Evaluate
\frac{3451}{11}\approx 313.727272727
Factor
\frac{7 \cdot 17 \cdot 29}{11} = 313\frac{8}{11} = 313.72727272727275
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\begin{array}{l}\phantom{11)}\phantom{1}\\11\overline{)3451}\\\end{array}
Use the 1^{st} digit 3 from dividend 3451
\begin{array}{l}\phantom{11)}0\phantom{2}\\11\overline{)3451}\\\end{array}
Since 3 is less than 11, use the next digit 4 from dividend 3451 and add 0 to the quotient
\begin{array}{l}\phantom{11)}0\phantom{3}\\11\overline{)3451}\\\end{array}
Use the 2^{nd} digit 4 from dividend 3451
\begin{array}{l}\phantom{11)}03\phantom{4}\\11\overline{)3451}\\\phantom{11)}\underline{\phantom{}33\phantom{99}}\\\phantom{11)9}1\\\end{array}
Find closest multiple of 11 to 34. We see that 3 \times 11 = 33 is the nearest. Now subtract 33 from 34 to get reminder 1. Add 3 to quotient.
\begin{array}{l}\phantom{11)}03\phantom{5}\\11\overline{)3451}\\\phantom{11)}\underline{\phantom{}33\phantom{99}}\\\phantom{11)9}15\\\end{array}
Use the 3^{rd} digit 5 from dividend 3451
\begin{array}{l}\phantom{11)}031\phantom{6}\\11\overline{)3451}\\\phantom{11)}\underline{\phantom{}33\phantom{99}}\\\phantom{11)9}15\\\phantom{11)}\underline{\phantom{9}11\phantom{9}}\\\phantom{11)99}4\\\end{array}
Find closest multiple of 11 to 15. We see that 1 \times 11 = 11 is the nearest. Now subtract 11 from 15 to get reminder 4. Add 1 to quotient.
\begin{array}{l}\phantom{11)}031\phantom{7}\\11\overline{)3451}\\\phantom{11)}\underline{\phantom{}33\phantom{99}}\\\phantom{11)9}15\\\phantom{11)}\underline{\phantom{9}11\phantom{9}}\\\phantom{11)99}41\\\end{array}
Use the 4^{th} digit 1 from dividend 3451
\begin{array}{l}\phantom{11)}0313\phantom{8}\\11\overline{)3451}\\\phantom{11)}\underline{\phantom{}33\phantom{99}}\\\phantom{11)9}15\\\phantom{11)}\underline{\phantom{9}11\phantom{9}}\\\phantom{11)99}41\\\phantom{11)}\underline{\phantom{99}33\phantom{}}\\\phantom{11)999}8\\\end{array}
Find closest multiple of 11 to 41. We see that 3 \times 11 = 33 is the nearest. Now subtract 33 from 41 to get reminder 8. Add 3 to quotient.
\text{Quotient: }313 \text{Reminder: }8
Since 8 is less than 11, stop the division. The reminder is 8. The topmost line 0313 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 313.
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}