How do you evaluate #5\frac { 7} { 8} + 6\frac { 3} { 5}#?
1 Answer
The answer is
Explanation:
Given:
#5 7/8 + 6 3/5#
Step 1: Separate the whole parts from the fraction parts:
#=color(green)5+color(magenta)(7/8)" "+" "color(green)6+color(magenta)(3/5)#
Step 2: Regroup:
#=color(green)(5+6)+color(magenta)(7/8+3/5)#
Step 3: Add the whole numbers:
#=color(green)(11)+color(magenta)(7/8+3/5)#
Step 4: Convert the fractions so they have a common denominator:
#=color(green)(11)+color(magenta)(7/8) * color(blue)(5/5)+color(magenta)(3/5) * color(blue)(8/8)#
#=color(green)(11)+color(magenta)(35/40+24/40)#
Step 5: Combine the two fractions into one:
#=color(green)(11)+color(magenta)((35+24)/40)#
#=color(green)(11)+color(magenta)(59/40)#
Step 6: Rewrite the new fraction as a proper one (if necessary):
#=color(green)(11)+color(magenta)((40+19)/40)#
#=color(green)(11)+color(magenta)(40/40+19/40)#
#=color(green)(11+1)+color(magenta)(19/40)#
Step 7: Add the whole numbers:
#=color(green)(12)+color(magenta)(19/40)#
Step 8: Reduce the fraction part to lowest terms, if you can:
(For this number, 19/40 is already in lowest terms)
#=12" "19/40#
Note: This long explanation is just to make it easy to follow along; after we understand the process, we can find shortcuts that help us avoid writing this many steps.
