Evaluate
101
Factor
101
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\begin{array}{l}\phantom{12)}\phantom{1}\\12\overline{)1212}\\\end{array}
Use the 1^{st} digit 1 from dividend 1212
\begin{array}{l}\phantom{12)}0\phantom{2}\\12\overline{)1212}\\\end{array}
Since 1 is less than 12, use the next digit 2 from dividend 1212 and add 0 to the quotient
\begin{array}{l}\phantom{12)}0\phantom{3}\\12\overline{)1212}\\\end{array}
Use the 2^{nd} digit 2 from dividend 1212
\begin{array}{l}\phantom{12)}01\phantom{4}\\12\overline{)1212}\\\phantom{12)}\underline{\phantom{}12\phantom{99}}\\\phantom{12)99}0\\\end{array}
Find closest multiple of 12 to 12. We see that 1 \times 12 = 12 is the nearest. Now subtract 12 from 12 to get reminder 0. Add 1 to quotient.
\begin{array}{l}\phantom{12)}01\phantom{5}\\12\overline{)1212}\\\phantom{12)}\underline{\phantom{}12\phantom{99}}\\\phantom{12)99}1\\\end{array}
Use the 3^{rd} digit 1 from dividend 1212
\begin{array}{l}\phantom{12)}010\phantom{6}\\12\overline{)1212}\\\phantom{12)}\underline{\phantom{}12\phantom{99}}\\\phantom{12)99}1\\\end{array}
Since 1 is less than 12, use the next digit 2 from dividend 1212 and add 0 to the quotient
\begin{array}{l}\phantom{12)}010\phantom{7}\\12\overline{)1212}\\\phantom{12)}\underline{\phantom{}12\phantom{99}}\\\phantom{12)99}12\\\end{array}
Use the 4^{th} digit 2 from dividend 1212
\begin{array}{l}\phantom{12)}0101\phantom{8}\\12\overline{)1212}\\\phantom{12)}\underline{\phantom{}12\phantom{99}}\\\phantom{12)99}12\\\phantom{12)}\underline{\phantom{99}12\phantom{}}\\\phantom{12)9999}0\\\end{array}
Find closest multiple of 12 to 12. We see that 1 \times 12 = 12 is the nearest. Now subtract 12 from 12 to get reminder 0. Add 1 to quotient.
\text{Quotient: }101 \text{Reminder: }0
Since 0 is less than 12, stop the division. The reminder is 0. The topmost line 0101 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 101.
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}