Evaluate
\frac{21}{10}=2.1
Factor
\frac{3 \cdot 7}{2 \cdot 5} = 2\frac{1}{10} = 2.1
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\begin{array}{l}\phantom{100)}\phantom{1}\\100\overline{)210}\\\end{array}
Use the 1^{st} digit 2 from dividend 210
\begin{array}{l}\phantom{100)}0\phantom{2}\\100\overline{)210}\\\end{array}
Since 2 is less than 100, use the next digit 1 from dividend 210 and add 0 to the quotient
\begin{array}{l}\phantom{100)}0\phantom{3}\\100\overline{)210}\\\end{array}
Use the 2^{nd} digit 1 from dividend 210
\begin{array}{l}\phantom{100)}00\phantom{4}\\100\overline{)210}\\\end{array}
Since 21 is less than 100, use the next digit 0 from dividend 210 and add 0 to the quotient
\begin{array}{l}\phantom{100)}00\phantom{5}\\100\overline{)210}\\\end{array}
Use the 3^{rd} digit 0 from dividend 210
\begin{array}{l}\phantom{100)}002\phantom{6}\\100\overline{)210}\\\phantom{100)}\underline{\phantom{}200\phantom{}}\\\phantom{100)9}10\\\end{array}
Find closest multiple of 100 to 210. We see that 2 \times 100 = 200 is the nearest. Now subtract 200 from 210 to get reminder 10. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }10
Since 10 is less than 100, stop the division. The reminder is 10. The topmost line 002 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 2.
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}