Let’s say we wanted to figure out what 3 7/ -7/3 - 11/3 is. Pause this video and see if you can have a go at it before we do it together.
All right, now let’s work on this together. You might be tempted to deal with the -7/3 and 11/3 first because they already have a common denominator, but you have to realize that subtraction doesn’t use the associative property.
What we could do is rewrite this in terms of addition. Subtracting something is the same thing as adding its opposite, so subtracting -7/3 is the same thing as adding 7/3, and subtracting 11/3 is the same thing as adding -11/3.
Now, addition can use the associative property. We can add these two first because they have the same denominator. So if we have 7/3 + -11/3, what is that going to get us? We can rewrite it as 3 7/ + -4/3.
If we want to have a common denominator, it looks like 21 is going to be the least common multiple of 7 and 3. So let’s rewrite each of these as something over 21. 3/7 to go from 7 to 21 you multiply by 3 (3 x 3 = 9), and to go from 3 to 21 we multiply by 7 (-4 x 7 = -28). This is equal to 9 + -28/21 which is the same thing as 9 - 28/21. We can calculate this as 9 - 28 = -19, so this is equal to -19/21 or -19/21, and we are done.