How To Do Short Division
How To Do Short Division
when the divisor is a 1 digit number, you can use a shorter form of division, called
short division. With short division, you divide, multiply, and subtract in your head.
Write the remainder, if there is one, in front of the next place, and continue dividing.
For Example, if you wanted to divide 6258 by 8, you:
1. Divide the 62 hundreds. Think: 8 into 62 goes 7 times. 62-56=6 write the 6 hundreds
next to the 5 tens.
2. Divide the 65 tens. 8 into 65 goes 8 times. 65 - 64 = 1. Write the 1 tens next to the8
3. Divide the 18 ones. 8 into 18 goes 2 times. 18- 16 = 2. Write the 2 remainder.
Of course, you have to be really good at multiplication and division to be able to do short
division, but IF your are good at it, it will allow you to do division faster than you could
punch it into a calculator!
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Short division is the method often used for dividing by a single-digit number. Let's first
look at the sharing process. For example let us share 65p between 5 children.
We can give each child one 10p coin. We then exchange the remaining 10p coin for
ten 1p coins, giving us 15 1p coins to share out.
Thus each child gets one 10p and three 1p coins. It is the process of exchanging a
ten for ten ones, or a hundred for 10 tens, that is used in short division.
If we divide 65 by 5 using short division we firstly divide 6 ( tens) by 5 to get 1
remainder 1(ten). We then exchange it for 10 units and add them to the 5 to make 15
units. 15 divided by 5 is 3 and so the answer is 13.
Let us divide 235 by 6. Firstly we find that the 2 (hundreds) cannot be divided by 6
and so we exchange them for 20 tens. We add these to the 3 tens to make 23 tens.
23 divided by six is 3 remainder 5(tens).
We convert these to 50 units and add them to the 5 to make 55. 55 divided by 6 is 9
remainder 1. Thus the answer is 39 remainder 1.
The procedure involves several steps. As an example, consider the problem of 950
divided by 4:
The dividend and divisor are written in the short division tableau:
Now instead of dividing the whole dividend (950) by the divisor (4), we will take as
many digits of the dividend as necessary (starting from the left) to form a number that
contains the divisor at least once, but less than ten times. In this case, that partial
dividend is 9.
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The first number to be divided by the divisor (4) is the partial dividend (9). We write
the integer part of the result (2) above the division bar over the leftmost digit of the
dividend, and we write the remainder (1) as a small digit (or digits) to the above and
to the right of the partial dividend (9).
Next we repeat step 2, using the small digits just written along with the next digit of
the dividend to form a new partial dividend (15).
Dividing the new partial dividend by the divisor (4), we write the results as before: the
quotient above the next digit of the dividend, and the remainder to the right. (Here 15
divided by 4 is 3, with a remainder of 3.)
We repeat step 2 until there are no digits remaining in the dividend. (In this example,
the next step is to find that 30 divided by 4 is 7, with a remainder of 2.)
The number written above the bar (237) is the quotient, and the result of the last
subtraction is the remainder for the entire problem (2).
The answer to the above example is expressed as 237 with remainder 2.
Alternatively, one can continue the above procedure to produce a decimal answer.
We continue the process by adding a decimal and zeroes as necessary to the right of
the dividend, treating each zero as another digit of the dividend. Thus the next step in
such a calculation would give the following:
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