Evaluate
\frac{70}{31}\approx 2.258064516
Factor
\frac{2 \cdot 5 \cdot 7}{31} = 2\frac{8}{31} = 2.2580645161290325
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\begin{array}{l}\phantom{155)}\phantom{1}\\155\overline{)350}\\\end{array}
Use the 1^{st} digit 3 from dividend 350
\begin{array}{l}\phantom{155)}0\phantom{2}\\155\overline{)350}\\\end{array}
Since 3 is less than 155, use the next digit 5 from dividend 350 and add 0 to the quotient
\begin{array}{l}\phantom{155)}0\phantom{3}\\155\overline{)350}\\\end{array}
Use the 2^{nd} digit 5 from dividend 350
\begin{array}{l}\phantom{155)}00\phantom{4}\\155\overline{)350}\\\end{array}
Since 35 is less than 155, use the next digit 0 from dividend 350 and add 0 to the quotient
\begin{array}{l}\phantom{155)}00\phantom{5}\\155\overline{)350}\\\end{array}
Use the 3^{rd} digit 0 from dividend 350
\begin{array}{l}\phantom{155)}002\phantom{6}\\155\overline{)350}\\\phantom{155)}\underline{\phantom{}310\phantom{}}\\\phantom{155)9}40\\\end{array}
Find closest multiple of 155 to 350. We see that 2 \times 155 = 310 is the nearest. Now subtract 310 from 350 to get reminder 40. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }40
Since 40 is less than 155, stop the division. The reminder is 40. The topmost line 002 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 2.
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}