Evaluate
\frac{62}{11}\approx 5.636363636
Factor
\frac{2 \cdot 31}{11} = 5\frac{7}{11} = 5.636363636363637
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\begin{array}{l}\phantom{22)}\phantom{1}\\22\overline{)124}\\\end{array}
Use the 1^{st} digit 1 from dividend 124
\begin{array}{l}\phantom{22)}0\phantom{2}\\22\overline{)124}\\\end{array}
Since 1 is less than 22, use the next digit 2 from dividend 124 and add 0 to the quotient
\begin{array}{l}\phantom{22)}0\phantom{3}\\22\overline{)124}\\\end{array}
Use the 2^{nd} digit 2 from dividend 124
\begin{array}{l}\phantom{22)}00\phantom{4}\\22\overline{)124}\\\end{array}
Since 12 is less than 22, use the next digit 4 from dividend 124 and add 0 to the quotient
\begin{array}{l}\phantom{22)}00\phantom{5}\\22\overline{)124}\\\end{array}
Use the 3^{rd} digit 4 from dividend 124
\begin{array}{l}\phantom{22)}005\phantom{6}\\22\overline{)124}\\\phantom{22)}\underline{\phantom{}110\phantom{}}\\\phantom{22)9}14\\\end{array}
Find closest multiple of 22 to 124. We see that 5 \times 22 = 110 is the nearest. Now subtract 110 from 124 to get reminder 14. Add 5 to quotient.
\text{Quotient: }5 \text{Reminder: }14
Since 14 is less than 22, stop the division. The reminder is 14. The topmost line 005 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 5.
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}