Evaluate
\frac{19}{15}\approx 1.266666667
Factor
\frac{19}{3 \cdot 5} = 1\frac{4}{15} = 1.2666666666666666
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\begin{array}{l}\phantom{30)}\phantom{1}\\30\overline{)38}\\\end{array}
Use the 1^{st} digit 3 from dividend 38
\begin{array}{l}\phantom{30)}0\phantom{2}\\30\overline{)38}\\\end{array}
Since 3 is less than 30, use the next digit 8 from dividend 38 and add 0 to the quotient
\begin{array}{l}\phantom{30)}0\phantom{3}\\30\overline{)38}\\\end{array}
Use the 2^{nd} digit 8 from dividend 38
\begin{array}{l}\phantom{30)}01\phantom{4}\\30\overline{)38}\\\phantom{30)}\underline{\phantom{}30\phantom{}}\\\phantom{30)9}8\\\end{array}
Find closest multiple of 30 to 38. We see that 1 \times 30 = 30 is the nearest. Now subtract 30 from 38 to get reminder 8. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }8
Since 8 is less than 30, stop the division. The reminder is 8. 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}