Question 283191
When you're dealing with fractions you need to get everything to the same denominator.
1/4 + 1/3 cannot be directly added using fractions.
The least common multiple of 4 and 3 is 12, so they can have the same denominator of 12.
{{{1/4 = 3/12}}}
{{{1/3 = 4/12}}}
So...
{{{1/4+1/3 = 3/12+4/12 = 7/12}}}
.
In this case, you're trying to add 9 3/4 + 8 5/6.
The least common multiple of 4 and 6 is 12.  We can figure this out by multiplying 4*6=24, but we notice that 4=2*2 and 6=2*3, so 12 is the LEAST common multiple.
.
So...
{{{9+3/4 = 9+9/12}}}
{{{8+5/6 = 8+10/12}}}
.
{{{ (9+9/12) + (8+10/12) = 17+19/12}}}
.
But 19/12 is more than 1, it is 
{{{ 19/12 = 12/12 + 7/12 = 1+7/12}}}
.
{{{17+19/12 = 17 + 12/12 + 7/12 = 17 + 1 + 7/12 = 18+7/12}}}
.
How do we know that 3/4 = 9/12?
.
Well, remember the idea is the 'least common multiple'.
.
To change 3/4 to 9/12 you simply look at how many times 4 goes into 12.  12/4 = 3
.
So you multiply 3/4 by 3/3  (Remember, you can multiply any number by 1, in this case 1 is 3/3.)
.
{{{(3/3)*(3/4) = 9/12}}}
.
Similarly, how did 5/6 become 10/12?
It is the same process:  12/6 = 2
Multiply 5/6 by 1, which in this case is 2/2.
.
{{{(2/2)*(5/6)=10/12}}}
.
Done