Evaluate
\frac{1222}{11}\approx 111.090909091
Factor
\frac{2 \cdot 13 \cdot 47}{11} = 111\frac{1}{11} = 111.0909090909091
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\begin{array}{l}\phantom{11)}\phantom{1}\\11\overline{)1222}\\\end{array}
Use the 1^{st} digit 1 from dividend 1222
\begin{array}{l}\phantom{11)}0\phantom{2}\\11\overline{)1222}\\\end{array}
Since 1 is less than 11, use the next digit 2 from dividend 1222 and add 0 to the quotient
\begin{array}{l}\phantom{11)}0\phantom{3}\\11\overline{)1222}\\\end{array}
Use the 2^{nd} digit 2 from dividend 1222
\begin{array}{l}\phantom{11)}01\phantom{4}\\11\overline{)1222}\\\phantom{11)}\underline{\phantom{}11\phantom{99}}\\\phantom{11)9}1\\\end{array}
Find closest multiple of 11 to 12. We see that 1 \times 11 = 11 is the nearest. Now subtract 11 from 12 to get reminder 1. Add 1 to quotient.
\begin{array}{l}\phantom{11)}01\phantom{5}\\11\overline{)1222}\\\phantom{11)}\underline{\phantom{}11\phantom{99}}\\\phantom{11)9}12\\\end{array}
Use the 3^{rd} digit 2 from dividend 1222
\begin{array}{l}\phantom{11)}011\phantom{6}\\11\overline{)1222}\\\phantom{11)}\underline{\phantom{}11\phantom{99}}\\\phantom{11)9}12\\\phantom{11)}\underline{\phantom{9}11\phantom{9}}\\\phantom{11)99}1\\\end{array}
Find closest multiple of 11 to 12. We see that 1 \times 11 = 11 is the nearest. Now subtract 11 from 12 to get reminder 1. Add 1 to quotient.
\begin{array}{l}\phantom{11)}011\phantom{7}\\11\overline{)1222}\\\phantom{11)}\underline{\phantom{}11\phantom{99}}\\\phantom{11)9}12\\\phantom{11)}\underline{\phantom{9}11\phantom{9}}\\\phantom{11)99}12\\\end{array}
Use the 4^{th} digit 2 from dividend 1222
\begin{array}{l}\phantom{11)}0111\phantom{8}\\11\overline{)1222}\\\phantom{11)}\underline{\phantom{}11\phantom{99}}\\\phantom{11)9}12\\\phantom{11)}\underline{\phantom{9}11\phantom{9}}\\\phantom{11)99}12\\\phantom{11)}\underline{\phantom{99}11\phantom{}}\\\phantom{11)999}1\\\end{array}
Find closest multiple of 11 to 12. We see that 1 \times 11 = 11 is the nearest. Now subtract 11 from 12 to get reminder 1. Add 1 to quotient.
\text{Quotient: }111 \text{Reminder: }1
Since 1 is less than 11, stop the division. The reminder is 1. The topmost line 0111 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 111.
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}