Evaluate
\frac{178}{37}\approx 4.810810811
Factor
\frac{2 \cdot 89}{37} = 4\frac{30}{37} = 4.8108108108108105
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\begin{array}{l}\phantom{74)}\phantom{1}\\74\overline{)356}\\\end{array}
Use the 1^{st} digit 3 from dividend 356
\begin{array}{l}\phantom{74)}0\phantom{2}\\74\overline{)356}\\\end{array}
Since 3 is less than 74, use the next digit 5 from dividend 356 and add 0 to the quotient
\begin{array}{l}\phantom{74)}0\phantom{3}\\74\overline{)356}\\\end{array}
Use the 2^{nd} digit 5 from dividend 356
\begin{array}{l}\phantom{74)}00\phantom{4}\\74\overline{)356}\\\end{array}
Since 35 is less than 74, use the next digit 6 from dividend 356 and add 0 to the quotient
\begin{array}{l}\phantom{74)}00\phantom{5}\\74\overline{)356}\\\end{array}
Use the 3^{rd} digit 6 from dividend 356
\begin{array}{l}\phantom{74)}004\phantom{6}\\74\overline{)356}\\\phantom{74)}\underline{\phantom{}296\phantom{}}\\\phantom{74)9}60\\\end{array}
Find closest multiple of 74 to 356. We see that 4 \times 74 = 296 is the nearest. Now subtract 296 from 356 to get reminder 60. Add 4 to quotient.
\text{Quotient: }4 \text{Reminder: }60
Since 60 is less than 74, stop the division. The reminder is 60. The topmost line 004 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 4.
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}