Evaluate
\frac{256}{3}\approx 85.333333333
Factor
\frac{2 ^ {8}}{3} = 85\frac{1}{3} = 85.33333333333333
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\begin{array}{l}\phantom{18)}\phantom{1}\\18\overline{)1536}\\\end{array}
Use the 1^{st} digit 1 from dividend 1536
\begin{array}{l}\phantom{18)}0\phantom{2}\\18\overline{)1536}\\\end{array}
Since 1 is less than 18, use the next digit 5 from dividend 1536 and add 0 to the quotient
\begin{array}{l}\phantom{18)}0\phantom{3}\\18\overline{)1536}\\\end{array}
Use the 2^{nd} digit 5 from dividend 1536
\begin{array}{l}\phantom{18)}00\phantom{4}\\18\overline{)1536}\\\end{array}
Since 15 is less than 18, use the next digit 3 from dividend 1536 and add 0 to the quotient
\begin{array}{l}\phantom{18)}00\phantom{5}\\18\overline{)1536}\\\end{array}
Use the 3^{rd} digit 3 from dividend 1536
\begin{array}{l}\phantom{18)}008\phantom{6}\\18\overline{)1536}\\\phantom{18)}\underline{\phantom{}144\phantom{9}}\\\phantom{18)99}9\\\end{array}
Find closest multiple of 18 to 153. We see that 8 \times 18 = 144 is the nearest. Now subtract 144 from 153 to get reminder 9. Add 8 to quotient.
\begin{array}{l}\phantom{18)}008\phantom{7}\\18\overline{)1536}\\\phantom{18)}\underline{\phantom{}144\phantom{9}}\\\phantom{18)99}96\\\end{array}
Use the 4^{th} digit 6 from dividend 1536
\begin{array}{l}\phantom{18)}0085\phantom{8}\\18\overline{)1536}\\\phantom{18)}\underline{\phantom{}144\phantom{9}}\\\phantom{18)99}96\\\phantom{18)}\underline{\phantom{99}90\phantom{}}\\\phantom{18)999}6\\\end{array}
Find closest multiple of 18 to 96. We see that 5 \times 18 = 90 is the nearest. Now subtract 90 from 96 to get reminder 6. Add 5 to quotient.
\text{Quotient: }85 \text{Reminder: }6
Since 6 is less than 18, stop the division. The reminder is 6. The topmost line 0085 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 85.
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}