Evaluate
\frac{923}{2}=461.5
Factor
\frac{13 \cdot 71}{2} = 461\frac{1}{2} = 461.5
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\begin{array}{l}\phantom{60)}\phantom{1}\\60\overline{)27690}\\\end{array}
Use the 1^{st} digit 2 from dividend 27690
\begin{array}{l}\phantom{60)}0\phantom{2}\\60\overline{)27690}\\\end{array}
Since 2 is less than 60, use the next digit 7 from dividend 27690 and add 0 to the quotient
\begin{array}{l}\phantom{60)}0\phantom{3}\\60\overline{)27690}\\\end{array}
Use the 2^{nd} digit 7 from dividend 27690
\begin{array}{l}\phantom{60)}00\phantom{4}\\60\overline{)27690}\\\end{array}
Since 27 is less than 60, use the next digit 6 from dividend 27690 and add 0 to the quotient
\begin{array}{l}\phantom{60)}00\phantom{5}\\60\overline{)27690}\\\end{array}
Use the 3^{rd} digit 6 from dividend 27690
\begin{array}{l}\phantom{60)}004\phantom{6}\\60\overline{)27690}\\\phantom{60)}\underline{\phantom{}240\phantom{99}}\\\phantom{60)9}36\\\end{array}
Find closest multiple of 60 to 276. We see that 4 \times 60 = 240 is the nearest. Now subtract 240 from 276 to get reminder 36. Add 4 to quotient.
\begin{array}{l}\phantom{60)}004\phantom{7}\\60\overline{)27690}\\\phantom{60)}\underline{\phantom{}240\phantom{99}}\\\phantom{60)9}369\\\end{array}
Use the 4^{th} digit 9 from dividend 27690
\begin{array}{l}\phantom{60)}0046\phantom{8}\\60\overline{)27690}\\\phantom{60)}\underline{\phantom{}240\phantom{99}}\\\phantom{60)9}369\\\phantom{60)}\underline{\phantom{9}360\phantom{9}}\\\phantom{60)999}9\\\end{array}
Find closest multiple of 60 to 369. We see that 6 \times 60 = 360 is the nearest. Now subtract 360 from 369 to get reminder 9. Add 6 to quotient.
\begin{array}{l}\phantom{60)}0046\phantom{9}\\60\overline{)27690}\\\phantom{60)}\underline{\phantom{}240\phantom{99}}\\\phantom{60)9}369\\\phantom{60)}\underline{\phantom{9}360\phantom{9}}\\\phantom{60)999}90\\\end{array}
Use the 5^{th} digit 0 from dividend 27690
\begin{array}{l}\phantom{60)}00461\phantom{10}\\60\overline{)27690}\\\phantom{60)}\underline{\phantom{}240\phantom{99}}\\\phantom{60)9}369\\\phantom{60)}\underline{\phantom{9}360\phantom{9}}\\\phantom{60)999}90\\\phantom{60)}\underline{\phantom{999}60\phantom{}}\\\phantom{60)999}30\\\end{array}
Find closest multiple of 60 to 90. We see that 1 \times 60 = 60 is the nearest. Now subtract 60 from 90 to get reminder 30. Add 1 to quotient.
\text{Quotient: }461 \text{Reminder: }30
Since 30 is less than 60, stop the division. The reminder is 30. The topmost line 00461 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 461.
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}