# 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 Ã· 2 = 3

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

_______Ã·_______= ______

```

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 Ã— ? = 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 Ã· 6 = ___

First, we __________ the division to the ______________problem 6 Ã— _ = 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 Ã· 6 = 3       _3_          6
6 )18        Ã— 3
18
```

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

```           ___         ___
5 )15        Ã—____

```
```           ___         ___
4 )12        Ã—____

```
```           ___         ____
6 )18        Ã—____

```

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      Ã—____
16
```

To solve we ask, "what times 3, equals 16?" Since 3 Ã— 5 = 15 and 3 Ã— 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      Ã—____
27

```

```
___   or     2
2 )25         Ã—?
25
```

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

```
___   or    3
3 )125        Ã—?
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        Ã—?
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        Ã—?
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 Ã— 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 Ã— 40 = 120

```
__40_  or    3
3 )125        Ã—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        Ã—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?"

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

```
_100_   or     8
8 )983         Ã—100
-800         800
183
```

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

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

```              20
_100_   or    8
8 )983         Ã—20
-800         160
183
-160
23
```

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

```
2
20
_100_   or   8
8 )983         Ã—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 Ã· 18 Â Â Â Â Â Â Â Â Â Â 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 Ã— 18
556
-180        10 Ã— 18
375
-180        10 Ã— 18
195
-180       +10 Ã— 18
16        130 r 16

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