Evaluate
34
Factor
2\times 17
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\begin{array}{l}\phantom{600)}\phantom{1}\\600\overline{)20400}\\\end{array}
Use the 1^{st} digit 2 from dividend 20400
\begin{array}{l}\phantom{600)}0\phantom{2}\\600\overline{)20400}\\\end{array}
Since 2 is less than 600, use the next digit 0 from dividend 20400 and add 0 to the quotient
\begin{array}{l}\phantom{600)}0\phantom{3}\\600\overline{)20400}\\\end{array}
Use the 2^{nd} digit 0 from dividend 20400
\begin{array}{l}\phantom{600)}00\phantom{4}\\600\overline{)20400}\\\end{array}
Since 20 is less than 600, use the next digit 4 from dividend 20400 and add 0 to the quotient
\begin{array}{l}\phantom{600)}00\phantom{5}\\600\overline{)20400}\\\end{array}
Use the 3^{rd} digit 4 from dividend 20400
\begin{array}{l}\phantom{600)}000\phantom{6}\\600\overline{)20400}\\\end{array}
Since 204 is less than 600, use the next digit 0 from dividend 20400 and add 0 to the quotient
\begin{array}{l}\phantom{600)}000\phantom{7}\\600\overline{)20400}\\\end{array}
Use the 4^{th} digit 0 from dividend 20400
\begin{array}{l}\phantom{600)}0003\phantom{8}\\600\overline{)20400}\\\phantom{600)}\underline{\phantom{}1800\phantom{9}}\\\phantom{600)9}240\\\end{array}
Find closest multiple of 600 to 2040. We see that 3 \times 600 = 1800 is the nearest. Now subtract 1800 from 2040 to get reminder 240. Add 3 to quotient.
\begin{array}{l}\phantom{600)}0003\phantom{9}\\600\overline{)20400}\\\phantom{600)}\underline{\phantom{}1800\phantom{9}}\\\phantom{600)9}2400\\\end{array}
Use the 5^{th} digit 0 from dividend 20400
\begin{array}{l}\phantom{600)}00034\phantom{10}\\600\overline{)20400}\\\phantom{600)}\underline{\phantom{}1800\phantom{9}}\\\phantom{600)9}2400\\\phantom{600)}\underline{\phantom{9}2400\phantom{}}\\\phantom{600)99999}0\\\end{array}
Find closest multiple of 600 to 2400. We see that 4 \times 600 = 2400 is the nearest. Now subtract 2400 from 2400 to get reminder 0. Add 4 to quotient.
\text{Quotient: }34 \text{Reminder: }0
Since 0 is less than 600, stop the division. The reminder is 0. The topmost line 00034 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 34.
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}