Evaluate
\frac{31}{19}\approx 1.631578947
Factor
\frac{31}{19} = 1\frac{12}{19} = 1.631578947368421
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\begin{array}{l}\phantom{76)}\phantom{1}\\76\overline{)124}\\\end{array}
Use the 1^{st} digit 1 from dividend 124
\begin{array}{l}\phantom{76)}0\phantom{2}\\76\overline{)124}\\\end{array}
Since 1 is less than 76, use the next digit 2 from dividend 124 and add 0 to the quotient
\begin{array}{l}\phantom{76)}0\phantom{3}\\76\overline{)124}\\\end{array}
Use the 2^{nd} digit 2 from dividend 124
\begin{array}{l}\phantom{76)}00\phantom{4}\\76\overline{)124}\\\end{array}
Since 12 is less than 76, use the next digit 4 from dividend 124 and add 0 to the quotient
\begin{array}{l}\phantom{76)}00\phantom{5}\\76\overline{)124}\\\end{array}
Use the 3^{rd} digit 4 from dividend 124
\begin{array}{l}\phantom{76)}001\phantom{6}\\76\overline{)124}\\\phantom{76)}\underline{\phantom{9}76\phantom{}}\\\phantom{76)9}48\\\end{array}
Find closest multiple of 76 to 124. We see that 1 \times 76 = 76 is the nearest. Now subtract 76 from 124 to get reminder 48. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }48
Since 48 is less than 76, stop the division. The reminder is 48. The topmost line 001 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 1.
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}