Evaluate
\frac{657}{133}\approx 4.939849624
Factor
\frac{3 ^ {2} \cdot 73}{7 \cdot 19} = 4\frac{125}{133} = 4.93984962406015
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\begin{array}{l}\phantom{133)}\phantom{1}\\133\overline{)657}\\\end{array}
Use the 1^{st} digit 6 from dividend 657
\begin{array}{l}\phantom{133)}0\phantom{2}\\133\overline{)657}\\\end{array}
Since 6 is less than 133, use the next digit 5 from dividend 657 and add 0 to the quotient
\begin{array}{l}\phantom{133)}0\phantom{3}\\133\overline{)657}\\\end{array}
Use the 2^{nd} digit 5 from dividend 657
\begin{array}{l}\phantom{133)}00\phantom{4}\\133\overline{)657}\\\end{array}
Since 65 is less than 133, use the next digit 7 from dividend 657 and add 0 to the quotient
\begin{array}{l}\phantom{133)}00\phantom{5}\\133\overline{)657}\\\end{array}
Use the 3^{rd} digit 7 from dividend 657
\begin{array}{l}\phantom{133)}004\phantom{6}\\133\overline{)657}\\\phantom{133)}\underline{\phantom{}532\phantom{}}\\\phantom{133)}125\\\end{array}
Find closest multiple of 133 to 657. We see that 4 \times 133 = 532 is the nearest. Now subtract 532 from 657 to get reminder 125. Add 4 to quotient.
\text{Quotient: }4 \text{Reminder: }125
Since 125 is less than 133, stop the division. The reminder is 125. The topmost line 004 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 4.
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}