Calculatrice de division longue

Your input: find $\frac{408.0}{160.0}$ using long division.

Move the decimal point 1 place to the right in both numbers. It is equivalent to multiplying the numbers by $10^{1}=10$:

$408.0 \cdot 10=4080$ and $160.0 \cdot 10=1600$.

Write the problem in the special format:

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccc}\phantom{0}&\phantom{0}&\phantom{0}&\phantom{2}\end{array}&\\1600&\phantom{-}\enclose{longdiv}{\begin{array}{cccc}4&0&8&0\end{array}}&\\&\begin{array}{llll}\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 1

How many $1600$'s are in $4$? The answer is $0$.

Write down the calculated result in the upper part of the table.

Now, $4-0 \cdot 1600 = 4 - 0= 4$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccc}\color{Chocolate}{0}&\phantom{0}&\phantom{0}&\phantom{2}\end{array}&\\\color{Magenta}{1600}&\phantom{-}\enclose{longdiv}{\begin{array}{cccc}\color{Chocolate}{4}& 0 \downarrow&8&0\end{array}}&\\&\begin{array}{llll}-&\phantom{0}&\phantom{8}&\phantom{0}\\\phantom{lll}0\\\hline\phantom{lll}4&0\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 2

How many $1600$'s are in $40$? The answer is $0$.

Write down the calculated result in the upper part of the table.

Now, $40-0 \cdot 1600 = 40 - 0= 40$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccc}0&\color{Crimson}{0}&\phantom{0}&\phantom{2}\end{array}&\\\color{Magenta}{1600}&\phantom{-}\enclose{longdiv}{\begin{array}{cccc}4&0& 8 \downarrow&0\end{array}}&\\&\begin{array}{llll}-&\phantom{0}&\phantom{8}&\phantom{0}\\\phantom{lll}0\\\hline\phantom{lll}\color{Crimson}{4}&\color{Crimson}{0}\\-&\phantom{0}&\phantom{8}&\phantom{0}\\\phantom{lll}&0\\\hline\phantom{lll}4&0&8\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 3

How many $1600$'s are in $408$? The answer is $0$.

Write down the calculated result in the upper part of the table.

Now, $408-0 \cdot 1600 = 408 - 0= 408$.

Bring down the next digit of the dividend.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccc}0&0&\color{Peru}{0}&\phantom{2}\end{array}&\\\color{Magenta}{1600}&\phantom{-}\enclose{longdiv}{\begin{array}{cccc}4&0&8& 0 \downarrow\end{array}}&\\&\begin{array}{llll}-&\phantom{0}&\phantom{8}&\phantom{0}\\\phantom{lll}0\\\hline\phantom{lll}4&0\\-&\phantom{0}&\phantom{8}&\phantom{0}\\\phantom{lll}&0\\\hline\phantom{lll}\color{Peru}{4}&\color{Peru}{0}&\color{Peru}{8}\\-&\phantom{0}&\phantom{8}&\phantom{0}\\\phantom{lll}&&0\\\hline\phantom{lll}4&0&8&0\end{array}&\begin{array}{c}\end{array}\end{array}$

Step 4

How many $1600$'s are in $4080$? The answer is $2$.

Write down the calculated result in the upper part of the table.

Now, $4080-2 \cdot 1600 = 4080 - 3200= 880$.

$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{cccc}0&0&0&\color{Chartreuse}{2}\end{array}&\\\color{Magenta}{1600}&\phantom{-}\enclose{longdiv}{\begin{array}{cccc}4&0&8&0\end{array}}&\\&\begin{array}{llll}-&\phantom{0}&\phantom{8}&\phantom{0}\\\phantom{lll}0\\\hline\phantom{lll}4&0\\-&\phantom{0}&\phantom{8}&\phantom{0}\\\phantom{lll}&0\\\hline\phantom{lll}4&0&8\\-&\phantom{0}&\phantom{8}&\phantom{0}\\\phantom{lll}&&0\\\hline\phantom{lll}\color{Chartreuse}{4}&\color{Chartreuse}{0}&\color{Chartreuse}{8}&\color{Chartreuse}{0}\\-&\phantom{0}&\phantom{8}&\phantom{0}\\\phantom{lll}3&2&0&0\\\hline\phantom{lll}&8&8&0\end{array}&\begin{array}{c}\end{array}\end{array}$

Since the remainder is greater than the divisor, then we are done.

Therefore, $\frac{4080}{1600}=2+\frac{880}{1600}=2+\frac{11}{20}$

Answer: $\frac{408.0}{160.0}=2+\frac{11}{20}$