# Two-Digit Division

Not all of**division**is done with numbers less than ten (10). As you learn more about dividing double-digit numbers, you will see

**patterns**similar to the patterns you saw in multiplication. Take a look at these examples before we move on...

25 = 5 x 5

25 ÷ 5 = 5

28 = 4 x 7

28 ÷ 7 = 4

28 ÷ 4 = 7

We think the patterns are very interesting. Division is like the

**reverse**of multiplication. That makes sense, since we keep telling you that multiplication is about putting groups together, while division pulls them apart. If you remember the two

**factors**that were used to create your original number (

**dividend**), checking your work should be easy.

**Example:**

You will be dividing the number twenty-four (24) into smaller parts. What are the possible factors?

You know that:

3 x 8 = 24

4 x 6 = 24

6 x 4 = 24

8 x 3 = 24

If you get the problem 24 ÷ 4 = ? you will know the answer is 6 because 6 x 4 = 24.

# Long and Short

Sometimes the answers will be easy and you will wind up with a single number in your**quotient**. Those easy problems are called

**short division**. The number you are dividing is less than ten times the value of the

**divisor**. Examples of short division include...

28 ÷ 4 = 7

64 ÷ 8 = 8

54 ÷ 9 = 6

99 ÷ 11 = 9

- or -

9 11 ) 99 - 99 0 |

It's as simple as pie. However, sometimes you will start with a dividend that is more than ten times the value of the divisor. It's then time for

**long division**. Here are some examples before we show you how to solve the problems.

24 ÷ 2 = 12 (See how you know have a quotient greater than 9?)

44 ÷ 4 = 11 (Four goes into forty-four eleven times.)

63 ÷ 3 = 21 (You can get 21 groups when you divide 63 by 3.)

80 ÷ 5 = 16 (There are 16 groups of 5 in the number 80. There is a sneaky remainder in this problem too.)

- or -

16 5 ) 80 - 5 30 - 30 0 |

## Related Activities

One and Two-Digit Division Quiz (No Remainders)
- Play Activity |
One and Two-Digit Division Quiz (No Remainders)
- Play Activity |

The key to solving these problems is to see that the number in the tens column of the dividend is already divisible by the divisor. In the problem 28 ÷ 2 = 12, the "2" in 28 is divisible by two (one time). You would write down a one (1) as the first number in your quotient and then move to the ones column and see that the "8" is divisible by two (four times). You then write a four (4) in the next place in your answer. When you hit these types of division problems, break them apart into bite-sized chunks.

(1) Do I have a two-digit number for a divisor?

• If yes, ask question 2.

• If no, do the division.

(2) Is the first number of my dividend bigger than my divisor?

• If yes, do the division in the tens column first, then move to the ones column.

• If no, you can divide the whole dividend by the divisor and your answer will be less than ten.

# Remainders

Yes, there are**remainders**when you divide two-digit numbers. Remember that the remainder will

**never**be larger than your divisor. It doesn't matter whether your answer is ten or greater, that remainder will always stay smaller than the divisor.

As you do long division, you will discover remainders in the middle of your division problems. It won't always be nice and even like when you divide sixty (62) by two (2). That even quotient of thirty-one (31) is just lucky. Think about the number fifty-four (54). When you divide by two, the 5 in the tens column is divisible by 2, but there is a remainder of 1. In long division, you hold on to that remainder for the division in the ones column. So, you actually have two small division problems.

**Example:**

54 ÷ 2 = ?

Step 1: 5 ÷ 2 = 2 with remainder of 1

Step 2: Combine the 1 with the 4 value from the ones column to make 14.

Step 3: 14 ÷ 2 = 7

Step 4: Put the two values together to get the answer of 27.

We're going to break it down into all of the steps now. We skipped over the subtraction to make things easier. In reality, you will do these steps. Start by looking at the first number of the dividend and think about how many times it can be divided by 2.

Step 1: 5 can only be divided by 2 two (2) times. 2 x 2 = 4

Step 2: 5 - 4 = 1. 1 is your remainder from division in the tens column.

Step 3: Bring down the 4 from the ones column in your dividend and place it to the right of your remainder (1), since the ones column is to the right of the tens column. This makes 14.

Step 4: 14 can be divided by 2 seven (7) times. 2 x 7 = 14

Step 5: 14 - 14 = 0. Since you have a difference of 0, the problem is over.

- or -

27 2 ) 54 - 4 14 - 14 0 |

You may be starting to notice another difference between multiplication and division. In your multiplication problems, you worked from right to left. You started multiplying the ones, then the tens, and moved your way up the numbers. In division we have been working from left to right. We start our division at the highest values of the dividend and work our way down. It's just one more thing you might notice when you are solving all of these problems.

To become more comfortable with division problems, you only need practice, practice, and more practice. It's always the same process.

(1) How many times can one number be divided?

(2) Multiply and subtract.

(3) Keep going through all of the numbers of the dividend.

## Related Activities

One and Two-Digit Division Quiz (With Remainders)
- Play Activity |
One and Two-Digit Division Quiz (No Remainders)
- Play Activity |

# Useful Reference Materials

**Wikipedia:**

*https://en.wikipedia.org/wiki/Arithmetic*

**Encyclopædia Britannica:**

*http://www.britannica.com/topic/arithmetic*

**Encyclopedia.com:**

*http://www.encyclopedia.com/topic/arithmetic.aspx*