Evaluate
5
Factor
5
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\begin{array}{l}\phantom{42)}\phantom{1}\\42\overline{)210}\\\end{array}
Use the 1^{st} digit 2 from dividend 210
\begin{array}{l}\phantom{42)}0\phantom{2}\\42\overline{)210}\\\end{array}
Since 2 is less than 42, use the next digit 1 from dividend 210 and add 0 to the quotient
\begin{array}{l}\phantom{42)}0\phantom{3}\\42\overline{)210}\\\end{array}
Use the 2^{nd} digit 1 from dividend 210
\begin{array}{l}\phantom{42)}00\phantom{4}\\42\overline{)210}\\\end{array}
Since 21 is less than 42, use the next digit 0 from dividend 210 and add 0 to the quotient
\begin{array}{l}\phantom{42)}00\phantom{5}\\42\overline{)210}\\\end{array}
Use the 3^{rd} digit 0 from dividend 210
\begin{array}{l}\phantom{42)}005\phantom{6}\\42\overline{)210}\\\phantom{42)}\underline{\phantom{}210\phantom{}}\\\phantom{42)999}0\\\end{array}
Find closest multiple of 42 to 210. We see that 5 \times 42 = 210 is the nearest. Now subtract 210 from 210 to get reminder 0. Add 5 to quotient.
\text{Quotient: }5 \text{Reminder: }0
Since 0 is less than 42, stop the division. The reminder is 0. 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}