Evaluate
\frac{321}{52}\approx 6.173076923
Factor
\frac{3 \cdot 107}{2 ^ {2} \cdot 13} = 6\frac{9}{52} = 6.173076923076923
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\begin{array}{l}\phantom{156)}\phantom{1}\\156\overline{)963}\\\end{array}
Use the 1^{st} digit 9 from dividend 963
\begin{array}{l}\phantom{156)}0\phantom{2}\\156\overline{)963}\\\end{array}
Since 9 is less than 156, use the next digit 6 from dividend 963 and add 0 to the quotient
\begin{array}{l}\phantom{156)}0\phantom{3}\\156\overline{)963}\\\end{array}
Use the 2^{nd} digit 6 from dividend 963
\begin{array}{l}\phantom{156)}00\phantom{4}\\156\overline{)963}\\\end{array}
Since 96 is less than 156, use the next digit 3 from dividend 963 and add 0 to the quotient
\begin{array}{l}\phantom{156)}00\phantom{5}\\156\overline{)963}\\\end{array}
Use the 3^{rd} digit 3 from dividend 963
\begin{array}{l}\phantom{156)}006\phantom{6}\\156\overline{)963}\\\phantom{156)}\underline{\phantom{}936\phantom{}}\\\phantom{156)9}27\\\end{array}
Find closest multiple of 156 to 963. We see that 6 \times 156 = 936 is the nearest. Now subtract 936 from 963 to get reminder 27. Add 6 to quotient.
\text{Quotient: }6 \text{Reminder: }27
Since 27 is less than 156, stop the division. The reminder is 27. The topmost line 006 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 6.
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}