Evaluate
\frac{233}{120}\approx 1.941666667
Factor
\frac{233}{2 ^ {3} \cdot 3 \cdot 5} = 1\frac{113}{120} = 1.9416666666666667
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\begin{array}{l}\phantom{120)}\phantom{1}\\120\overline{)233}\\\end{array}
Use the 1^{st} digit 2 from dividend 233
\begin{array}{l}\phantom{120)}0\phantom{2}\\120\overline{)233}\\\end{array}
Since 2 is less than 120, use the next digit 3 from dividend 233 and add 0 to the quotient
\begin{array}{l}\phantom{120)}0\phantom{3}\\120\overline{)233}\\\end{array}
Use the 2^{nd} digit 3 from dividend 233
\begin{array}{l}\phantom{120)}00\phantom{4}\\120\overline{)233}\\\end{array}
Since 23 is less than 120, use the next digit 3 from dividend 233 and add 0 to the quotient
\begin{array}{l}\phantom{120)}00\phantom{5}\\120\overline{)233}\\\end{array}
Use the 3^{rd} digit 3 from dividend 233
\begin{array}{l}\phantom{120)}001\phantom{6}\\120\overline{)233}\\\phantom{120)}\underline{\phantom{}120\phantom{}}\\\phantom{120)}113\\\end{array}
Find closest multiple of 120 to 233. We see that 1 \times 120 = 120 is the nearest. Now subtract 120 from 233 to get reminder 113. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }113
Since 113 is less than 120, stop the division. The reminder is 113. The topmost line 001 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 1.
Examples
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{ 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}