Question
Dear Mitch,
A few weeks ago you promised you would show a way to add or subtract fractions with different denominators without having to find any common denominators. First you showed the regular ways to add or subtract fractions by finding common denominators by doing that prime factoring thing, and you explained how to do it a couple of other ways. So now could you please show the one I mean?
Sincerely,
Nancy B. G.
Clayton, MO.
Answer
Dear Nancy,
Yes. I'll do that now, but I just have to just say one last time that it is very important to do all you can to learn about fractions and understand how to use them in many different ways, because if you do not you will forever be missing out on some of the most interesting and important areas of math.
Still, as promised, here's one of the quickest ways to add and subtract fractions with different denominators WITHOUT having to change the denominators to match.
Watch:
1 1
− + − = −−
2 3
With this method, you just have to do a few quick and easy bits of multiplying to get it going. First, multiply from the bottom of the first fraction by the top of the second fraction, and put that number above the second fraction.
2
1 1
− + − = −−
2 3
Next, multiply the bottom of the second fraction by the top of the first fraction (here it's 3 and 1), and your answer (3) goes above the first fraction. (as shown.)
3 2
1 1
− + − = −−
2 3
Next multiply the two bottoms together:
3 2
1 1
− + − = −
2 x 3 = 6
And write that on the other side of the equal sign, on the new fraction's bottom (Denominator). Finally, using your new top numbers you perform whatever the operation happens to be. Here, it's addition, so 3 + 2 gives you 5.
3 2
1 1 5
− + − = −
2 x 3 = 6
Answer: 5
−
6
And that's it!
Hope that helps,
Mitch