Fun with 2-digit divisors - Long division examples

How to Divide Double Digits

Dividing double digits is very similar to long division with a single-digit divisor, but it does require some extra multiplication and thinking.

Example: 236 & divide; 28 becomes

 

1. Guess how many times the divisor (the 28, in our example) can go into the dividend (the 236, in our example), then write down that number.
   
2. 3
   Multiply your guess and the divisor (which in our example is 28) and write the result under the original dividend.
   
3. 4
   Subtract the dividend and the multiplication result from step 3.
   
4. 5
   Continue the guess-multiply-subtract process until you reach zero OR a subtotal which is smaller than the divisor.
5. 6
   Decide how to deal with the remainder. When the result of the subtraction is smaller than the divisor, you have a remainder. You can write the remainder as a fraction, using the divisor as the denominator.
   • In our example, the answer would be 8 12/28, which would reduce in lowest terms to 8 3/7.
6. 7
   If you want to produce a decimal rather than a fraction, you need to add a ".0" to the end of your original dividend. (In our example, the 236 becomes 236.0)
7. 8
   Bring down the zero and stick it on the end of your latest subtraction result.
   
8. 9
   Estimate how many times your divisor can go into this new subtotal and write that down.
   
9. 10
   Multiply again...
   
10. 11
    ...then subtract again.
    
11. 12
    Keep repeating the "stick on a zero/estimate/multiply/subtract" process until you have enough decimal places OR until it subtracts to zero, whichever comes first.
    
    Tips

    In this example, we were working with 28. Keep in mind that 10 x 28 = 280, which means that 5 x 28 is half of that, or 140. Since 236 is between 280 and 140, your first guess should be between 5 and 10. That's one reason why 8 is a good number.

    Warning

    • If, at any point, your subtraction results in a number larger than your divisor, your guess wasn't high enough. Erase that entire step and try a larger guess.
    • If, at any point, your subtraction results in a negative number, your guess was too high. Erase that entire step and try a smaller guess.

    Things You'll Need
    
    

    • Pencil
    • Paper
    • Calculator (the quickest way)

Divide 987654321 by 123456789 in long division?

Solution for 987654321 ÷ 123456789 − with remainder

Step 1 Long division works from left to right. Since 123456789 is a 9-digit number, it will not go into 9, the first digit of 987654321, and so successive digits are added until a number greater than 123456789 is found. In this case 8 digits are added to make 987654321. Note the other digits in the original number have been turned grey to emphasise this and grey zeroes have been placed above to show where division was not possible with fewer digits. The closest we can get to 987654321 without exceeding it is 987654312 which is 8 × 123456789. These values have been added to the division, highlighted in red.

0 0 0 0 0 0 0 0 8  rem 9 123456789 9 8 7 6 5 4 3 2 1 9 8 7 6 5 4 3 1 2

123456789 × table 1 × 123456789 = 123456789 2 × 123456789 = 246913578 3 × 123456789 = 370370367 4 × 123456789 = 493827156 5 × 123456789 = 617283945 6 × 123456789 = 740740734 7 × 123456789 = 864197523 8 × 123456789 = 987654312 9 × 123456789 = 1111111101

Step 2 Finally, subtract 987654312 from 987654321 giving 9. Since there are no other digits to bring down, 9 is therefore also the remainder for the whole sum. So 987654321 ÷ 123456789 = 8 rem 9	8  rem 9 123456789 9 8 7 6 5 4 3 2 1 9 8 7 6 5 4 3 1 2 9
123456789 × table 1 × 123456789 = 123456789 2 × 123456789 = 246913578 3 × 123456789 = 370370367 4 × 123456789 = 493827156 5 × 123456789 = 617283945 6 × 123456789 = 740740734 7 × 123456789 = 864197523 8 × 123456789 = 987654312 9 × 123456789 = 1111111101

How to do double digit long division?

How to divide a four digit number by a two digit number (e.g. 4138 ÷ 17):

• Place the divisor before the division bracket and place the dividend (4138) under it.

       
17)4138

• Examine the first digit of the dividend(4). It is smaller than 17 so can't be divided by 17 to produce a whole number. Next take the first two digits of the dividend (41) and determine how many 17's it contains. In this case 41 holds two seventeens (2*17=34) but not three (3*17=51). Place the 2 above the division bracket.

    2  
17)4138

• Multiply the 2 by 17 and place the result (34) below the 41 of the dividend.

    2 
17)4138
   34

• Draw a line under the 34 and subtract it from 41 (41-34=7). Bring down the 3 from the 4138 and place it to the right of the 7.

    2 
17)4138
   34
    73

• Divide 73 by 17 and place that answer above the division bracket and to the right of the two.

    24 
17)4138
   34
    73

• Multiply the 4 of the quotient by the divisor (17) to get 68 and place this below the 73 under the dividend. Subtract 68 from 73 to give an answer of 5. Bring down the 8 from the dividend 4138 and place it next to the 5

    24 
17)4138
   34
    73
    68
     58

• Divide 58 by 17 and place that answer (3) above the division bracket and to the right of the four.

    243
17)4138
   34
    73
    68
     58

• Multiply the 3 of the quotient by the divisor (17) to get 51 and place this below the 58 under the dividend. Subtract 51 from 58 to give an answer of 7.

    243
17)4138
   34
    73
    68
     58
     51
      7

• There are no more digits in the dividend to bring down so the 7 is a remainder. The final answer could be written in several ways.
  243 remainder 7 or sometimes 243r7
  or as a mixed number 243  7/17

How to do Long division tricks for kids?

"In arithmetic, long division is a standard procedure suitable for dividing simple or complex multidigit numbers. It breaks down a division problem into a series of easier steps. As in all division problems, one number, called the dividend, is divided by another, called the divisor, producing a result called the quotient. It enables computations involving arbitrarily large numbers to be performed by following a series of simple steps"

Source: Wikipedia.org 

 

Specific Skills: Division Facts Tips & Tricks 

DIVISION FACTS TIPS & TRICKS GR 3-4 

Solution for 742 ÷ 31 - with remainder

Step 1 Long division works from left to right. Since 31 will not go into 7, a grey 0 has been placed over the 7 and we combine the first two digits to make 74. Note the other digits in the original number have been turned grey to emphasise this. The closest we can get to 74 without exceeding it is 62 which is 2 × 31. These values have been added to the division, highlighted in red.	0 2  rem 29 31 7 4 2 6 2
31 × table 1 × 31 = 31 2 × 31 = 62 3 × 31 = 93 4 × 31 = 124 5 × 31 = 155 6 × 31 = 186 7 × 31 = 217 8 × 31 = 248 9 × 31 = 279

Step 2 Next, work out the remainder by subtracting 62 from 74. This gives us 12. Bring down the 2 to make a new target of 122.	2  rem 29 31 7 4 2 6 2 1 2 2
31 × table 1 × 31 = 31 2 × 31 = 62 3 × 31 = 93 4 × 31 = 124 5 × 31 = 155 6 × 31 = 186 7 × 31 = 217 8 × 31 = 248 9 × 31 = 279

Step 3 With a target of 122, the closest we can get is 93 by multiplying 31 by 3. Write the 93 below the 122 as shown.	2 3  rem 29 31 7 4 2 6 2 1 2 2 9 3
31 × table 1 × 31 = 31 2 × 31 = 62 3 × 31 = 93 4 × 31 = 124 5 × 31 = 155 6 × 31 = 186 7 × 31 = 217 8 × 31 = 248 9 × 31 = 279

Step 4 Finally, subtract 93 from 122 giving 29. Since there are no other digits to bring down, 29 is therefore also the remainder for the whole sum. So 742 ÷ 31 = 23 rem 29	2 3  rem 29 31 7 4 2 6 2 1 2 2 9 3 2 9
31 × table 1 × 31 = 31 2 × 31 = 62 3 × 31 = 93 4 × 31 = 124 5 × 31 = 155 6 × 31 = 186 7 × 31 = 217 8 × 31 = 248 9 × 31 = 279

Long division traditional method

How to explain long division to children?

 
Master Long Division Practice Workbook: Improve Your Math Fluency Series (Volume 8)

Basic Math and Pre-Algebra Workbook For Dummies 

Division, Ages 7-12 (Workbook w/Music CD) 

 

Solution for 768978 ÷ 358 - with remainder

Step 1 Long division works from left to right. Since 358 will not go into 7, a grey 0 has been placed over the 7 and we combine the first two digits to make 76. In this case, 76 is still too small. A further 0 is added above 6 and a third digit is added to make 768. Note the other digits in the original number have been turned grey to emphasise this. The closest we can get to 768 without exceeding it is 716 which is 2 × 358. These values have been added to the division, highlighted in red.

0 0 2  rem 352 358 7 6 8 9 7 8 7 1 6

358 × table 1 × 358 = 358 2 × 358 = 716 3 × 358 = 1074 4 × 358 = 1432 5 × 358 = 1790 6 × 358 = 2148 7 × 358 = 2506 8 × 358 = 2864 9 × 358 = 3222

Step 2 Next, work out the remainder by subtracting 716 from 768. This gives us 52. Bring down the 9 to make a new target of 529.	2  rem 352 358 7 6 8 9 7 8 7 1 6 5 2 9
358 × table 1 × 358 = 358 2 × 358 = 716 3 × 358 = 1074 4 × 358 = 1432 5 × 358 = 1790 6 × 358 = 2148 7 × 358 = 2506 8 × 358 = 2864 9 × 358 = 3222

Step 3 With a target of 529, the closest we can get is 358 by multiplying 358 by 1. Write the 358 below the 529 as shown.	2 1  rem 352 358 7 6 8 9 7 8 7 1 6 5 2 9 3 5 8
358 × table 1 × 358 = 358 2 × 358 = 716 3 × 358 = 1074 4 × 358 = 1432 5 × 358 = 1790 6 × 358 = 2148 7 × 358 = 2506 8 × 358 = 2864 9 × 358 = 3222

Step 4 Next, work out the remainder by subtracting 358 from 529. This gives us 171. Bring down the 7 to make a new target of 1717.	2 1  rem 352 358 7 6 8 9 7 8 7 1 6 5 2 9 3 5 8 1 7 1 7
358 × table 1 × 358 = 358 2 × 358 = 716 3 × 358 = 1074 4 × 358 = 1432 5 × 358 = 1790 6 × 358 = 2148 7 × 358 = 2506 8 × 358 = 2864 9 × 358 = 3222

Step 5 With a target of 1717, the closest we can get is 1432 by multiplying 358 by 4. Write the 1432 below the 1717 as shown.	2 1 4  rem 352 358 7 6 8 9 7 8 7 1 6 5 2 9 3 5 8 1 7 1 7 1 4 3 2
358 × table 1 × 358 = 358 2 × 358 = 716 3 × 358 = 1074 4 × 358 = 1432 5 × 358 = 1790 6 × 358 = 2148 7 × 358 = 2506 8 × 358 = 2864 9 × 358 = 3222

Step 6 Next, work out the remainder by subtracting 1432 from 1717. This gives us 285. Bring down the 8 to make a new target of 2858.	2 1 4  rem 352 358 7 6 8 9 7 8 7 1 6 5 2 9 3 5 8 1 7 1 7 1 4 3 2 2 8 5 8
358 × table 1 × 358 = 358 2 × 358 = 716 3 × 358 = 1074 4 × 358 = 1432 5 × 358 = 1790 6 × 358 = 2148 7 × 358 = 2506 8 × 358 = 2864 9 × 358 = 3222

Step 7 With a target of 2858, the closest we can get is 2506 by multiplying 358 by 7. Write the 2506 below the 2858 as shown.	2 1 4 7  rem 352 358 7 6 8 9 7 8 7 1 6 5 2 9 3 5 8 1 7 1 7 1 4 3 2 2 8 5 8 2 5 0 6
358 × table 1 × 358 = 358 2 × 358 = 716 3 × 358 = 1074 4 × 358 = 1432 5 × 358 = 1790 6 × 358 = 2148 7 × 358 = 2506 8 × 358 = 2864 9 × 358 = 3222

Step 8 Finally, subtract 2506 from 2858 giving 352. Since there are no other digits to bring down, 352 is therefore also the remainder for the whole sum. So 768978 ÷ 358 = 2147 rem 352	2 1 4 7  rem 352 358 7 6 8 9 7 8 7 1 6 5 2 9 3 5 8 1 7 1 7 1 4 3 2 2 8 5 8 2 5 0 6 3 5 2
358 × table 1 × 358 = 358 2 × 358 = 716 3 × 358 = 1074 4 × 358 = 1432 5 × 358 = 1790 6 × 358 = 2148 7 × 358 = 2506 8 × 358 = 2864 9 × 358 = 3222