Evaluate
\frac{26}{15}\approx 1.733333333
Factor
\frac{2 \cdot 13}{3 \cdot 5} = 1\frac{11}{15} = 1.7333333333333334
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\begin{array}{l}\phantom{45)}\phantom{1}\\45\overline{)78}\\\end{array}
Use the 1^{st} digit 7 from dividend 78
\begin{array}{l}\phantom{45)}0\phantom{2}\\45\overline{)78}\\\end{array}
Since 7 is less than 45, use the next digit 8 from dividend 78 and add 0 to the quotient
\begin{array}{l}\phantom{45)}0\phantom{3}\\45\overline{)78}\\\end{array}
Use the 2^{nd} digit 8 from dividend 78
\begin{array}{l}\phantom{45)}01\phantom{4}\\45\overline{)78}\\\phantom{45)}\underline{\phantom{}45\phantom{}}\\\phantom{45)}33\\\end{array}
Find closest multiple of 45 to 78. We see that 1 \times 45 = 45 is the nearest. Now subtract 45 from 78 to get reminder 33. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }33
Since 33 is less than 45, stop the division. The reminder is 33. 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}