Evaluate
\frac{173}{30}\approx 5.766666667
Factor
\frac{173}{2 \cdot 3 \cdot 5} = 5\frac{23}{30} = 5.766666666666667
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\begin{array}{l}\phantom{60)}\phantom{1}\\60\overline{)346}\\\end{array}
Use the 1^{st} digit 3 from dividend 346
\begin{array}{l}\phantom{60)}0\phantom{2}\\60\overline{)346}\\\end{array}
Since 3 is less than 60, use the next digit 4 from dividend 346 and add 0 to the quotient
\begin{array}{l}\phantom{60)}0\phantom{3}\\60\overline{)346}\\\end{array}
Use the 2^{nd} digit 4 from dividend 346
\begin{array}{l}\phantom{60)}00\phantom{4}\\60\overline{)346}\\\end{array}
Since 34 is less than 60, use the next digit 6 from dividend 346 and add 0 to the quotient
\begin{array}{l}\phantom{60)}00\phantom{5}\\60\overline{)346}\\\end{array}
Use the 3^{rd} digit 6 from dividend 346
\begin{array}{l}\phantom{60)}005\phantom{6}\\60\overline{)346}\\\phantom{60)}\underline{\phantom{}300\phantom{}}\\\phantom{60)9}46\\\end{array}
Find closest multiple of 60 to 346. We see that 5 \times 60 = 300 is the nearest. Now subtract 300 from 346 to get reminder 46. Add 5 to quotient.
\text{Quotient: }5 \text{Reminder: }46
Since 46 is less than 60, stop the division. The reminder is 46. The topmost line 005 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 5.
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}