Division Tips and Tricks


Division is easy to learn if you know how to add and multiply WELL.

Tip #1

Let’s look at a division problem to learn the key terms and how to solve them. The problem below labels the parts of a division problem.

                                  _3_ <--- quotient (The Answer)
  (What's dividing) divisor---> 2 )6   <--- dividend (What's being divided up)

Here is the same problem in a different form, 6 ÷ 2 = 3

In words, we would say; six, divided by two, equals three.

6/2.gif

Another way to look at it: you have 6 things to go into 2 boxes. How many will be in each box?

In the space provided, label the parts of the following division problem and put it into a new form.




                 _4_  <--- __________
________--->   3 )12     <--- ____________   

_______÷_______= ______

In the space below, write the problem in words or as it would be said aloud.

Let's look at the same problem without an answer.

                                 ___  <--- quotient ( The Answer)
  (What's dividing) divisor---> 3)12   <--- dividend (What's being divided up)





TO SOLVE THIS DIVISION PROBLEM WE ASK:

"3, TIMES WHAT, EQUALS 12?" -OR- "WHAT TIMES 3 EQUALS 12?"

This converts the division into 3 × ? = 12. Which we can easily solve with a 4.

Let's practice with another division problem, fill in the blanks:

To solve the problem 18 ÷ 6 = ___

First, we __________ the division to the ______________problem 6 × _ = 18 As a multiplication champion, you'll know that the answer is ____.


In summary, the following are all the same problems in different formats.





18 ÷ 6 = 3       _3_          6
               6 )18        × 3
                              18

In the spaces below, convert the following divisions to multiplications and solve.

           ___         ___  
         5 )15        ×____
                        
           ___         ___
         4 )12        ×____
                        

           ___         ____ 
         6 )18        ×____
                        

Now, go here for division worksheets you can use with converting divisions to multiplications (no remainders).


Tip #2

Sometimes with division problems the answer will result in an what's called a remainder. So, let's learn to solve a problem using long division and find out what a remainder is.

Here is the problem:

           ___         3
         3 )16      ×____
                      16

To solve we ask, "what times 3, equals 16?" Since 3 × 5 = 15 and 3 × 6 = 18 the closest we can get is 15 without going over the dividend number. Let's write that in and subtract 16 - 15 = 1 as shown below.

       __5_r1   The "r" stands for remainder   
     3 )16           
       -15 
         1    

A remainder occurs whenever one number is NOT totally divisible by another number. The remainder is really a fraction. In the above problem, we could write the result as 5 and 1/3

Solve the following problems using long division and multiplication, show the remainders as fractions if possible:

           ___  or     4
         4 )27      ×____
                      27





___ or 2
2 )25 ×?
25




As we progress along in division, we might run into problems like the following:

___ or 3
3 )125 ×?
125



Step 1:

Work the problem from the 100s, to the 10s then to the 1s -or- from left to right.


___ or 3
3 )125 ×?
125

Start by looking at the number in the 100s column (1) and ask yourself, "3 times what equals 1? or, "how many 3s in 1?" (the 1 comes from the 1 in 125). Since 1 can't be divided by 3 easily, skip it and look at the number to the right of it in the 10s place or the 2.

Step #2


___ or 3
3 )125 ×?
125

Now put the 1 and 2 together for a 12 and ask,"what times 3 equals 12?" or, "how many 3s in 12?"

The 12 comes from the 12 in 125.

HELLO!

4 × 3 = 12. We've solved part of the problem...YES!

Step 3:

Now, here's the twist, add 0s to the 4 and to the 12 and make them a 40 and a 120. So now your multiplication should be 3 × 40 = 120


__40_ or 3
3 )125 ×40

-120 120
5


Place the 40 OVER the problem in
the quotient area as shown.

Now, place the 120 UNDER the 125 as shown above and below.

__40_ or 3
3 )125 ×40
-120 120
5

Step 4:

Subtract 120 from 125 and you should get 5.

Now ask, "what time 3 equals 5?" or "how many 3s in 5?"

If you answered 1, great!

Now put a 1 above the 40 in the quotient area and subtract 3 from 5 as shown below.

               1
__40_ or 3
3 )125 ×1

-120 3
5
-3
2

Now add the quotients together and bring the 2 up from the bottom of the problem and you should have the complete answer...41 r2.


Tip #3

How to solve even tougher problems.

To solve tougher division problems, break dividends into 100s 10s and 1s then estimate to find solutions. In a problem like:


___ or 8
8 )983 ×?
983

Working from left to right we start to estimate with 100's and ask, "8 times what equals 900" or "what times 8 equals 900?"

division gif

Then, in estimating 100s we find that 100 × 8 = 800 and that 200 × 8 = 1600... but we can't subtract 1600 from 983. So, lets start with 100 × 8 = 800 and subtract 800 from 983.


_100_ or 8
8 )983 ×100

-800 800
183

Now we ask, "how many 8s in 183?"

We know that 8 × 2 = 16 so we estimate by 10s and find that 8 × 20 = 160. Wow, that close, let's subtract that amount next.

              20
_100_ or 8
8 )983 ×20

-800 160
183
-160
23

Now, all we have to find out is how many 8s in 23. Sheesh, 8 × 2 = 16 and that's close. Let's subtract that amount next and finish this problem.


2
20
_100_ or 8
8 )983 ×2
-800 16
183
-160

23
-16
7

Then add the numbers in the quotient and post the remainder with it and you get 122 r7.


Here's another look at that with an even tougher problem.

2,356 ÷ 18           18s

estimate how many 100s of 18s in 2,300
then, how many 10s of 18s
then, how many ones of 18

__
18 )2356
-1800 100 × 18
556
-180 10 × 18
375
-180 10 × 18
195
-180 +10 × 18
16 130 r 16