Evaluate
\frac{28}{3}\approx 9.333333333
Factor
\frac{2 ^ {2} \cdot 7}{3} = 9\frac{1}{3} = 9.333333333333334
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\begin{array}{l}\phantom{45)}\phantom{1}\\45\overline{)420}\\\end{array}
Use the 1^{st} digit 4 from dividend 420
\begin{array}{l}\phantom{45)}0\phantom{2}\\45\overline{)420}\\\end{array}
Since 4 is less than 45, use the next digit 2 from dividend 420 and add 0 to the quotient
\begin{array}{l}\phantom{45)}0\phantom{3}\\45\overline{)420}\\\end{array}
Use the 2^{nd} digit 2 from dividend 420
\begin{array}{l}\phantom{45)}00\phantom{4}\\45\overline{)420}\\\end{array}
Since 42 is less than 45, use the next digit 0 from dividend 420 and add 0 to the quotient
\begin{array}{l}\phantom{45)}00\phantom{5}\\45\overline{)420}\\\end{array}
Use the 3^{rd} digit 0 from dividend 420
\begin{array}{l}\phantom{45)}009\phantom{6}\\45\overline{)420}\\\phantom{45)}\underline{\phantom{}405\phantom{}}\\\phantom{45)9}15\\\end{array}
Find closest multiple of 45 to 420. We see that 9 \times 45 = 405 is the nearest. Now subtract 405 from 420 to get reminder 15. Add 9 to quotient.
\text{Quotient: }9 \text{Reminder: }15
Since 15 is less than 45, stop the division. The reminder is 15. The topmost line 009 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 9.
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}