Description of the long division with remainder
Long division is the division of two integers, which produces a quotient and a remainder.
If a natural number \(a\) divides by a natural number \(b\), then it is calculated how many times the number \(b\) is contained in \(a\). The result is the quotient \(q\) and possibly a remainder \(r\).
We can write \(a = b · q + r\)
Example \(17 / 5 = 3\) remainder \(2\)
The remainder is therefore the difference between the dividend and the largest multiple of the divisor
\(17 - (3 · 5) = 2\)
A remainder arises only if the dividend is not a multiple of the divisor. In other words, if the dividend is not divisible by the divisor.
Dividing numbers with different signs gets the following results.
\(7\,/\, 3 = 2\) Rest \(1\)
\(-7 \,/\, 3 = -2\) Rest \(-1\)
\(7\, / -3 = -2\) Rest \(1\)
\(-7\,/ -3 = 2\) Rest \(-1\)
\(145:3=\)Divide the first digit of the left number by the right number. If that doesn't work, add the second digit on the left, here 14.
\(\color{blue}{14}53:\color{blue}{3}=\color{blue}{4}\)Now multiply the result by the right number, write the product under the digits used in the left number and form the difference.
\(\color{blue}{14}5:\color{blue}{3}=\color{blue}{4}\)Then you pull the next digit of the left number down and calculate again.
\(\color{blue}{\underline{12}}\;\;⇐\; {3·4}\)
\(\color{blue}{\;\;2}\)
\(14\color{blue}{5}:3=4\)The result is 48 remainder 1
\(\underline{12} \)
\(\;\;2\color{blue}{5}\)
\(14\color{blue}{5}:3=48\)
\(\underline{12} \)
\(\;\;2\color{blue}{5}\)
\(\;\;\underline{24} \;\;⇐\; {3·8}\)
\(\;\;\;\;1\)
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