Similar to the case of multiplication in Math, division of numbers is usually done with the method of short division, or long division.
This page looks at how to effectively approach division sums with short division.
How to do Short Division Introduction
If we wanted to divide 248 by 2. 248 ÷ 2
248 is the DIVIDEND , 2 is the DIVISOR
The final answer to the division sum is the QUOTIENT.
With short division, a division sum is set up in the following way:
QUOTIENT
DIVISOR DIVIDEND
Thus for 248 ÷ 2, we lay out as follows.
\begin{array}{r} \\[-2pt] 2 {\bf{|}} {\overline{\space 248 \space\space}} \end{array}
From here we carry out the division in steps from left to right to obtain the answer, the QUOTIENT.
1)
2 goes into 2 once with no remainder, so a 1 is placed above the 4 in the QUOTIENT section.
\begin{array}{r} 1 \space\space\space\space\space\space\\[-2pt] 2 {\bf{|}} {\overline{\space 248 \space\space}} \end{array}
2)
2 goes into 4 two times with no remainder, so next we place a 2 in the QUOTIENT above the 6
\begin{array}{r} 12 \space\space\space\space\\[-2pt] 2 {\bf{|}} {\overline{\space 248 \space\space}} \end{array}
3)
Finally 2 goes into 8 four times, so a 4 is the last entry in the QUOTIENT, above the 8.
\begin{array}{r} 124 \space\space\\[-2pt] 2 {\bf{|}} {\overline{\space 248 \space\space}} \end{array}
We now have obtained the answer to the division sum. 248 ÷ 2 = 124
Short Division Examples
(1.1)
740 ÷ 4 ?
Solution
\begin{array}{r} \\[-2pt] \bf 4 {\bf{|}} {\overline{\space 740 \space\space}} \end{array}
1)
4 goes into 7 once, with a remainder of 3.
What happens here, is that the 1 goes above in the answer as usual, while the remainder 3 gets placed alongside the next number in the dividend to the right, which is 4
The effect of placing the remainder 3 below is that it turns 4 into 34 .
\begin{array}{r} 1 \space\space\space\space\space\space\space\\[-2pt] 4 {\bf{|}} {\overline{\space 7{\tiny{3}}40 \space\space}} \end{array}
2)
Now 4 goes into 34 eight times, with a remainder of 2.
\begin{array}{r} 1\space8 \space\space\space\space\space\\[-2pt] 4 {\bf{|}} {\overline{\space 7{\tiny{3}}4{\tiny{2}}0 \space\space}} \end{array}
3)
For the last step 4 goes into 20 exactly five times, and there is no remainder.
\begin{array}{r} 1\space8 \space5 \space\space\\[-2pt] 4 {\bf{|}} {\overline{\space 7{\tiny{3}}4{\tiny{2}}0 \space\space}} \end{array}
740 ÷ 4 = 185
(1.2)
284 ÷ 4 ?
Solution
\begin{array}{r} \\[-2pt] \bf 4 {\bf{|}} {\overline{\space 284 \space\space}} \end{array}
1)
4 doesn’t go into 2, so 0 is placed above in the answer.
\begin{array}{r} 0 \space\space\space\space\space\space\\[-2pt] 4 {\bf{|}} {\overline{\space 284 \space\space}} \end{array}
2)
We now move along and think about how many times 4 goes into 28, which is seven times, with no remainder.
\begin{array}{r} 07 \space\space\space\space\\[-2pt] 4 {\bf{|}} {\overline{\space 284 \space\space}} \end{array}
3)
Lastly 4 goes into 4 exactly once.
\begin{array}{r} 071 \space\space\\[-2pt] 4 {\bf{|}} {\overline{\space 284 \space\space}} \end{array}
284 ÷ 4 = 71
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