How To Add Fractions With Variables In The Numerator

let's figure out what 11 and12/16 minus 5 and 8/16 is. and then we might haveto simplify it down to lowest terms. so the way i like to do theseis to kind of separate out the whole numberpart of the mixed

How To Add Fractions With Variables In The Numerator, numbers from thefractional part. so i can rewrite thisnumber right over here as 11 plus 12/16. and from that, i amgoing to subtract--

and i'll put parentheseshere because i'm going to break this part open. i'm going tosubtract 5 plus 8/16. 5 and 8/16-- samething as 5 plus 8/16. but i have to remember,i'm subtracting it. i'm subtractingthis whole thing. so i could rewrite it as--i'll rewrite this part-- 11 plus 12/16. and i'm subtracting 5 plus 8/16.

so i can distributethe negative sign. so it's going to be minus5, negative 1 times 5. and then negative 1times positive 8/16. so it's going to be minus 8/16. and then i like to do thewhole number parts separately and then the fractionalparts separately. so let's do thewhole number parts. we have 11 minus 5. i'll write it here, 11 minus 5.

we'll do that part. that's the whole number part. and then we have plus 12/16. let me do this in pink maybe,plus 12/16, minus 8/16. and 11 minus 5 is 6. and i have 6 plus. and then our denominatorsare the same here, so we're going to getsomething over 16. and 12 minus 8 is 4.

so this is the samething as 6 plus 4 over 16, which is thesame thing as-- writing it as a mixed number-- 6 and 4/16. and this is the right quantity,but we can simplify it. 4/16 can be simplified. both the numerator and thedenominator are divisible by 4. they both have the factor 4. so let's divide both thenumerator and denominator by 4. divided by 4.

since we're dividingby the same thing, we're not changing its quantity. and so this isequal to-- we still have the whole number part,6, but the fraction part is now 1, 1/4. so we get 6 and 1/4.