Evaluate
\frac{42}{29}\approx 1.448275862
Factor
\frac{2 \cdot 3 \cdot 7}{29} = 1\frac{13}{29} = 1.4482758620689655
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\begin{array}{l}\phantom{29)}\phantom{1}\\29\overline{)42}\\\end{array}
Use the 1^{st} digit 4 from dividend 42
\begin{array}{l}\phantom{29)}0\phantom{2}\\29\overline{)42}\\\end{array}
Since 4 is less than 29, use the next digit 2 from dividend 42 and add 0 to the quotient
\begin{array}{l}\phantom{29)}0\phantom{3}\\29\overline{)42}\\\end{array}
Use the 2^{nd} digit 2 from dividend 42
\begin{array}{l}\phantom{29)}01\phantom{4}\\29\overline{)42}\\\phantom{29)}\underline{\phantom{}29\phantom{}}\\\phantom{29)}13\\\end{array}
Find closest multiple of 29 to 42. We see that 1 \times 29 = 29 is the nearest. Now subtract 29 from 42 to get reminder 13. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }13
Since 13 is less than 29, stop the division. The reminder is 13. 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}