Long division is a little different to short division, but isn’t as difficult as many often perceive it to be.
Here we’ll show 2 examples of solving division sums with long division steps. With one example being long division and remainders.
Long Division Steps,
Long Division and Remainders Examples
1.1
648 ÷ 12 ?
Solution
1)
The first step here in using the long division method is to set the numbers up like we would with a short division sum.
12 648
For the first bit of division, 12 doesn’t go into 6, so we put a 0 above in the solution section.
0
12 648
But now looking at the first two numbers in the dividend together, 12 does go into 64.
Not an exact amount of times, but with “LONG” division, at this stage we ignore any remainders, so 12 goes into 64 five times.
05
12 648
2)
Next we multiply the divisor 12 by this 5. 12 × 5 = 60
We then place this number below 64 in the dividend, subtract, then place the result below.
05
12 648
− 60
4
3)
Now the next number in the dividend in brought down alongside the 4.
Here this is 8, so we will have 48.
05
12 648
− 60
48
This new 48 is now divided by the divisor 12, and the result is placed appropriately above in the answer. 48 ÷ 12 = 4
054
12 648
− 60
48
4)
Then it’s the same process again, the 4 from the answer is multiplied by the divisor 12.
Then followed by being subtracted from the number sitting above.
4 × 12 = 48
054
12 648
− 60
48
− 48
0
The result from the last subtraction is 0, and with no numbers left in the dividend to bring down, the long division sum is complete.
With no remainder in the answer.
648 ÷ 12 = 54
1.2
483 ÷ 15 ?
Solution
1)
15 483
Firstly, 15 doesn’t go into 4, so a 0 goes above.
0
15 483
Ignoring remainders at this point as usual, 15 does go into 48 three times.
03
15 483
2)
Next we multiply the divisor 15 by the 3. 15 × 3 = 45
We then place this number below 48 in the dividend, subtract, then place the result below.
03
15 483
− 45
3
3)
The next number in the dividend is now brought down and combined with the 3, giving us 33.
03
15 483
− 45
33
This 33, again ignoring remainders, can now be divided by the divisor 15, with the result is placed in the appropriate place above in the answer.
33 ÷ 15 = 2
032
15 483
− 45
33
4)
Now following same process again, this 2 from the answer is multiplied by the divisor 15.
Followed by being subtracted from the number above again.
032
15 483
− 45
33
− 30
3
The last result is 3 this time instead of zero.
This is what happens when we have long division and remainders, a non zero last result.
Now as there are no numbers left in the dividend to bring down, the long division steps are complete, with the final 3 being our remainder.
438 ÷ 15 = 32 remainder 3