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

Question

Noah Archer · Accepted Answer

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

Levi Adams · Answer

#5/8#

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#

Zoe Adams · Answer

undefined To add $ -\frac{9}{8} + \frac{7}{4} $, you need to find a common denominator, which in this case is 8. Then, you can add the numerators together. So, it becomes:

$-\frac{9}{8} + \frac{7}{4} = -\frac{9}{8} + \frac{14}{8} = \frac{-9 + 14}{8} = \frac{5}{8}$.