Evaluate
\frac{10}{3}\approx 3.333333333
Factor
\frac{2 \cdot 5}{3} = 3\frac{1}{3} = 3.3333333333333335
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\begin{array}{l}\phantom{36)}\phantom{1}\\36\overline{)120}\\\end{array}
Use the 1^{st} digit 1 from dividend 120
\begin{array}{l}\phantom{36)}0\phantom{2}\\36\overline{)120}\\\end{array}
Since 1 is less than 36, use the next digit 2 from dividend 120 and add 0 to the quotient
\begin{array}{l}\phantom{36)}0\phantom{3}\\36\overline{)120}\\\end{array}
Use the 2^{nd} digit 2 from dividend 120
\begin{array}{l}\phantom{36)}00\phantom{4}\\36\overline{)120}\\\end{array}
Since 12 is less than 36, use the next digit 0 from dividend 120 and add 0 to the quotient
\begin{array}{l}\phantom{36)}00\phantom{5}\\36\overline{)120}\\\end{array}
Use the 3^{rd} digit 0 from dividend 120
\begin{array}{l}\phantom{36)}003\phantom{6}\\36\overline{)120}\\\phantom{36)}\underline{\phantom{}108\phantom{}}\\\phantom{36)9}12\\\end{array}
Find closest multiple of 36 to 120. We see that 3 \times 36 = 108 is the nearest. Now subtract 108 from 120 to get reminder 12. Add 3 to quotient.
\text{Quotient: }3 \text{Reminder: }12
Since 12 is less than 36, stop the division. The reminder is 12. The topmost line 003 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 3.
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}