Evaluate
\frac{4}{3}\approx 1.333333333
Factor
\frac{2 ^ {2}}{3} = 1\frac{1}{3} = 1.3333333333333333
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\begin{array}{l}\phantom{42)}\phantom{1}\\42\overline{)56}\\\end{array}
Use the 1^{st} digit 5 from dividend 56
\begin{array}{l}\phantom{42)}0\phantom{2}\\42\overline{)56}\\\end{array}
Since 5 is less than 42, use the next digit 6 from dividend 56 and add 0 to the quotient
\begin{array}{l}\phantom{42)}0\phantom{3}\\42\overline{)56}\\\end{array}
Use the 2^{nd} digit 6 from dividend 56
\begin{array}{l}\phantom{42)}01\phantom{4}\\42\overline{)56}\\\phantom{42)}\underline{\phantom{}42\phantom{}}\\\phantom{42)}14\\\end{array}
Find closest multiple of 42 to 56. We see that 1 \times 42 = 42 is the nearest. Now subtract 42 from 56 to get reminder 14. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }14
Since 14 is less than 42, stop the division. The reminder is 14. 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}