Evaluate
21
Factor
3\times 7
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\begin{array}{l}\phantom{30)}\phantom{1}\\30\overline{)630}\\\end{array}
Use the 1^{st} digit 6 from dividend 630
\begin{array}{l}\phantom{30)}0\phantom{2}\\30\overline{)630}\\\end{array}
Since 6 is less than 30, use the next digit 3 from dividend 630 and add 0 to the quotient
\begin{array}{l}\phantom{30)}0\phantom{3}\\30\overline{)630}\\\end{array}
Use the 2^{nd} digit 3 from dividend 630
\begin{array}{l}\phantom{30)}02\phantom{4}\\30\overline{)630}\\\phantom{30)}\underline{\phantom{}60\phantom{9}}\\\phantom{30)9}3\\\end{array}
Find closest multiple of 30 to 63. We see that 2 \times 30 = 60 is the nearest. Now subtract 60 from 63 to get reminder 3. Add 2 to quotient.
\begin{array}{l}\phantom{30)}02\phantom{5}\\30\overline{)630}\\\phantom{30)}\underline{\phantom{}60\phantom{9}}\\\phantom{30)9}30\\\end{array}
Use the 3^{rd} digit 0 from dividend 630
\begin{array}{l}\phantom{30)}021\phantom{6}\\30\overline{)630}\\\phantom{30)}\underline{\phantom{}60\phantom{9}}\\\phantom{30)9}30\\\phantom{30)}\underline{\phantom{9}30\phantom{}}\\\phantom{30)999}0\\\end{array}
Find closest multiple of 30 to 30. We see that 1 \times 30 = 30 is the nearest. Now subtract 30 from 30 to get reminder 0. Add 1 to quotient.
\text{Quotient: }21 \text{Reminder: }0
Since 0 is less than 30, stop the division. The reminder is 0. 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}