Evaluate
\frac{68}{35}\approx 1.942857143
Factor
\frac{2 ^ {2} \cdot 17}{5 \cdot 7} = 1\frac{33}{35} = 1.9428571428571428
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\begin{array}{l}\phantom{350)}\phantom{1}\\350\overline{)680}\\\end{array}
Use the 1^{st} digit 6 from dividend 680
\begin{array}{l}\phantom{350)}0\phantom{2}\\350\overline{)680}\\\end{array}
Since 6 is less than 350, use the next digit 8 from dividend 680 and add 0 to the quotient
\begin{array}{l}\phantom{350)}0\phantom{3}\\350\overline{)680}\\\end{array}
Use the 2^{nd} digit 8 from dividend 680
\begin{array}{l}\phantom{350)}00\phantom{4}\\350\overline{)680}\\\end{array}
Since 68 is less than 350, use the next digit 0 from dividend 680 and add 0 to the quotient
\begin{array}{l}\phantom{350)}00\phantom{5}\\350\overline{)680}\\\end{array}
Use the 3^{rd} digit 0 from dividend 680
\begin{array}{l}\phantom{350)}001\phantom{6}\\350\overline{)680}\\\phantom{350)}\underline{\phantom{}350\phantom{}}\\\phantom{350)}330\\\end{array}
Find closest multiple of 350 to 680. We see that 1 \times 350 = 350 is the nearest. Now subtract 350 from 680 to get reminder 330. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }330
Since 330 is less than 350, stop the division. The reminder is 330. 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}