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