Jakokulmalaskin

Your input: find $$$\frac{408}{160}$$$ using long division.

Write the problem in the special format:

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccc}\phantom{0}&\phantom{0}&\phantom{2}\end{array}&\\160&\phantom{-}\enclose{longdiv}{\begin{array}{ccc}4&0&8\end{array}}&\\&\begin{array}{lll}\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 1

How many $$$160$$$'s are in $$$4$$$?

The answer is $$$0$$$.

Write down $$$0$$$ in the upper part of the table.

Now, $$$4-160 \cdot 0 = 4 - 0= 4$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccc}\color{Crimson}{0}&\phantom{0}&\phantom{2}\end{array}&\\\color{Magenta}{160}&\phantom{-}\enclose{longdiv}{\begin{array}{ccc}\color{Crimson}{4}& 0 \downarrow&8\end{array}}&\\&\begin{array}{lll}-&\phantom{0}&\phantom{8}\\\phantom{lll}0\\\hline\phantom{lll}4&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 2

How many $$$160$$$'s are in $$$40$$$?

The answer is $$$0$$$.

Write down $$$0$$$ in the upper part of the table.

Now, $$$40-160 \cdot 0 = 40 - 0= 40$$$.

Bring down the next digit of the dividend.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccc}0&\color{Chartreuse}{0}&\phantom{2}\end{array}&\\\color{Magenta}{160}&\phantom{-}\enclose{longdiv}{\begin{array}{ccc}4&0& 8 \downarrow\end{array}}&\\&\begin{array}{lll}-&\phantom{0}&\phantom{8}\\\phantom{lll}0\\\hline\phantom{lll}\color{Chartreuse}{4}&\color{Chartreuse}{0}\\-&\phantom{0}&\phantom{8}\\\phantom{lll}&0\\\hline\phantom{lll}4&0&8\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$$160$$$'s are in $$$408$$$?

The answer is $$$2$$$.

Write down $$$2$$$ in the upper part of the table.

Now, $$$408-160 \cdot 2 = 408 - 320= 88$$$.

$$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccc}0&0&\color{Peru}{2}\end{array}&\\\color{Magenta}{160}&\phantom{-}\enclose{longdiv}{\begin{array}{ccc}4&0&8\end{array}}&\\&\begin{array}{lll}-&\phantom{0}&\phantom{8}\\\phantom{lll}0\\\hline\phantom{lll}4&0\\-&\phantom{0}&\phantom{8}\\\phantom{lll}&0\\\hline\phantom{lll}\color{Peru}{4}&\color{Peru}{0}&\color{Peru}{8}\\-&\phantom{0}&\phantom{8}\\\phantom{lll}3&2&0\\\hline\phantom{lll}&8&8\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Since the remainder is less than the divisor, we are done.

Therefore, $$$\frac{408}{160}=2+\frac{88}{160}=2+\frac{11}{20}$$$

Answer: $$$\frac{408}{160}=2+\frac{11}{20}$$$