division in easy way

How to Teach Long Division

In this article I explain how to teach long division in several steps. Instead of showing the whole algorithm to the students at once, we truly take it "step by step".

Before a child is ready to learn long division, he/she has to know:

• multiplication tables (at least fairly well)
• basic division concept, based on multiplication tables
  (for example 28 ÷ 7 or 56 ÷ 8)
• basic division with remainders (for example 54 ÷ 7 or 23 ÷ 5)
  

One reason why long division is difficult

Long division is an algorithm that repeats the basic steps of
1) Divide; 2) Multiply; 3) Subtract; 4) Drop down the next digit.

Of these steps, #2 and #3 can become difficult and confusing to students because they don't seemingly have to do with division—they have to do with finding the remainder. In fact, to point that out, I like to combine them into a single "multiply & subtract" step.

To avoid the confusion, I advocate teaching long division in such a fashion that children are NOT exposed to all of those steps at first. Instead, you can teach it in several "steps":

• Step 1: Division is even in all the digits. Here, students practice just the dividing part.
• Step 2: A remainder in the ones. Now, students practice the "multiply & subtract" part and connect that with finding the remainder.
• Step 3: A remainder in the tens. Students now use the whole algorithm, including "dropping down the next digit", using 2-digit dividends.
• Step 4: A remainder in any of the place values. Students practice the whole algorithm using longer dividends.

Step 1: Division is even in all the digits

We divide numbers where each of the hundreds, tens, and ones digits are evenly divisible by the divisor. The GOAL in this first, easy step is to get students used to two things:

1. To get used to the long division "corner" so that the quotient is written on top.
2. To get used to asking how many times does the divisor go into the various digits of the dividend.

Example problems for this step follow. Students should check each division by multiplication.
 

a.

4 

) 

8 4 

b.

3 

) 

6 6 0 

c.

4 

) 

8 0 4 0 

In this step, students also learn to look at the first two digits of the dividend if the divisor does not "go into" the first digit:

 

 

h   t   o

 

 

0 

4 

) 

2 4 8 

 

 

 

h   t   o

 

 

0 6 2

4 

) 

2 4 8 

4 does not go into 2. You can put zero in the quotient in the hundreds place or omit it. But 4 does go into 24, six times. Put 6 in the quotient.

Explanation:

The 2 of 248 is of course 200 in reality. If you divided 200 by 4, the result would be less than 100, so that is why the quotient won't have any whole hundreds.

But then you combine the 2 hundreds with the 4 tens. That makes 24 tens, and you CAN divide 24 tens by 4. The result 6 tens goes as part of  the quotient.

Check the final answer: 4 × 62 = 248.

More example problems follow. Divide. Check your answer by multiplying the quotient and the divisor.

a.

3 

) 

1 2 3 

b.

4 

) 

2 8 4 

 

 

 

 

c.

6 

) 

3 6 0 

d.

8 

) 

2 4 8 

 

 

 

 

Step 2: A Remainder in the ones

Now, there is a remainder in the ones (units). Thousands, hundreds, and tens digits still divide evenly by the divisor. First, students can solve the remainder mentally and simply write the remainder right after the quotient:

		h   t   o
		0 4 1 R1
4	)	1 6 5

4 does not go into 1 (hundred). So combine the 1 hundred with the 6 tens (160).

4 goes into 16 four times.

4 goes into 5 once, leaving a remainder of 1.

		th  h  t   o
		0 4 0 0 R7
8	)	3 2 0 7

8 does not go into 3 of the thousands. So combine the 3 thousands with the 2 hundreds (3,200).

8 goes into 32 four times (3,200 ÷ 8 = 400)
8 goes into 0 zero times (tens).
8 goes into 7 zero times, and leaves a remainder of 7.

Next, students learn to find the remainder using the process of "multiply & subtract". This is a very important step! The "multiply & subtract" part is often very confusing to students, so here we practice it in the easiest possible place: in the very end of the division, in the ones colum (instead of in the tens or hundreds column). Of course, this assumes that students have already learned to find the remainder in easy division problems that are based on the multiplication tables (such as 45 ÷ 7 or 18 ÷ 5).

In the problems before, you just wrote down the remainder of the ones. Usually, we write down the subtraction that actually finds the remainder. Look carefully:

		h   t   o
		0 6 1
4	)	2 4 7
		− 4
		3

When dividing the ones, 4 goes into 7 one time. Multiply 1 × 4 = 4, write that four under the 7, and subract. This finds us the remainder of 3.

Check: 4 × 61 + 3 = 247

		th   h   t   o
		0 4 0 2
4	)	1 6 0 9
		− 8
		1

When dividing the ones, 4 goes into 9 two times. Multiply 2 × 4 = 8, write that eight under the 9, and subract. This finds us the remainder of 1.

Check: 4 × 402 + 1 = 1,609