Evaluate
\frac{230}{159}\approx 1.446540881
Factor
\frac{2 \cdot 5 \cdot 23}{3 \cdot 53} = 1\frac{71}{159} = 1.4465408805031446
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\begin{array}{l}\phantom{318)}\phantom{1}\\318\overline{)460}\\\end{array}
Use the 1^{st} digit 4 from dividend 460
\begin{array}{l}\phantom{318)}0\phantom{2}\\318\overline{)460}\\\end{array}
Since 4 is less than 318, use the next digit 6 from dividend 460 and add 0 to the quotient
\begin{array}{l}\phantom{318)}0\phantom{3}\\318\overline{)460}\\\end{array}
Use the 2^{nd} digit 6 from dividend 460
\begin{array}{l}\phantom{318)}00\phantom{4}\\318\overline{)460}\\\end{array}
Since 46 is less than 318, use the next digit 0 from dividend 460 and add 0 to the quotient
\begin{array}{l}\phantom{318)}00\phantom{5}\\318\overline{)460}\\\end{array}
Use the 3^{rd} digit 0 from dividend 460
\begin{array}{l}\phantom{318)}001\phantom{6}\\318\overline{)460}\\\phantom{318)}\underline{\phantom{}318\phantom{}}\\\phantom{318)}142\\\end{array}
Find closest multiple of 318 to 460. We see that 1 \times 318 = 318 is the nearest. Now subtract 318 from 460 to get reminder 142. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }142
Since 142 is less than 318, stop the division. The reminder is 142. The topmost line 001 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 1.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}