Evaluate
\frac{42}{13}\approx 3.230769231
Factor
\frac{2 \cdot 3 \cdot 7}{13} = 3\frac{3}{13} = 3.230769230769231
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\begin{array}{l}\phantom{52)}\phantom{1}\\52\overline{)168}\\\end{array}
Use the 1^{st} digit 1 from dividend 168
\begin{array}{l}\phantom{52)}0\phantom{2}\\52\overline{)168}\\\end{array}
Since 1 is less than 52, use the next digit 6 from dividend 168 and add 0 to the quotient
\begin{array}{l}\phantom{52)}0\phantom{3}\\52\overline{)168}\\\end{array}
Use the 2^{nd} digit 6 from dividend 168
\begin{array}{l}\phantom{52)}00\phantom{4}\\52\overline{)168}\\\end{array}
Since 16 is less than 52, use the next digit 8 from dividend 168 and add 0 to the quotient
\begin{array}{l}\phantom{52)}00\phantom{5}\\52\overline{)168}\\\end{array}
Use the 3^{rd} digit 8 from dividend 168
\begin{array}{l}\phantom{52)}003\phantom{6}\\52\overline{)168}\\\phantom{52)}\underline{\phantom{}156\phantom{}}\\\phantom{52)9}12\\\end{array}
Find closest multiple of 52 to 168. We see that 3 \times 52 = 156 is the nearest. Now subtract 156 from 168 to get reminder 12. Add 3 to quotient.
\text{Quotient: }3 \text{Reminder: }12
Since 12 is less than 52, stop the division. The reminder is 12. The topmost line 003 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 3.
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}