Answer:24 times
Step-by-step explanation:Hi there!
First of all, division is the opposite of multiplication. So if I
divide 72 by 3 I should get 24, since 3*24 = 72.
(You might notice that our division looks sort of like the
multiplication:
24
X 3
___
12
60
----
72
just in a different order.)
OK, back to long division.
The process of long division goes sort of like this:
1. Write the problem
2. Make a guess of what the answer will be
3. Check your guess, fix it if you need to
4. "Bring down"
5. Repeat steps 2-4 until you're out of digits
So for 72 divided by three, the process would go like this:
1. Write the problem
----
3|72
That means 72 divided by 3, also called 3 into 72, etc.
2. Make a guess of what the answer is.
Let's cover up the 2 in 72 for a minute: (This lets us ignore the place
value, etc.)
----
3|7?
Now let's ask: How many times does 3 go into 7?
You can make whatever guess you want. But since we have a good idea of
what the answer should be, let's guess 2.
Now we write the 2 above the 7 like this:
2
----
3|7?
Now, to check that we're right, we need to subtract 2 3's from 7.
We do this by multiplying 2X3 (to get 6) and then writing:
2
----
3| 7?
-6
__
1
We need the 2 from 72 again, so let's write it in again. In fact, we're
going to "bring it down" next to the 1 to make 12. Then we'll guess how
many times 3 goes into 12, and so on.
Anyway:
2
----
3| 72
-6 | <---that's supposed to be an arrow reminding you that we're
__\ / bringing down the 2 to make 12
12
Ok. So, how many times does 3 go into 12? Let's guess 4 (sorry, I'm
cheating since I know the answer already!)
24
----
3| 72
-6
-
12
Now let's multiply 3 X 4. Wow! We get 12. If we subtract 12-12
24
----
3| 72
-6
-
12
- 12
---
0
Now, we can check to make sure that 3 X 24 really does equal 72, and
we're done.
. The third solution can be easily found using the rational root theorem, and it's equal to -1.