Evaluate
\frac{257}{134}\approx 1.917910448
Factor
\frac{257}{2 \cdot 67} = 1\frac{123}{134} = 1.9179104477611941
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\begin{array}{l}\phantom{134)}\phantom{1}\\134\overline{)257}\\\end{array}
Use the 1^{st} digit 2 from dividend 257
\begin{array}{l}\phantom{134)}0\phantom{2}\\134\overline{)257}\\\end{array}
Since 2 is less than 134, use the next digit 5 from dividend 257 and add 0 to the quotient
\begin{array}{l}\phantom{134)}0\phantom{3}\\134\overline{)257}\\\end{array}
Use the 2^{nd} digit 5 from dividend 257
\begin{array}{l}\phantom{134)}00\phantom{4}\\134\overline{)257}\\\end{array}
Since 25 is less than 134, use the next digit 7 from dividend 257 and add 0 to the quotient
\begin{array}{l}\phantom{134)}00\phantom{5}\\134\overline{)257}\\\end{array}
Use the 3^{rd} digit 7 from dividend 257
\begin{array}{l}\phantom{134)}001\phantom{6}\\134\overline{)257}\\\phantom{134)}\underline{\phantom{}134\phantom{}}\\\phantom{134)}123\\\end{array}
Find closest multiple of 134 to 257. We see that 1 \times 134 = 134 is the nearest. Now subtract 134 from 257 to get reminder 123. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }123
Since 123 is less than 134, stop the division. The reminder is 123. The topmost line 001 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 1.
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}