Question

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

Answer 1

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`

Answer 2

`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`