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.

    000000008 rem 9

    123456789987654321

    987654312

    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

    123456789987654321

    987654312

    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
    [Read More...]


    How to do Long division with decimals in divisor?



    Another type of division you’ll encounter is division with decimals in both the divisor and the dividend. It might look something like this:
    In this situation, you move the decimal place the number of spaces in the divisor until the decimal is at the end of the number; you move the decimal the same number of spaces in the dividend: this does NOT necessarily mean the decimal will land at the end of the dividend. Here’s an example:
    Your new problem looks like this (note the change in decimal places in both the divisor and dividend):
    Now you continue to work the problem out, remembering to bring your decimal up into your quotient at the appropriate time (it will be in red in the diagram).
    Thus, your final answer is simply 16.
    Let’s try one more example of moving the decimal over in order to solve the problem.
    becomes
    After the decimals are moved, it looks like this:
    After you move the decimals, continue the problem, like this:
    Thus, your final answer is 6.25.

    We’ve already practiced long division, but so far our answers have all come out even (in other words, our last subtraction problem ended in an answer of 0). However, sometimes our division problems will not come out evenly, and we will have another number (not 0) when we do the last subtraction problem. This leftover number is called a remainder, and it is written as part of the quotient. Follow along with this example:

    The red circled number at the bottom our remainder. You do not have to circle the remainder; we just circled ours so that you know which number it is. After you have your remainder, you write it on top of the division bar, with an r in front of it, like this: 25 r 3.
    When your division ends with a remainder, you must make sure that your remainder is less than your divisor. If your remainder is more than your divisor, you need to go back and check your division, because it is incorrect. We can still use our multiplication method to check our division; you will multiply the quotient (25) by the divisor (5), and then add our remainder to the answer to the multiplication problem, like this:

    Let’s try that one more time. Here’s a new example:

    Our answer to this problem is 23 r 1; note that we always write the remainder after the quotient, on top of the division bar. Also notice that our remainder (1) is smaller than our divisor (6).
    Now let’s check our work, like this:

    There are also several different ways to write remainders. The standard way is shown above, with an r in front of the number. However, you can also write remainders as fractions and as decimals.

    Long Division with Remainders as Fractions

    Now that you understand the basics of long division, you may be asked to write your remainder as a fraction. Don’t worry! It’s not hard at all. You’re going to do long division the same way—divide, multiply, subtract, bring down, and then you’re going to get a remainder. Instead of writing r and then the number, you are going to take your remainder and make it the numerator of a fraction. The denominator comes from the divisor—you use the same number you’re dividing by in your denominator.
    Let’s look at the following example:

    Notice that you do not use the r at all in front of your remainder when you’re turning it into a fraction. However, you do still write the fraction as part of the quotient (answer to your division problem).
    Also, you would check this division problem the same way as a normal division problem; multiply the quotient (23) by the divisor (6) and then add the remainder (1). Do not do anything with the fraction in order to check this problem.

    Long Division with Remainders as Decimals

    Another way you may be asked to express a remainder is in the form of a decimal. When you’re asked to express your remainder as a decimal, you first complete division as usual, until you get to the point you usually end at, where you have nothing else to bring down. Instead of stopping here, however, you are going to keep going with division. You will add a decimal point (.) after the last number given in the dividend, and you will also place a decimal point in the quotient after the number you have so far. After the decimal in the dividend, you will add a zero (0) and continue division. You will keep adding zeroes until your subtraction step results in an answer of 0 as well. Follow along with this example:

    Notice that we added a decimal after the 6 in the dividend, as well as a decimal after the 5 in our quotient. Then, we started adding zeroes to the dividend. This time, it only took us one added zero before our remainder was zero.
    Now, let’s look at a problem where you’d have to add more than one zero to the dividend:

    When you have your quotient with a decimal, you check the answer differently than if it had a remainder as a fraction or just a remainder written with r. Instead of adding the remainder separately, you just multiply the quotient (including decimal) by the divisor, like this:
    [Read More...]


    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
    [Read More...]


    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"


    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.

    02
     rem 29

    31742

    62

    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

    31742

    62

    122

    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.

    23 rem 29

    31742

    62

    122

    93

    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

    23 rem 29

    31742

    62

    122

    93

    29

    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

    [Read More...]


    Ho to explain long division to children?



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

    002


     rem 352

    358768978

    716

    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

    358768978

    716

    529

    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.

    21

     rem 352

    358768978

    716

    529

    358

    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.

    21

     rem 352

    358768978

    716

    529

    358

    1717

    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.

    214
     rem 352

    358768978

    716

    529

    358

    1717

    1432

    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.

    214
     rem 352

    358768978

    716

    529

    358

    1717

    1432

    2858

    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.

    2147 rem 352

    358768978

    716

    529

    358

    1717

    1432

    2858

    2506

    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

    2147 rem 352

    358768978

    716

    529

    358

    1717

    1432

    2858

    2506

    352

    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
    [Read More...]


     
    Return to top of page Copyright © 2010 Copyright 2010 (C) Cool Maths - Cool Math - CoolMath4Kids - Cool math games - Free Math Games for Kids of All Ages - Math Cool Games for Kids - Maths Games - Cool Math for Kids - Maths Games - Cool Maths Games for kids Coordinates www.thecoolmath.info. All right reseved.