How do you evaluate #5/8+5/6#?

Question

Julian Avila · Accepted Answer

#1 color(white)(.)11/24#

A fraction is split up into 2 parts

#("Part 1")/("Part 2") -> ("count of how many you have")/("size indicator of what you are counting")#

The size indicator is how many it take to make 1 of something.

#("Part 1")/("Part 2") -> ("numerator")/("denominator")#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ #color(red)("You can not directly add or subtract the counts unless")##color(red)("they have the same size indictor (denominator).")#

Both 8 and 6 will divide exactly into 24. So we will make both of the denominators 24.

#color(blue)("Consider "5/8)# Note that #3xx8=24#

Multiply by 1 but in the form of #1=3/3#

#color(blue)(5/8xx1" "=" " 5/8xx3/3 " "=" "15/24)#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ #color(blue)("Consider "5/6)# Note that #4xx6=24#

Multiply by 1 but in the form of #1=4/4#

#color(blue)(5/6xx1" "=" "5/6xx4/4" "=" "20/24)# '~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#color(green)("Putting it all together in detail")#

#color(green)("With practice you will be able to do a lot of this in your head and")##color(green)("jump steps.")#

#5/8+5/6" " =" "color(blue)(15/24+20/24)" "=" "(15+20)/24#

#color(white)(..)#

But #15+20 = 35 = 24+11#

#color(white)(..)#

#=(24+11)/24#

#=24/24+11/24#

#1+11/24#

# = 1 11/24#

Zoe Adams · Answer

By finding a common denominator or using a pretty cool trick. Answer is in the explanation.

The least common multiple between 6 and 8 is 24. #8*3# is 24 so we must multiply its 5 by 3 which is 15 making the first fraction #15/24#. #6*4# is 24 so we must multiply its 5 by 4 which is 20 making the second fraction #20/24#. Now we can add 15 and 20 to get #35/24# which is our final answer. There's another method that I think is much easier and quicker however it may be a more difficult concept to grasp. I will illustrate it using variables. If you're adding two fractions, #a/b + c/d#, the final fraction will be #(ad+bc)/(bd)#. If we apply this to the current problem we will get #(5*6+5*8)/(6*8) = (30+40)/48 = 70/48 = 35/24#

Jeremiah Andrews · Answer

undefined To evaluate $ \frac{5}{8} + \frac{5}{6} $, you first need to find a common denominator, which in this case is 24. Then, you can add the fractions together:

$$ \frac{5}{8} + \frac{5}{6} = \frac{15}{24} + \frac{20}{24} = \frac{35}{24} $$

The sum can also be expressed as 1 and $ \frac{11}{24} $.