Evaluate
15
Factor
3\times 5
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\begin{array}{l}\phantom{800)}\phantom{1}\\800\overline{)12000}\\\end{array}
Use the 1^{st} digit 1 from dividend 12000
\begin{array}{l}\phantom{800)}0\phantom{2}\\800\overline{)12000}\\\end{array}
Since 1 is less than 800, use the next digit 2 from dividend 12000 and add 0 to the quotient
\begin{array}{l}\phantom{800)}0\phantom{3}\\800\overline{)12000}\\\end{array}
Use the 2^{nd} digit 2 from dividend 12000
\begin{array}{l}\phantom{800)}00\phantom{4}\\800\overline{)12000}\\\end{array}
Since 12 is less than 800, use the next digit 0 from dividend 12000 and add 0 to the quotient
\begin{array}{l}\phantom{800)}00\phantom{5}\\800\overline{)12000}\\\end{array}
Use the 3^{rd} digit 0 from dividend 12000
\begin{array}{l}\phantom{800)}000\phantom{6}\\800\overline{)12000}\\\end{array}
Since 120 is less than 800, use the next digit 0 from dividend 12000 and add 0 to the quotient
\begin{array}{l}\phantom{800)}000\phantom{7}\\800\overline{)12000}\\\end{array}
Use the 4^{th} digit 0 from dividend 12000
\begin{array}{l}\phantom{800)}0001\phantom{8}\\800\overline{)12000}\\\phantom{800)}\underline{\phantom{9}800\phantom{9}}\\\phantom{800)9}400\\\end{array}
Find closest multiple of 800 to 1200. We see that 1 \times 800 = 800 is the nearest. Now subtract 800 from 1200 to get reminder 400. Add 1 to quotient.
\begin{array}{l}\phantom{800)}0001\phantom{9}\\800\overline{)12000}\\\phantom{800)}\underline{\phantom{9}800\phantom{9}}\\\phantom{800)9}4000\\\end{array}
Use the 5^{th} digit 0 from dividend 12000
\begin{array}{l}\phantom{800)}00015\phantom{10}\\800\overline{)12000}\\\phantom{800)}\underline{\phantom{9}800\phantom{9}}\\\phantom{800)9}4000\\\phantom{800)}\underline{\phantom{9}4000\phantom{}}\\\phantom{800)99999}0\\\end{array}
Find closest multiple of 800 to 4000. We see that 5 \times 800 = 4000 is the nearest. Now subtract 4000 from 4000 to get reminder 0. Add 5 to quotient.
\text{Quotient: }15 \text{Reminder: }0
Since 0 is less than 800, stop the division. The reminder is 0. The topmost line 00015 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 15.
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}