Evaluate
\frac{42}{23}\approx 1.826086957
Factor
\frac{2 \cdot 3 \cdot 7}{23} = 1\frac{19}{23} = 1.826086956521739
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\begin{array}{l}\phantom{23)}\phantom{1}\\23\overline{)42}\\\end{array}
Use the 1^{st} digit 4 from dividend 42
\begin{array}{l}\phantom{23)}0\phantom{2}\\23\overline{)42}\\\end{array}
Since 4 is less than 23, use the next digit 2 from dividend 42 and add 0 to the quotient
\begin{array}{l}\phantom{23)}0\phantom{3}\\23\overline{)42}\\\end{array}
Use the 2^{nd} digit 2 from dividend 42
\begin{array}{l}\phantom{23)}01\phantom{4}\\23\overline{)42}\\\phantom{23)}\underline{\phantom{}23\phantom{}}\\\phantom{23)}19\\\end{array}
Find closest multiple of 23 to 42. We see that 1 \times 23 = 23 is the nearest. Now subtract 23 from 42 to get reminder 19. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }19
Since 19 is less than 23, stop the division. The reminder is 19. 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}