Evaluate
\frac{36}{31}\approx 1.161290323
Factor
\frac{2 ^ {2} \cdot 3 ^ {2}}{31} = 1\frac{5}{31} = 1.1612903225806452
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\begin{array}{l}\phantom{62)}\phantom{1}\\62\overline{)72}\\\end{array}
Use the 1^{st} digit 7 from dividend 72
\begin{array}{l}\phantom{62)}0\phantom{2}\\62\overline{)72}\\\end{array}
Since 7 is less than 62, use the next digit 2 from dividend 72 and add 0 to the quotient
\begin{array}{l}\phantom{62)}0\phantom{3}\\62\overline{)72}\\\end{array}
Use the 2^{nd} digit 2 from dividend 72
\begin{array}{l}\phantom{62)}01\phantom{4}\\62\overline{)72}\\\phantom{62)}\underline{\phantom{}62\phantom{}}\\\phantom{62)}10\\\end{array}
Find closest multiple of 62 to 72. We see that 1 \times 62 = 62 is the nearest. Now subtract 62 from 72 to get reminder 10. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }10
Since 10 is less than 62, stop the division. The reminder is 10. 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}