Evaluate
\frac{8}{7}\approx 1.142857143
Factor
\frac{2 ^ {3}}{7} = 1\frac{1}{7} = 1.1428571428571428
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\begin{array}{l}\phantom{42)}\phantom{1}\\42\overline{)48}\\\end{array}
Use the 1^{st} digit 4 from dividend 48
\begin{array}{l}\phantom{42)}0\phantom{2}\\42\overline{)48}\\\end{array}
Since 4 is less than 42, use the next digit 8 from dividend 48 and add 0 to the quotient
\begin{array}{l}\phantom{42)}0\phantom{3}\\42\overline{)48}\\\end{array}
Use the 2^{nd} digit 8 from dividend 48
\begin{array}{l}\phantom{42)}01\phantom{4}\\42\overline{)48}\\\phantom{42)}\underline{\phantom{}42\phantom{}}\\\phantom{42)9}6\\\end{array}
Find closest multiple of 42 to 48. We see that 1 \times 42 = 42 is the nearest. Now subtract 42 from 48 to get reminder 6. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }6
Since 6 is less than 42, stop the division. The reminder is 6. 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}