# Long Division Calculator

The calculator will divide any two numbers (positive or negative, integer or decimal), with steps shown. Enter the dividend and the divisor and get the quotient to the given precision without remainder or quotient with remainder.

• In general, you can skip the multiplication sign, so 5x is equivalent to 5*x.
• In general, you can skip parentheses, but be very careful: e^3x is e^3x, and e^(3x) is e^(3x).
• Also, be careful when you write fractions: 1/x^2 ln(x) is 1/x^2 ln(x), and 1/(x^2 ln(x)) is 1/(x^2 ln(x)).
• If you skip parentheses or a multiplication sign, type at least a whitespace, i.e. write sin x (or even better sin(x)) instead of sinx.
• Sometimes I see expressions like tan^2xsec^3x: this will be parsed as tan^(2*3)(x sec(x)). To get tan^2(x)sec^3(x), use parentheses: tan^2(x)sec^3(x).
• Similarly, tanxsec^3x will be parsed as tan(xsec^3(x)). To get tan(x)sec^3(x), use parentheses: tan(x)sec^3(x).
• From the table below, you can notice that sech is not supported, but you can still enter it using the identity sech(x)=1/cosh(x).
• If you get an error, double check your expression, add parentheses and multiplication signs where needed, and consult the table below.
• All suggestions and improvements are welcome. Please leave them in comments.
The following table contains the supported operations and functions:
 Type Get Constants e e pi pi i i (imaginary unit) Operations a+b a+b a-b a-b a*b a*b a^b, a**b a^b sqrt(x), x^(1/2) sqrt(x) cbrt(x), x^(1/3) root(3)(x) root(x,n), x^(1/n) root(n)(x) x^(a/b) x^(a/b) abs(x) |x| Functions e^x e^x ln(x), log(x) ln(x) ln(x)/ln(a) log_a(x) Trigonometric Functions sin(x) sin(x) cos(x) cos(x) tan(x) tan(x), tg(x) cot(x) cot(x), ctg(x) sec(x) sec(x) csc(x) csc(x), cosec(x) Inverse Trigonometric Functions asin(x), arcsin(x), sin^-1(x) asin(x) acos(x), arccos(x), cos^-1(x) acos(x) atan(x), arctan(x), tan^-1(x) atan(x) acot(x), arccot(x), cot^-1(x) acot(x) asec(x), arcsec(x), sec^-1(x) asec(x) acsc(x), arccsc(x), csc^-1(x) acsc(x) Hyperbolic Functions sinh(x) sinh(x) cosh(x) cosh(x) tanh(x) tanh(x) coth(x) coth(x) 1/cosh(x) sech(x) 1/sinh(x) csch(x) Inverse Hyperbolic Functions asinh(x), arcsinh(x), sinh^-1(x) asinh(x) acosh(x), arccosh(x), cosh^-1(x) acosh(x) atanh(x), arctanh(x), tanh^-1(x) atanh(x) acoth(x), arccoth(x), cot^-1(x) acoth(x) acosh(1/x) asech(x) asinh(1/x) acsch(x)

Divide by

Calculate the quotient to decimal points

If you don't enter quotient precision, long division will be performed with the remainder.
Sometimes, precision is not needed, e.g. 7/2=3.5.

Write all suggestions in comments below.

## Solution

Your input: find $$\frac{408}{160}$$$using the long division. Write the problem in a 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 $$4$$$? Answer is $$0$$$. Write down the calculated result in the upper part of the table. Now, $$4-0 \cdot 160 = 4 - 0= 4$$$.

Bring down the next digit of the dividend.

$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccc}\color{Purple}{0}&\phantom{0}&\phantom{2}\end{array}&\\\color{Magenta}{160}&\phantom{-}\enclose{longdiv}{\begin{array}{ccc}\color{Purple}{4}& 0 \downarrow&8\end{array}}&\\&\begin{array}{lll}-&\phantom{0}&\phantom{8}\\\phantom{lll}0\\\hline\phantom{lll}4&0\end{array}&\begin{array}{c}\end{array}\end{array}$$$Step 2 How many $$160$$$'s are in $$40$$$? Answer is $$0$$$.

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

Now, $$40-0 \cdot 160 = 40 - 0= 40$$$. Bring down the next digit of the dividend. $$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccc}0&\color{DarkCyan}{0}&\phantom{2}\end{array}&\\\color{Magenta}{160}&\phantom{-}\enclose{longdiv}{\begin{array}{ccc}4&0& 8 \downarrow\end{array}}&\\&\begin{array}{lll}-&\phantom{0}&\phantom{8}\\\phantom{lll}0\\\hline\phantom{lll}\color{DarkCyan}{4}&\color{DarkCyan}{0}\\-&\phantom{0}&\phantom{8}\\\phantom{lll}&0\\\hline\phantom{lll}4&0&8\end{array}&\begin{array}{c}\end{array}\end{array}$$$

Step 3

How many $$160$$$'s are in $$408$$$? Answer is $$2$$$. Write down the calculated result in the upper part of the table. Now, $$408-2 \cdot 160 = 408 - 320= 88$$$.

$$\require{enclose}\begin{array}{rlc}&\phantom{-\enclose{longdiv}{}}\begin{array}{ccc}0&0&\color{Brown}{2}\end{array}&\\\color{Magenta}{160}&\phantom{-}\enclose{longdiv}{\begin{array}{ccc}4&0&8\end{array}}&\\&\begin{array}{lll}-&\phantom{0}&\phantom{8}\\\phantom{lll}0\\\hline\phantom{lll}4&0\\-&\phantom{0}&\phantom{8}\\\phantom{lll}&0\\\hline\phantom{lll}\color{Brown}{4}&\color{Brown}{0}&\color{Brown}{8}\\-&\phantom{0}&\phantom{8}\\\phantom{lll}3&2&0\\\hline\phantom{lll}&8&8\end{array}&\begin{array}{c}\end{array}\end{array}$$$Since the remainder is greater than the divisor, then we are done. Therefore, $$\frac{408}{160}=2+\frac{88}{160}=2+\frac{11}{20}$$$

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