Evaluate
\frac{142}{135}\approx 1.051851852
Factor
\frac{2 \cdot 71}{3 ^ {3} \cdot 5} = 1\frac{7}{135} = 1.0518518518518518
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\begin{array}{l}\phantom{675)}\phantom{1}\\675\overline{)710}\\\end{array}
Use the 1^{st} digit 7 from dividend 710
\begin{array}{l}\phantom{675)}0\phantom{2}\\675\overline{)710}\\\end{array}
Since 7 is less than 675, use the next digit 1 from dividend 710 and add 0 to the quotient
\begin{array}{l}\phantom{675)}0\phantom{3}\\675\overline{)710}\\\end{array}
Use the 2^{nd} digit 1 from dividend 710
\begin{array}{l}\phantom{675)}00\phantom{4}\\675\overline{)710}\\\end{array}
Since 71 is less than 675, use the next digit 0 from dividend 710 and add 0 to the quotient
\begin{array}{l}\phantom{675)}00\phantom{5}\\675\overline{)710}\\\end{array}
Use the 3^{rd} digit 0 from dividend 710
\begin{array}{l}\phantom{675)}001\phantom{6}\\675\overline{)710}\\\phantom{675)}\underline{\phantom{}675\phantom{}}\\\phantom{675)9}35\\\end{array}
Find closest multiple of 675 to 710. We see that 1 \times 675 = 675 is the nearest. Now subtract 675 from 710 to get reminder 35. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }35
Since 35 is less than 675, stop the division. The reminder is 35. 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}