can you show step by step how to work the following 3/4-7/9+2/3

Now, let's stop here for a moment. How did we get the LCM? We have to find a number that all the denominators go into evenly. But how do we do that?

We can multiply four and three, and we get twelve. But what about nine? Does nine go into twelve evenly? No; therefore twelve isn't the LCM. Now let's try multiplying nine and three. Nine times three is twenty-seven, but four can't evenly go into twenty-seven. Because of this, twenty-seven isn't the LCM. Lastly, let's try multiplying four and nine. Four times nine is thirty-six, but does three go into thirty-six? Because three times twelve is thirty-six, we have found our LCM.

You can do it this way, but there is an easier way to solve the problem.

All you have to do is multiply the denominators (in this case, it would be four, nine, and three) and you have your common multiple. But be aware! If you do this all the time, you won't always find the least common multiple. After you have solved the problem, the answer may need to be simplified. But, after you simplify, the answer will be the same as if you did it the other way.

Now, we have it where the denominators of ALL the fractions are 36. But we are still not done here.

?/36 - ?/36 + ?/36

Lets look at the first fraction. The original denominator was 4.

In order to get the numerator, ask yourslef this:

How did we go from four to thirty-six?

You then think:

Four times what is thirty-six?

or

Thirty-six divided by four is what?

The answer: nine

Four times nine is thirty-six

Thirty-six divided by four is nine

Our next step:

Because we multiplied four by nine, we are going to multiply the numerator (three) by nine

Therefore, we have 3 times 9 in the numerator, which becomes 27.

27/36 - ?/36 + ?/36

We now look at the second fraction. The original denominator was 9.

How did we go from nine to thirty-six?

Nine times what is thiry-six?

Nine times four is thirty-six.

We multiplied nine and four, so we're going to multiply the numerator (seven) by four

Therefore, we have 7 times 4 in the numerator, which becomes 28.

27/36 - 28/36 + ?/36

Lastly, we look at the last fraction. The original denominator was 3.

How did we go from three to thirty-six?

Three times what is thirty-six?

Three times twelve is thirty-six.

We multiplied three and twelve, so we're going to multiply the numerator (two) by twelve

Therefore, we have 2 times 12 in the numerator, which becomes 24.

Yassss! We now have our problem that we can finally solve!

27/36 - 28/36 + 24/36

-1/36 + 24/36

23/36

We get -1/36 by subtracting 27/36 and 28/36. When we do this, the denominator stays the same. So really, we're subtracting 27 and 28, which is -1.

We then need to add -1/36 and 24/36, but once again, the denominators stay the same. So really, we're adding -1 and 24, which is 23.

Hope this helps! Let me know if you have any questions! :)