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Two-Digit DivisionNot all of division is done with numbers less than ten (10). As you learn about dividing double-digit numbers, you will see patterns similar to the patterns you saw in multiplication. Take a look at these before we move on...
5 x 5 = 25
25 ÷ 5 = 5
4 x 7 = 28
28 ÷ 7 = 4
28 ÷ 4 = 7
Interesting. Division is like the reverse of multiplication. That makes sense since we keep telling you that multiplication is about putting groups together and division pulls them apart. If you remember the two factors that were used to create a number, the division should be easy.
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
So if you get the problem 24 ÷ 4 = ? You know the answer is 6 because 6 x 4 = 24.
Long and ShortSometimes the answers will be easy when you wind up with a single number. Those easy problems are short division. The number you are dividing is less than ten (1) times the value of the divisor. Examples of short division include...
28 ÷ 4 = 7
64 ÷ 8 = 8
54 ÷ 9 = 6
99 ÷ 11 = 9
It's as simple as pie. 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. Some examples...
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
80 ÷ 5 = 16
The key to solving these problems is to see that the number in the tens column 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) 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 ones column of your answer (quotient). When you hit these 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 it is, do the division in the tens column first, then move to the ones column.
- If not, you can divide the whole dividend by the divisor and your answer is less than ten.
RemaindersYes, 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 (60) by two (2). That even quotient of thirty (30) is just lucky. Think about the number fifty-four (54). When you divide by two, that 5 is divisible by 2, but the re is a remainder of 1. In long division, you hold onto that remainder for the division in the ones column. So you actually have two divisions.
Example: 54 ÷ 2 = ?
(1) 5 ÷ 2 = 2 with remainder of 1
(2) combine the 1 with the 4 value from the ones column to make 14.
(3) 14 ÷ 2 = 7
(4) Put the two values together to get the answer of 27
Practice, practice, and more practice.
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