Evaluate
21
Factor
3\times 7
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\begin{array}{l}\phantom{50)}\phantom{1}\\50\overline{)1050}\\\end{array}
Use the 1^{st} digit 1 from dividend 1050
\begin{array}{l}\phantom{50)}0\phantom{2}\\50\overline{)1050}\\\end{array}
Since 1 is less than 50, use the next digit 0 from dividend 1050 and add 0 to the quotient
\begin{array}{l}\phantom{50)}0\phantom{3}\\50\overline{)1050}\\\end{array}
Use the 2^{nd} digit 0 from dividend 1050
\begin{array}{l}\phantom{50)}00\phantom{4}\\50\overline{)1050}\\\end{array}
Since 10 is less than 50, use the next digit 5 from dividend 1050 and add 0 to the quotient
\begin{array}{l}\phantom{50)}00\phantom{5}\\50\overline{)1050}\\\end{array}
Use the 3^{rd} digit 5 from dividend 1050
\begin{array}{l}\phantom{50)}002\phantom{6}\\50\overline{)1050}\\\phantom{50)}\underline{\phantom{}100\phantom{9}}\\\phantom{50)99}5\\\end{array}
Find closest multiple of 50 to 105. We see that 2 \times 50 = 100 is the nearest. Now subtract 100 from 105 to get reminder 5. Add 2 to quotient.
\begin{array}{l}\phantom{50)}002\phantom{7}\\50\overline{)1050}\\\phantom{50)}\underline{\phantom{}100\phantom{9}}\\\phantom{50)99}50\\\end{array}
Use the 4^{th} digit 0 from dividend 1050
\begin{array}{l}\phantom{50)}0021\phantom{8}\\50\overline{)1050}\\\phantom{50)}\underline{\phantom{}100\phantom{9}}\\\phantom{50)99}50\\\phantom{50)}\underline{\phantom{99}50\phantom{}}\\\phantom{50)9999}0\\\end{array}
Find closest multiple of 50 to 50. We see that 1 \times 50 = 50 is the nearest. Now subtract 50 from 50 to get reminder 0. Add 1 to quotient.
\text{Quotient: }21 \text{Reminder: }0
Since 0 is less than 50, stop the division. The reminder is 0. The topmost line 0021 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}