Jun 30, 2010

How to do long division step by step?


Video on teaching kids how to do two-digit quotient division
Step by step on how do three digit division problems

How to do long division step by step?


How to long division with remainder? How to divide a three digit number by a one digit number (e.g 416 ÷ 7)?

Dividing a three digit number by a one digit number (for example 416 ÷ 7) involves several steps.
  • Place the divisor before the division bracket and place the dividend (416) under it.
  • 
         
    7)416
  • Examine the first digit of the dividend(4). It is smaller than 7 so can't be divided by 7 to produce a whole number. Next take the first two digits of the dividend (41) and determine how many 7's it contains. In this case 41 holds five sevens (5*7=35) but not six (6*7=42). Place the 5 above the division bracket.
  • 
       5 
    7)416
  • Multiply the 5 by 7 and place the result (35) below the 41 of the dividend.
  • 
       5 
    7)416
      35
  • Draw a line under the 35 and subtract it from 41 (41-35=6). Bring down the 6 from the 416 and place it to the right of the other 6.
  • 
       5 
    7)416
      35
       66
  • Divide 66 by 7 and place that answer above the division bracket to the right of the five.
  • 
       59
    7)416
      35
       66
  • Multiply the 9 of the quotient by the divisor (7) to get 63 and place this below the 66. Subtract 63 from 66 to give an answer of 3. The number 3 is called the remainder and indicates that there were three left over.
  • 
       59 R 3
    7)416
      35
       66
       63
        3
How to long division without remainder? How to divide a three digit number by a one digit number (e.g 413 ÷ 7)?
  • Place the divisor before the division bracket and place the dividend (413) under it.
  • 
         
    7)413
  • Examine the first digit of the dividend(4). It is smaller than 7 so it can't be divided by 7 to produce a whole number. Next take the first two digits of the dividend (41) and determine how many 7's it contains. In this case 41 holds five sevens (5*7=35) but not six (6*7=42). Place the 5 above the division bracket.
  • 
       5 
    7)413
  • Multiply the 5 by 7 and place the result (35) below the 41 of the dividend.
  • 
       5 
    7)413
      35
  • Draw a line under the 35 and subtract it from 41 (41-35=6). Bring down the 3 from the 413 and place it to the right of the 6.
  • 
       5 
    7)413
      35
       63
  • Divide 63 by 7 and place that answer above the division bracket to the right of the five.
  • 
       59
    7)413
      35
       63
  • Multiply the 9 of the quotient by the divisor (7) to get 63 and place this below the 63 under the dividend. Subtract 63 from 63 to give an answer of 0. This indicates that there is nothing left over and 7 can be evenly divided into 413 to produce a quotient of 59.
  • 
       59
    7)413
      35
       63
       63
        0
More books about long division for kids

How to do Long Division with Remainders?

When we are given a long division to do it will not always work out to a whole number. Sometimes there will be numbers left over. These are known as remainders. Taking an example similar to that on the Long Division page it becomes more clear: 435 ÷ 25. If you feel happy with the process on the Long Division
page you can skip the first bit.
 
4 ÷ 25 = 0 remainder 4 The first number of the dividend is divided by the divisor.

The whole number result is placed at the top. Any remainders are ignored at this point.
25 × 0 = 0 The answer from the first operation is multiplied by the divisor. The result is placed under the number divided into.
4 – 0 = 4 Now we take away the bottom number from the top number.

Bring down the next number of the dividend.
43 ÷ 25 = 1 remainder 18 Divide this number by the divisor.

The whole number result is placed at the top. Any remainders are ignored at this point.
25 × 1 = 25 The answer from the above operation is multiplied by the divisor. The result is placed under the last number divided into.
43 – 25 = 18 Now we take away the bottom number from the top number.

Bring down the next number of the dividend.
185 ÷ 25 = 7 remainder 10 Divide this number by the divisor.

The whole number result is placed at the top. Any remainders are ignored at this point.
25 × 7 = 175 The answer from the above operation is multiplied by the divisor. The result is placed under the number divided into.
185 – 175 = 10 Now we take away the bottom number from the top number.


There is still 10 left over but no more numbers to bring down.

With a long division with remainders the answer is expressed as 17 remainder 10 as shown in the diagram


How to explain long division to children?

Solution for 531219 ÷ 579 - with remainder

Step 1

Long division works from left to right. Since 579 will not go into 5, a grey 0 has been placed over the 5 and we combine the first two digits to make 53. In this case, 53 is still too small. A further 0 is added above 3 and a third digit is added to make 531. Note the other digits in the original number have been turned grey to emphasise this.
The closest we can get to 531 without exceeding it is 5211 which is 9 × 579. These values have been added to the division, highlighted in red.

0009

 rem 276

579531219

5211

579 × table
1 × 579 =579
2 × 579 =1158
3 × 579 =1737
4 × 579 =2316
5 × 579 =2895
6 × 579 =3474
7 × 579 =4053
8 × 579 =4632
9 × 579 =5211



Step 2

Next, work out the remainder by subtracting 5211 from 5312. This gives us 101. Bring down the 1 to make a new target of 1011.

9

 rem 276

579531219

5211

1011

579 × table
1 × 579 =579
2 × 579 =1158
3 × 579 =1737
4 × 579 =2316
5 × 579 =2895
6 × 579 =3474
7 × 579 =4053
8 × 579 =4632
9 × 579 =5211






Step 3

With a target of 1011, the closest we can get is 579 by multiplying 579 by 1. Write the 579 below the 1011 as shown.

91
 rem 276

579531219

5211

1011

579

579 × table
1 × 579 =579
2 × 579 =1158
3 × 579 =1737
4 × 579 =2316
5 × 579 =2895
6 × 579 =3474
7 × 579 =4053
8 × 579 =4632
9 × 579 =5211




Step 4

Next, work out the remainder by subtracting 579 from 1011. This gives us 432. Bring down the 9 to make a new target of 4329.

91
 rem 276

579531219

5211

1011

579

4329

579 × table
1 × 579 =579
2 × 579 =1158
3 × 579 =1737
4 × 579 =2316
5 × 579 =2895
6 × 579 =3474
7 × 579 =4053
8 × 579 =4632
9 × 579 =5211



Step 5

With a target of 4329, the closest we can get is 4053 by multiplying 579 by 7. Write the 4053 below the 4329 as shown.

917 rem 276

579531219

5211

1011

579

4329

4053

579 × table
1 × 579 =579
2 × 579 =1158
3 × 579 =1737
4 × 579 =2316
5 × 579 =2895
6 × 579 =3474
7 × 579 =4053
8 × 579 =4632
9 × 579 =5211


Step 6

Finally, subtract 4053 from 4329 giving 276. Since there are no other digits to bring down, 276 is therefore also the remainder for the whole sum.
So 531219 ÷ 579 = 917 rem 276

917 rem 276

579531219

5211

1011

579

4329

4053

276

579 × table
1 × 579 =579
2 × 579 =1158
3 × 579 =1737
4 × 579 =2316
5 × 579 =2895
6 × 579 =3474
7 × 579 =4053
8 × 579 =4632
9 × 579 =5211

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