Evaluate
\frac{29}{21}\approx 1.380952381
Factor
\frac{29}{3 \cdot 7} = 1\frac{8}{21} = 1.380952380952381
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\begin{array}{l}\phantom{42)}\phantom{1}\\42\overline{)58}\\\end{array}
Use the 1^{st} digit 5 from dividend 58
\begin{array}{l}\phantom{42)}0\phantom{2}\\42\overline{)58}\\\end{array}
Since 5 is less than 42, use the next digit 8 from dividend 58 and add 0 to the quotient
\begin{array}{l}\phantom{42)}0\phantom{3}\\42\overline{)58}\\\end{array}
Use the 2^{nd} digit 8 from dividend 58
\begin{array}{l}\phantom{42)}01\phantom{4}\\42\overline{)58}\\\phantom{42)}\underline{\phantom{}42\phantom{}}\\\phantom{42)}16\\\end{array}
Find closest multiple of 42 to 58. We see that 1 \times 42 = 42 is the nearest. Now subtract 42 from 58 to get reminder 16. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }16
Since 16 is less than 42, stop the division. The reminder is 16. 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}