Evaluate
\frac{26}{21}\approx 1.238095238
Factor
\frac{2 \cdot 13}{3 \cdot 7} = 1\frac{5}{21} = 1.2380952380952381
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\begin{array}{l}\phantom{63)}\phantom{1}\\63\overline{)78}\\\end{array}
Use the 1^{st} digit 7 from dividend 78
\begin{array}{l}\phantom{63)}0\phantom{2}\\63\overline{)78}\\\end{array}
Since 7 is less than 63, use the next digit 8 from dividend 78 and add 0 to the quotient
\begin{array}{l}\phantom{63)}0\phantom{3}\\63\overline{)78}\\\end{array}
Use the 2^{nd} digit 8 from dividend 78
\begin{array}{l}\phantom{63)}01\phantom{4}\\63\overline{)78}\\\phantom{63)}\underline{\phantom{}63\phantom{}}\\\phantom{63)}15\\\end{array}
Find closest multiple of 63 to 78. We see that 1 \times 63 = 63 is the nearest. Now subtract 63 from 78 to get reminder 15. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }15
Since 15 is less than 63, stop the division. The reminder is 15. 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}