Mental Division: 2 Digit by 1 Digit Numbers

We have learned how to multiply 2-digit by 1-digit numbers mentally and in this post, we are going to discuss its corresponding method in division. Division seems to be the most difficult operation in mental calculation, but with the right strategy, it can be done. In the discussion, we will start with easy examples and then proceed to more complicated examples later.

Example 1: 52 ÷ 4

Solution:

We can separate 52 into 40 and 12. Then, we can divide 40 by 4 which is equal to 10. Next, we can divide 12 by 4 which is equal to 3. So, we have 10 + 3 = 13.

40/4 = 10

12/4 = 3

So, the answer is 10 + 3 = 13. 

Example 2: What is 87 ÷ 3

Solution

Sometimes, the strategy lies on how you separate numbers. In this case, we can separate 87 it into 60 and 27 (can you think of other ways?).

Now, 60/3 = 20 and 27/3 = 9.

So the quotient is 20 + 9 = 29.

Example 3: 312 ÷ 4

Solution 1

In this problem, we can separate 312 into 300 and 12. Now, 300 divided by 4 is 75 (remember, half of 300 is 150 and half of 150 is 75). Now, 12 divided by 4 is equal to 3. So, the correct answer is 75 + 3 = 78.

Solution 2

If the first solution is too difficult, there is another solution. Sometimes, we can separate the numbers into three numbers or more. For example, we can separate 312 into 200, 100, and 12. These 3 numbers are easier to divide, but the process is longer. That is,

200/4 = 50

100/4 = 25

and

12/4 = 3.

Now, 50 + 25 + 3 = 78.

The strategies about separating numbers into two or more numbers can be used a strategy to do mental division. If you are using pen and paper, and if you can divide fast, then the standard method maybe faster.

Exercises

Let’s do some exercise using the method above.

1.  84 ÷ 3

2. 112 ÷ 4

3. 96 ÷ 6

4. 204 ÷ 4

5. 350÷ 5

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