Evaluate
\frac{31}{10}=3.1
Factor
\frac{31}{2 \cdot 5} = 3\frac{1}{10} = 3.1
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\begin{array}{l}\phantom{40)}\phantom{1}\\40\overline{)124}\\\end{array}
Use the 1^{st} digit 1 from dividend 124
\begin{array}{l}\phantom{40)}0\phantom{2}\\40\overline{)124}\\\end{array}
Since 1 is less than 40, use the next digit 2 from dividend 124 and add 0 to the quotient
\begin{array}{l}\phantom{40)}0\phantom{3}\\40\overline{)124}\\\end{array}
Use the 2^{nd} digit 2 from dividend 124
\begin{array}{l}\phantom{40)}00\phantom{4}\\40\overline{)124}\\\end{array}
Since 12 is less than 40, use the next digit 4 from dividend 124 and add 0 to the quotient
\begin{array}{l}\phantom{40)}00\phantom{5}\\40\overline{)124}\\\end{array}
Use the 3^{rd} digit 4 from dividend 124
\begin{array}{l}\phantom{40)}003\phantom{6}\\40\overline{)124}\\\phantom{40)}\underline{\phantom{}120\phantom{}}\\\phantom{40)99}4\\\end{array}
Find closest multiple of 40 to 124. We see that 3 \times 40 = 120 is the nearest. Now subtract 120 from 124 to get reminder 4. Add 3 to quotient.
\text{Quotient: }3 \text{Reminder: }4
Since 4 is less than 40, stop the division. The reminder is 4. The topmost line 003 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 3.
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}