Evaluate
42
Factor
2\times 3\times 7
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\begin{array}{l}\phantom{20)}\phantom{1}\\20\overline{)840}\\\end{array}
Use the 1^{st} digit 8 from dividend 840
\begin{array}{l}\phantom{20)}0\phantom{2}\\20\overline{)840}\\\end{array}
Since 8 is less than 20, use the next digit 4 from dividend 840 and add 0 to the quotient
\begin{array}{l}\phantom{20)}0\phantom{3}\\20\overline{)840}\\\end{array}
Use the 2^{nd} digit 4 from dividend 840
\begin{array}{l}\phantom{20)}04\phantom{4}\\20\overline{)840}\\\phantom{20)}\underline{\phantom{}80\phantom{9}}\\\phantom{20)9}4\\\end{array}
Find closest multiple of 20 to 84. We see that 4 \times 20 = 80 is the nearest. Now subtract 80 from 84 to get reminder 4. Add 4 to quotient.
\begin{array}{l}\phantom{20)}04\phantom{5}\\20\overline{)840}\\\phantom{20)}\underline{\phantom{}80\phantom{9}}\\\phantom{20)9}40\\\end{array}
Use the 3^{rd} digit 0 from dividend 840
\begin{array}{l}\phantom{20)}042\phantom{6}\\20\overline{)840}\\\phantom{20)}\underline{\phantom{}80\phantom{9}}\\\phantom{20)9}40\\\phantom{20)}\underline{\phantom{9}40\phantom{}}\\\phantom{20)999}0\\\end{array}
Find closest multiple of 20 to 40. We see that 2 \times 20 = 40 is the nearest. Now subtract 40 from 40 to get reminder 0. Add 2 to quotient.
\text{Quotient: }42 \text{Reminder: }0
Since 0 is less than 20, stop the division. The reminder is 0. The topmost line 042 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 42.
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}