Evaluate
\frac{29}{15}\approx 1.933333333
Factor
\frac{29}{3 \cdot 5} = 1\frac{14}{15} = 1.9333333333333333
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\begin{array}{l}\phantom{45)}\phantom{1}\\45\overline{)87}\\\end{array}
Use the 1^{st} digit 8 from dividend 87
\begin{array}{l}\phantom{45)}0\phantom{2}\\45\overline{)87}\\\end{array}
Since 8 is less than 45, use the next digit 7 from dividend 87 and add 0 to the quotient
\begin{array}{l}\phantom{45)}0\phantom{3}\\45\overline{)87}\\\end{array}
Use the 2^{nd} digit 7 from dividend 87
\begin{array}{l}\phantom{45)}01\phantom{4}\\45\overline{)87}\\\phantom{45)}\underline{\phantom{}45\phantom{}}\\\phantom{45)}42\\\end{array}
Find closest multiple of 45 to 87. We see that 1 \times 45 = 45 is the nearest. Now subtract 45 from 87 to get reminder 42. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }42
Since 42 is less than 45, stop the division. The reminder is 42. 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}