Evaluate
\frac{107}{5}=21.4
Factor
\frac{107}{5} = 21\frac{2}{5} = 21.4
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\begin{array}{l}\phantom{25)}\phantom{1}\\25\overline{)535}\\\end{array}
Use the 1^{st} digit 5 from dividend 535
\begin{array}{l}\phantom{25)}0\phantom{2}\\25\overline{)535}\\\end{array}
Since 5 is less than 25, use the next digit 3 from dividend 535 and add 0 to the quotient
\begin{array}{l}\phantom{25)}0\phantom{3}\\25\overline{)535}\\\end{array}
Use the 2^{nd} digit 3 from dividend 535
\begin{array}{l}\phantom{25)}02\phantom{4}\\25\overline{)535}\\\phantom{25)}\underline{\phantom{}50\phantom{9}}\\\phantom{25)9}3\\\end{array}
Find closest multiple of 25 to 53. We see that 2 \times 25 = 50 is the nearest. Now subtract 50 from 53 to get reminder 3. Add 2 to quotient.
\begin{array}{l}\phantom{25)}02\phantom{5}\\25\overline{)535}\\\phantom{25)}\underline{\phantom{}50\phantom{9}}\\\phantom{25)9}35\\\end{array}
Use the 3^{rd} digit 5 from dividend 535
\begin{array}{l}\phantom{25)}021\phantom{6}\\25\overline{)535}\\\phantom{25)}\underline{\phantom{}50\phantom{9}}\\\phantom{25)9}35\\\phantom{25)}\underline{\phantom{9}25\phantom{}}\\\phantom{25)9}10\\\end{array}
Find closest multiple of 25 to 35. We see that 1 \times 25 = 25 is the nearest. Now subtract 25 from 35 to get reminder 10. Add 1 to quotient.
\text{Quotient: }21 \text{Reminder: }10
Since 10 is less than 25, stop the division. The reminder is 10. The topmost line 021 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 21.
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}