Evaluate
\frac{43}{6}\approx 7.166666667
Factor
\frac{43}{2 \cdot 3} = 7\frac{1}{6} = 7.166666666666667
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\begin{array}{l}\phantom{30)}\phantom{1}\\30\overline{)215}\\\end{array}
Use the 1^{st} digit 2 from dividend 215
\begin{array}{l}\phantom{30)}0\phantom{2}\\30\overline{)215}\\\end{array}
Since 2 is less than 30, use the next digit 1 from dividend 215 and add 0 to the quotient
\begin{array}{l}\phantom{30)}0\phantom{3}\\30\overline{)215}\\\end{array}
Use the 2^{nd} digit 1 from dividend 215
\begin{array}{l}\phantom{30)}00\phantom{4}\\30\overline{)215}\\\end{array}
Since 21 is less than 30, use the next digit 5 from dividend 215 and add 0 to the quotient
\begin{array}{l}\phantom{30)}00\phantom{5}\\30\overline{)215}\\\end{array}
Use the 3^{rd} digit 5 from dividend 215
\begin{array}{l}\phantom{30)}007\phantom{6}\\30\overline{)215}\\\phantom{30)}\underline{\phantom{}210\phantom{}}\\\phantom{30)99}5\\\end{array}
Find closest multiple of 30 to 215. We see that 7 \times 30 = 210 is the nearest. Now subtract 210 from 215 to get reminder 5. Add 7 to quotient.
\text{Quotient: }7 \text{Reminder: }5
Since 5 is less than 30, stop the division. The reminder is 5. The topmost line 007 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 7.
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}