Evaluate
\frac{12}{7}\approx 1.714285714
Factor
\frac{2 ^ {2} \cdot 3}{7} = 1\frac{5}{7} = 1.7142857142857142
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\begin{array}{l}\phantom{35)}\phantom{1}\\35\overline{)60}\\\end{array}
Use the 1^{st} digit 6 from dividend 60
\begin{array}{l}\phantom{35)}0\phantom{2}\\35\overline{)60}\\\end{array}
Since 6 is less than 35, use the next digit 0 from dividend 60 and add 0 to the quotient
\begin{array}{l}\phantom{35)}0\phantom{3}\\35\overline{)60}\\\end{array}
Use the 2^{nd} digit 0 from dividend 60
\begin{array}{l}\phantom{35)}01\phantom{4}\\35\overline{)60}\\\phantom{35)}\underline{\phantom{}35\phantom{}}\\\phantom{35)}25\\\end{array}
Find closest multiple of 35 to 60. We see that 1 \times 35 = 35 is the nearest. Now subtract 35 from 60 to get reminder 25. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }25
Since 25 is less than 35, stop the division. The reminder is 25. The topmost line 01 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}