Evaluate
\frac{137}{25}=5.48
Factor
\frac{137}{5 ^ {2}} = 5\frac{12}{25} = 5.48
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\begin{array}{l}\phantom{50)}\phantom{1}\\50\overline{)274}\\\end{array}
Use the 1^{st} digit 2 from dividend 274
\begin{array}{l}\phantom{50)}0\phantom{2}\\50\overline{)274}\\\end{array}
Since 2 is less than 50, use the next digit 7 from dividend 274 and add 0 to the quotient
\begin{array}{l}\phantom{50)}0\phantom{3}\\50\overline{)274}\\\end{array}
Use the 2^{nd} digit 7 from dividend 274
\begin{array}{l}\phantom{50)}00\phantom{4}\\50\overline{)274}\\\end{array}
Since 27 is less than 50, use the next digit 4 from dividend 274 and add 0 to the quotient
\begin{array}{l}\phantom{50)}00\phantom{5}\\50\overline{)274}\\\end{array}
Use the 3^{rd} digit 4 from dividend 274
\begin{array}{l}\phantom{50)}005\phantom{6}\\50\overline{)274}\\\phantom{50)}\underline{\phantom{}250\phantom{}}\\\phantom{50)9}24\\\end{array}
Find closest multiple of 50 to 274. We see that 5 \times 50 = 250 is the nearest. Now subtract 250 from 274 to get reminder 24. Add 5 to quotient.
\text{Quotient: }5 \text{Reminder: }24
Since 24 is less than 50, stop the division. The reminder is 24. 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}