Evaluate
\frac{149}{30}\approx 4.966666667
Factor
\frac{149}{2 \cdot 3 \cdot 5} = 4\frac{29}{30} = 4.966666666666667
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\begin{array}{l}\phantom{30)}\phantom{1}\\30\overline{)149}\\\end{array}
Use the 1^{st} digit 1 from dividend 149
\begin{array}{l}\phantom{30)}0\phantom{2}\\30\overline{)149}\\\end{array}
Since 1 is less than 30, use the next digit 4 from dividend 149 and add 0 to the quotient
\begin{array}{l}\phantom{30)}0\phantom{3}\\30\overline{)149}\\\end{array}
Use the 2^{nd} digit 4 from dividend 149
\begin{array}{l}\phantom{30)}00\phantom{4}\\30\overline{)149}\\\end{array}
Since 14 is less than 30, use the next digit 9 from dividend 149 and add 0 to the quotient
\begin{array}{l}\phantom{30)}00\phantom{5}\\30\overline{)149}\\\end{array}
Use the 3^{rd} digit 9 from dividend 149
\begin{array}{l}\phantom{30)}004\phantom{6}\\30\overline{)149}\\\phantom{30)}\underline{\phantom{}120\phantom{}}\\\phantom{30)9}29\\\end{array}
Find closest multiple of 30 to 149. We see that 4 \times 30 = 120 is the nearest. Now subtract 120 from 149 to get reminder 29. Add 4 to quotient.
\text{Quotient: }4 \text{Reminder: }29
Since 29 is less than 30, stop the division. The reminder is 29. The topmost line 004 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 4.
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}