Evaluate
93
Factor
3\times 31
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\begin{array}{l}\phantom{17)}\phantom{1}\\17\overline{)1581}\\\end{array}
Use the 1^{st} digit 1 from dividend 1581
\begin{array}{l}\phantom{17)}0\phantom{2}\\17\overline{)1581}\\\end{array}
Since 1 is less than 17, use the next digit 5 from dividend 1581 and add 0 to the quotient
\begin{array}{l}\phantom{17)}0\phantom{3}\\17\overline{)1581}\\\end{array}
Use the 2^{nd} digit 5 from dividend 1581
\begin{array}{l}\phantom{17)}00\phantom{4}\\17\overline{)1581}\\\end{array}
Since 15 is less than 17, use the next digit 8 from dividend 1581 and add 0 to the quotient
\begin{array}{l}\phantom{17)}00\phantom{5}\\17\overline{)1581}\\\end{array}
Use the 3^{rd} digit 8 from dividend 1581
\begin{array}{l}\phantom{17)}009\phantom{6}\\17\overline{)1581}\\\phantom{17)}\underline{\phantom{}153\phantom{9}}\\\phantom{17)99}5\\\end{array}
Find closest multiple of 17 to 158. We see that 9 \times 17 = 153 is the nearest. Now subtract 153 from 158 to get reminder 5. Add 9 to quotient.
\begin{array}{l}\phantom{17)}009\phantom{7}\\17\overline{)1581}\\\phantom{17)}\underline{\phantom{}153\phantom{9}}\\\phantom{17)99}51\\\end{array}
Use the 4^{th} digit 1 from dividend 1581
\begin{array}{l}\phantom{17)}0093\phantom{8}\\17\overline{)1581}\\\phantom{17)}\underline{\phantom{}153\phantom{9}}\\\phantom{17)99}51\\\phantom{17)}\underline{\phantom{99}51\phantom{}}\\\phantom{17)9999}0\\\end{array}
Find closest multiple of 17 to 51. We see that 3 \times 17 = 51 is the nearest. Now subtract 51 from 51 to get reminder 0. Add 3 to quotient.
\text{Quotient: }93 \text{Reminder: }0
Since 0 is less than 17, stop the division. The reminder is 0. The topmost line 0093 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 93.
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}