Answers
Sep 20, 2016

#-9/8+7/4=5/8#

Explanation:

WE have denominators #4# and #8# here and their GCD is #8#, hence we can add them by converting them to common GCD.

#-9/8+7/4#

= #-9/8+(7xx2)/(4xx2)#

= #-9/8+14/8#

= #(-9+14)/8#

= #5/8#

Sep 21, 2016

#5/8#

Explanation:

Fraction#->("count")/("size indicator")->("numerator")/("denominator")#
#color(white)(.)#

Size indicator is how many of what you are counting to make a whole 1 of something.

#color(white)(.)#
,~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Point 1")#

We need to add/subtract counts but we can only do this 'directly' if the 'size indicators' (denominators) are the same.

#color(blue)("Point 2")#
Multiply by 1 and you do not change the intrinsic value. However, 1 comes in many forms. So we can change the way something looks but not change its intrinsic value.
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Given:#" "-9/8+7/4#

Change the order:

#7/4-9/8#

This is the same in value as:

#(7/4color(magenta)(xx1))-9/8#

But write 1 as #1=2/2# giving:

#(7/4color(magenta)(xx2/2))-9/8" "->" "(7xx2)/(4xx2)-9/8#

#14/8-9/8 = 5/8#