Evaluate
6
Factor
2\times 3
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\begin{array}{l}\phantom{38)}\phantom{1}\\38\overline{)228}\\\end{array}
Use the 1^{st} digit 2 from dividend 228
\begin{array}{l}\phantom{38)}0\phantom{2}\\38\overline{)228}\\\end{array}
Since 2 is less than 38, use the next digit 2 from dividend 228 and add 0 to the quotient
\begin{array}{l}\phantom{38)}0\phantom{3}\\38\overline{)228}\\\end{array}
Use the 2^{nd} digit 2 from dividend 228
\begin{array}{l}\phantom{38)}00\phantom{4}\\38\overline{)228}\\\end{array}
Since 22 is less than 38, use the next digit 8 from dividend 228 and add 0 to the quotient
\begin{array}{l}\phantom{38)}00\phantom{5}\\38\overline{)228}\\\end{array}
Use the 3^{rd} digit 8 from dividend 228
\begin{array}{l}\phantom{38)}006\phantom{6}\\38\overline{)228}\\\phantom{38)}\underline{\phantom{}228\phantom{}}\\\phantom{38)999}0\\\end{array}
Find closest multiple of 38 to 228. We see that 6 \times 38 = 228 is the nearest. Now subtract 228 from 228 to get reminder 0. Add 6 to quotient.
\text{Quotient: }6 \text{Reminder: }0
Since 0 is less than 38, stop the division. The reminder is 0. The topmost line 006 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 6.
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}