Evaluate
\frac{116}{105}\approx 1.104761905
Factor
\frac{2 ^ {2} \cdot 29}{3 \cdot 5 \cdot 7} = 1\frac{11}{105} = 1.1047619047619048
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\begin{array}{l}\phantom{210)}\phantom{1}\\210\overline{)232}\\\end{array}
Use the 1^{st} digit 2 from dividend 232
\begin{array}{l}\phantom{210)}0\phantom{2}\\210\overline{)232}\\\end{array}
Since 2 is less than 210, use the next digit 3 from dividend 232 and add 0 to the quotient
\begin{array}{l}\phantom{210)}0\phantom{3}\\210\overline{)232}\\\end{array}
Use the 2^{nd} digit 3 from dividend 232
\begin{array}{l}\phantom{210)}00\phantom{4}\\210\overline{)232}\\\end{array}
Since 23 is less than 210, use the next digit 2 from dividend 232 and add 0 to the quotient
\begin{array}{l}\phantom{210)}00\phantom{5}\\210\overline{)232}\\\end{array}
Use the 3^{rd} digit 2 from dividend 232
\begin{array}{l}\phantom{210)}001\phantom{6}\\210\overline{)232}\\\phantom{210)}\underline{\phantom{}210\phantom{}}\\\phantom{210)9}22\\\end{array}
Find closest multiple of 210 to 232. We see that 1 \times 210 = 210 is the nearest. Now subtract 210 from 232 to get reminder 22. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }22
Since 22 is less than 210, stop the division. The reminder is 22. 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}