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

2 Answers
Jul 10, 2016

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

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

Jul 12, 2016

1 color(white)(.)11/24

Explanation:

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