Evaluate
\frac{457}{5}=91.4
Factor
\frac{457}{5} = 91\frac{2}{5} = 91.4
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\begin{array}{l}\phantom{30)}\phantom{1}\\30\overline{)2742}\\\end{array}
Use the 1^{st} digit 2 from dividend 2742
\begin{array}{l}\phantom{30)}0\phantom{2}\\30\overline{)2742}\\\end{array}
Since 2 is less than 30, use the next digit 7 from dividend 2742 and add 0 to the quotient
\begin{array}{l}\phantom{30)}0\phantom{3}\\30\overline{)2742}\\\end{array}
Use the 2^{nd} digit 7 from dividend 2742
\begin{array}{l}\phantom{30)}00\phantom{4}\\30\overline{)2742}\\\end{array}
Since 27 is less than 30, use the next digit 4 from dividend 2742 and add 0 to the quotient
\begin{array}{l}\phantom{30)}00\phantom{5}\\30\overline{)2742}\\\end{array}
Use the 3^{rd} digit 4 from dividend 2742
\begin{array}{l}\phantom{30)}009\phantom{6}\\30\overline{)2742}\\\phantom{30)}\underline{\phantom{}270\phantom{9}}\\\phantom{30)99}4\\\end{array}
Find closest multiple of 30 to 274. We see that 9 \times 30 = 270 is the nearest. Now subtract 270 from 274 to get reminder 4. Add 9 to quotient.
\begin{array}{l}\phantom{30)}009\phantom{7}\\30\overline{)2742}\\\phantom{30)}\underline{\phantom{}270\phantom{9}}\\\phantom{30)99}42\\\end{array}
Use the 4^{th} digit 2 from dividend 2742
\begin{array}{l}\phantom{30)}0091\phantom{8}\\30\overline{)2742}\\\phantom{30)}\underline{\phantom{}270\phantom{9}}\\\phantom{30)99}42\\\phantom{30)}\underline{\phantom{99}30\phantom{}}\\\phantom{30)99}12\\\end{array}
Find closest multiple of 30 to 42. We see that 1 \times 30 = 30 is the nearest. Now subtract 30 from 42 to get reminder 12. Add 1 to quotient.
\text{Quotient: }91 \text{Reminder: }12
Since 12 is less than 30, stop the division. The reminder is 12. The topmost line 0091 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 91.
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}