-4 1/5 * -3 1/3

Sorry....but we DON'T need "common denominators" when we multiply fractions.....besides multiplying (-3 or so)  times (-4 or so) couldn't possibly give us 210 !!!.......that answer lacks the "reasonableness test "

Here's the way to do this..........

Convert both fractions to improper ones

-4 + 1/5 = -21/5    and  -3 + 1/3  = -10/3

Now....just multiply them together

(-21/ 5) (-10/3)....however...wait.......here's a trick to make it easier.......a negative times a negative will produce a positive result - we can "drop" the negative signs - and we can also "swap" denominators and "cancel" before we multiply....so we have...

(21/3) (10/5) = (7)(2) = 14 !!!

And that's definitely NOT 210 !!!

First, convert both of them to improper fractions:

-4 1/5

1. Multiply the whole number (4) by the denominator (5) to get 20 (ignore - signs for now)

2. Add the numerator (1) to get 21

3. Put it over the denominator to get 21/5. Now add a minus sign to get $${\mathtt{\,-\,}}{\frac{{\mathtt{21}}}{{\mathtt{5}}}}$$

Do the same for the other fraction to get $${\mathtt{\,-\,}}{\frac{{\mathtt{10}}}{{\mathtt{3}}}}$$

Now find the Least Common Multiple (LCM) for the denominators, 3 and 5. Keep multiplying 5 until you get a number that works for both 3 and 5. In this case, it is 15. 3*5=15 and 5*3=15. Multiply them by those numbers so that the denominator is 15:

$${\mathtt{\,-\,}}{\frac{{\mathtt{21}}}{{\mathtt{5}}}}$$ X $${\frac{{\mathtt{3}}}{{\mathtt{3}}}}$$ = $${\mathtt{\,-\,}}{\frac{{\mathtt{63}}}{{\mathtt{15}}}}$$

Do the same for $${\mathtt{\,-\,}}{\frac{{\mathtt{10}}}{{\mathtt{3}}}}$$, but multiply by 5/5 instead of 3/3. This will give you $${\mathtt{\,-\,}}{\frac{{\mathtt{50}}}{{\mathtt{15}}}}$$. Now that they both have the same denominator, you can multiply them together.

$${\mathtt{\,-\,}}{\frac{{\mathtt{50}}}{{\mathtt{15}}}}$$ X $${\mathtt{\,-\,}}{\frac{{\mathtt{63}}}{{\mathtt{15}}}}$$

Cross reduce if you're in the mood, but to keep things short I'll skip it.

-50*-63=3150 (remember that negative*negative=positive)

Leave the denominators alone.

This gives you $${\frac{{\mathtt{3\,150}}}{{\mathtt{15}}}}$$. You can then simplify it. 3150 is divisible by 15, so you can divide to get $${\frac{{\mathtt{210}}}{{\mathtt{1}}}}$$, or just plain 210.

Good luck.