Lesson A shortcut to adding and subtracting fractions

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This Lesson (A shortcut to adding and subtracting fractions) was created by by jgr45(31)

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Contrary to popular belief, there is a fast way to add and subtract fractions with unlike denominators, and it does not involve finding a common denominator.  It uses the following formulas, provided that no denominator is ever zero:

{{{a/b}}} + {{{c/d}}} = {{{(ad + bc)/bd}}}

and

{{{a/b}}} - {{{c/d}}} = {{{(ad - bc)/bd}}}

The steps are as follows:

1) Take the cross products and add/subtract them

2) Put the resulting sum or difference over the product of the denominators

3) Reduce if possible.

Some examples:

{{{2/5}}} + {{{3/8}}}

First, take the cross products.  2x8=16 and 5x3=15.  Add 16 and 15 to get 31.  This is your numerator.  To get the denominator, multiply 5 and 8 to get 40, giving you {{{31/40}}}, which is the exact same answer you would get with common denominators.

Now let's try a subtraction problem:

{{{2/3}}} - {{{3/5}}}

Again, take the cross products...2x5=10 and 3x3=9. Subtract 10 minus 9 to get 1.  This is the numerator, To get the denominator, multiply the original denominators, 3 and 5, to get 15.  So the answer to this one is {{{1/15}}}.

Also, if you have numerators of 1, that makes the problem even easier because you're multiplying by 1 in your cross-products.  In that case your answer would simply be the sum/difference of the denominators over the product of the denominators.  For example, {{{1/4}}} + {{{1/3}}} = {{{7/12}}}, and {{{1/3}}} - {{{1/7}}} = {{{4/21}}}.