Evaluate
\frac{33}{26}\approx 1.269230769
Factor
\frac{3 \cdot 11}{2 \cdot 13} = 1\frac{7}{26} = 1.2692307692307692
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\begin{array}{l}\phantom{78)}\phantom{1}\\78\overline{)99}\\\end{array}
Use the 1^{st} digit 9 from dividend 99
\begin{array}{l}\phantom{78)}0\phantom{2}\\78\overline{)99}\\\end{array}
Since 9 is less than 78, use the next digit 9 from dividend 99 and add 0 to the quotient
\begin{array}{l}\phantom{78)}0\phantom{3}\\78\overline{)99}\\\end{array}
Use the 2^{nd} digit 9 from dividend 99
\begin{array}{l}\phantom{78)}01\phantom{4}\\78\overline{)99}\\\phantom{78)}\underline{\phantom{}78\phantom{}}\\\phantom{78)}21\\\end{array}
Find closest multiple of 78 to 99. We see that 1 \times 78 = 78 is the nearest. Now subtract 78 from 99 to get reminder 21. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }21
Since 21 is less than 78, stop the division. The reminder is 21. 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}