Evaluate
\frac{61}{10}=6.1
Factor
\frac{61}{2 \cdot 5} = 6\frac{1}{10} = 6.1
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\begin{array}{l}\phantom{300)}\phantom{1}\\300\overline{)1830}\\\end{array}
Use the 1^{st} digit 1 from dividend 1830
\begin{array}{l}\phantom{300)}0\phantom{2}\\300\overline{)1830}\\\end{array}
Since 1 is less than 300, use the next digit 8 from dividend 1830 and add 0 to the quotient
\begin{array}{l}\phantom{300)}0\phantom{3}\\300\overline{)1830}\\\end{array}
Use the 2^{nd} digit 8 from dividend 1830
\begin{array}{l}\phantom{300)}00\phantom{4}\\300\overline{)1830}\\\end{array}
Since 18 is less than 300, use the next digit 3 from dividend 1830 and add 0 to the quotient
\begin{array}{l}\phantom{300)}00\phantom{5}\\300\overline{)1830}\\\end{array}
Use the 3^{rd} digit 3 from dividend 1830
\begin{array}{l}\phantom{300)}000\phantom{6}\\300\overline{)1830}\\\end{array}
Since 183 is less than 300, use the next digit 0 from dividend 1830 and add 0 to the quotient
\begin{array}{l}\phantom{300)}000\phantom{7}\\300\overline{)1830}\\\end{array}
Use the 4^{th} digit 0 from dividend 1830
\begin{array}{l}\phantom{300)}0006\phantom{8}\\300\overline{)1830}\\\phantom{300)}\underline{\phantom{}1800\phantom{}}\\\phantom{300)99}30\\\end{array}
Find closest multiple of 300 to 1830. We see that 6 \times 300 = 1800 is the nearest. Now subtract 1800 from 1830 to get reminder 30. Add 6 to quotient.
\text{Quotient: }6 \text{Reminder: }30
Since 30 is less than 300, stop the division. The reminder is 30. The topmost line 0006 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 6.
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}