Evaluate
\frac{64}{21}\approx 3.047619048
Factor
\frac{2 ^ {6}}{3 \cdot 7} = 3\frac{1}{21} = 3.0476190476190474
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\begin{array}{l}\phantom{42)}\phantom{1}\\42\overline{)128}\\\end{array}
Use the 1^{st} digit 1 from dividend 128
\begin{array}{l}\phantom{42)}0\phantom{2}\\42\overline{)128}\\\end{array}
Since 1 is less than 42, use the next digit 2 from dividend 128 and add 0 to the quotient
\begin{array}{l}\phantom{42)}0\phantom{3}\\42\overline{)128}\\\end{array}
Use the 2^{nd} digit 2 from dividend 128
\begin{array}{l}\phantom{42)}00\phantom{4}\\42\overline{)128}\\\end{array}
Since 12 is less than 42, use the next digit 8 from dividend 128 and add 0 to the quotient
\begin{array}{l}\phantom{42)}00\phantom{5}\\42\overline{)128}\\\end{array}
Use the 3^{rd} digit 8 from dividend 128
\begin{array}{l}\phantom{42)}003\phantom{6}\\42\overline{)128}\\\phantom{42)}\underline{\phantom{}126\phantom{}}\\\phantom{42)99}2\\\end{array}
Find closest multiple of 42 to 128. We see that 3 \times 42 = 126 is the nearest. Now subtract 126 from 128 to get reminder 2. Add 3 to quotient.
\text{Quotient: }3 \text{Reminder: }2
Since 2 is less than 42, stop the division. The reminder is 2. The topmost line 003 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 3.
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}