Evaluate
\frac{314}{57}\approx 5.50877193
Factor
\frac{2 \cdot 157}{3 \cdot 19} = 5\frac{29}{57} = 5.508771929824562
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\begin{array}{l}\phantom{114)}\phantom{1}\\114\overline{)628}\\\end{array}
Use the 1^{st} digit 6 from dividend 628
\begin{array}{l}\phantom{114)}0\phantom{2}\\114\overline{)628}\\\end{array}
Since 6 is less than 114, use the next digit 2 from dividend 628 and add 0 to the quotient
\begin{array}{l}\phantom{114)}0\phantom{3}\\114\overline{)628}\\\end{array}
Use the 2^{nd} digit 2 from dividend 628
\begin{array}{l}\phantom{114)}00\phantom{4}\\114\overline{)628}\\\end{array}
Since 62 is less than 114, use the next digit 8 from dividend 628 and add 0 to the quotient
\begin{array}{l}\phantom{114)}00\phantom{5}\\114\overline{)628}\\\end{array}
Use the 3^{rd} digit 8 from dividend 628
\begin{array}{l}\phantom{114)}005\phantom{6}\\114\overline{)628}\\\phantom{114)}\underline{\phantom{}570\phantom{}}\\\phantom{114)9}58\\\end{array}
Find closest multiple of 114 to 628. We see that 5 \times 114 = 570 is the nearest. Now subtract 570 from 628 to get reminder 58. Add 5 to quotient.
\text{Quotient: }5 \text{Reminder: }58
Since 58 is less than 114, stop the division. The reminder is 58. The topmost line 005 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 5.
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}