Evaluate
11
Factor
11
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\begin{array}{l}\phantom{13)}\phantom{1}\\13\overline{)143}\\\end{array}
Use the 1^{st} digit 1 from dividend 143
\begin{array}{l}\phantom{13)}0\phantom{2}\\13\overline{)143}\\\end{array}
Since 1 is less than 13, use the next digit 4 from dividend 143 and add 0 to the quotient
\begin{array}{l}\phantom{13)}0\phantom{3}\\13\overline{)143}\\\end{array}
Use the 2^{nd} digit 4 from dividend 143
\begin{array}{l}\phantom{13)}01\phantom{4}\\13\overline{)143}\\\phantom{13)}\underline{\phantom{}13\phantom{9}}\\\phantom{13)9}1\\\end{array}
Find closest multiple of 13 to 14. We see that 1 \times 13 = 13 is the nearest. Now subtract 13 from 14 to get reminder 1. Add 1 to quotient.
\begin{array}{l}\phantom{13)}01\phantom{5}\\13\overline{)143}\\\phantom{13)}\underline{\phantom{}13\phantom{9}}\\\phantom{13)9}13\\\end{array}
Use the 3^{rd} digit 3 from dividend 143
\begin{array}{l}\phantom{13)}011\phantom{6}\\13\overline{)143}\\\phantom{13)}\underline{\phantom{}13\phantom{9}}\\\phantom{13)9}13\\\phantom{13)}\underline{\phantom{9}13\phantom{}}\\\phantom{13)999}0\\\end{array}
Find closest multiple of 13 to 13. We see that 1 \times 13 = 13 is the nearest. Now subtract 13 from 13 to get reminder 0. Add 1 to quotient.
\text{Quotient: }11 \text{Reminder: }0
Since 0 is less than 13, stop the division. The reminder is 0. The topmost line 011 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 11.
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}