Evaluate
69
Factor
3\times 23
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\begin{array}{l}\phantom{20)}\phantom{1}\\20\overline{)1380}\\\end{array}
Use the 1^{st} digit 1 from dividend 1380
\begin{array}{l}\phantom{20)}0\phantom{2}\\20\overline{)1380}\\\end{array}
Since 1 is less than 20, use the next digit 3 from dividend 1380 and add 0 to the quotient
\begin{array}{l}\phantom{20)}0\phantom{3}\\20\overline{)1380}\\\end{array}
Use the 2^{nd} digit 3 from dividend 1380
\begin{array}{l}\phantom{20)}00\phantom{4}\\20\overline{)1380}\\\end{array}
Since 13 is less than 20, use the next digit 8 from dividend 1380 and add 0 to the quotient
\begin{array}{l}\phantom{20)}00\phantom{5}\\20\overline{)1380}\\\end{array}
Use the 3^{rd} digit 8 from dividend 1380
\begin{array}{l}\phantom{20)}006\phantom{6}\\20\overline{)1380}\\\phantom{20)}\underline{\phantom{}120\phantom{9}}\\\phantom{20)9}18\\\end{array}
Find closest multiple of 20 to 138. We see that 6 \times 20 = 120 is the nearest. Now subtract 120 from 138 to get reminder 18. Add 6 to quotient.
\begin{array}{l}\phantom{20)}006\phantom{7}\\20\overline{)1380}\\\phantom{20)}\underline{\phantom{}120\phantom{9}}\\\phantom{20)9}180\\\end{array}
Use the 4^{th} digit 0 from dividend 1380
\begin{array}{l}\phantom{20)}0069\phantom{8}\\20\overline{)1380}\\\phantom{20)}\underline{\phantom{}120\phantom{9}}\\\phantom{20)9}180\\\phantom{20)}\underline{\phantom{9}180\phantom{}}\\\phantom{20)9999}0\\\end{array}
Find closest multiple of 20 to 180. We see that 9 \times 20 = 180 is the nearest. Now subtract 180 from 180 to get reminder 0. Add 9 to quotient.
\text{Quotient: }69 \text{Reminder: }0
Since 0 is less than 20, stop the division. The reminder is 0. The topmost line 0069 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 69.
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}