Evaluate
\frac{1360}{9}\approx 151.111111111
Factor
\frac{2 ^ {4} \cdot 5 \cdot 17}{3 ^ {2}} = 151\frac{1}{9} = 151.11111111111111
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\begin{array}{l}\phantom{450)}\phantom{1}\\450\overline{)68000}\\\end{array}
Use the 1^{st} digit 6 from dividend 68000
\begin{array}{l}\phantom{450)}0\phantom{2}\\450\overline{)68000}\\\end{array}
Since 6 is less than 450, use the next digit 8 from dividend 68000 and add 0 to the quotient
\begin{array}{l}\phantom{450)}0\phantom{3}\\450\overline{)68000}\\\end{array}
Use the 2^{nd} digit 8 from dividend 68000
\begin{array}{l}\phantom{450)}00\phantom{4}\\450\overline{)68000}\\\end{array}
Since 68 is less than 450, use the next digit 0 from dividend 68000 and add 0 to the quotient
\begin{array}{l}\phantom{450)}00\phantom{5}\\450\overline{)68000}\\\end{array}
Use the 3^{rd} digit 0 from dividend 68000
\begin{array}{l}\phantom{450)}001\phantom{6}\\450\overline{)68000}\\\phantom{450)}\underline{\phantom{}450\phantom{99}}\\\phantom{450)}230\\\end{array}
Find closest multiple of 450 to 680. We see that 1 \times 450 = 450 is the nearest. Now subtract 450 from 680 to get reminder 230. Add 1 to quotient.
\begin{array}{l}\phantom{450)}001\phantom{7}\\450\overline{)68000}\\\phantom{450)}\underline{\phantom{}450\phantom{99}}\\\phantom{450)}2300\\\end{array}
Use the 4^{th} digit 0 from dividend 68000
\begin{array}{l}\phantom{450)}0015\phantom{8}\\450\overline{)68000}\\\phantom{450)}\underline{\phantom{}450\phantom{99}}\\\phantom{450)}2300\\\phantom{450)}\underline{\phantom{}2250\phantom{9}}\\\phantom{450)99}50\\\end{array}
Find closest multiple of 450 to 2300. We see that 5 \times 450 = 2250 is the nearest. Now subtract 2250 from 2300 to get reminder 50. Add 5 to quotient.
\begin{array}{l}\phantom{450)}0015\phantom{9}\\450\overline{)68000}\\\phantom{450)}\underline{\phantom{}450\phantom{99}}\\\phantom{450)}2300\\\phantom{450)}\underline{\phantom{}2250\phantom{9}}\\\phantom{450)99}500\\\end{array}
Use the 5^{th} digit 0 from dividend 68000
\begin{array}{l}\phantom{450)}00151\phantom{10}\\450\overline{)68000}\\\phantom{450)}\underline{\phantom{}450\phantom{99}}\\\phantom{450)}2300\\\phantom{450)}\underline{\phantom{}2250\phantom{9}}\\\phantom{450)99}500\\\phantom{450)}\underline{\phantom{99}450\phantom{}}\\\phantom{450)999}50\\\end{array}
Find closest multiple of 450 to 500. We see that 1 \times 450 = 450 is the nearest. Now subtract 450 from 500 to get reminder 50. Add 1 to quotient.
\text{Quotient: }151 \text{Reminder: }50
Since 50 is less than 450, stop the division. The reminder is 50. The topmost line 00151 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 151.
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}