Evaluate
\frac{3564}{23}\approx 154.956521739
Factor
\frac{2 ^ {2} \cdot 3 ^ {4} \cdot 11}{23} = 154\frac{22}{23} = 154.95652173913044
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\begin{array}{l}\phantom{23)}\phantom{1}\\23\overline{)3564}\\\end{array}
Use the 1^{st} digit 3 from dividend 3564
\begin{array}{l}\phantom{23)}0\phantom{2}\\23\overline{)3564}\\\end{array}
Since 3 is less than 23, use the next digit 5 from dividend 3564 and add 0 to the quotient
\begin{array}{l}\phantom{23)}0\phantom{3}\\23\overline{)3564}\\\end{array}
Use the 2^{nd} digit 5 from dividend 3564
\begin{array}{l}\phantom{23)}01\phantom{4}\\23\overline{)3564}\\\phantom{23)}\underline{\phantom{}23\phantom{99}}\\\phantom{23)}12\\\end{array}
Find closest multiple of 23 to 35. We see that 1 \times 23 = 23 is the nearest. Now subtract 23 from 35 to get reminder 12. Add 1 to quotient.
\begin{array}{l}\phantom{23)}01\phantom{5}\\23\overline{)3564}\\\phantom{23)}\underline{\phantom{}23\phantom{99}}\\\phantom{23)}126\\\end{array}
Use the 3^{rd} digit 6 from dividend 3564
\begin{array}{l}\phantom{23)}015\phantom{6}\\23\overline{)3564}\\\phantom{23)}\underline{\phantom{}23\phantom{99}}\\\phantom{23)}126\\\phantom{23)}\underline{\phantom{}115\phantom{9}}\\\phantom{23)9}11\\\end{array}
Find closest multiple of 23 to 126. We see that 5 \times 23 = 115 is the nearest. Now subtract 115 from 126 to get reminder 11. Add 5 to quotient.
\begin{array}{l}\phantom{23)}015\phantom{7}\\23\overline{)3564}\\\phantom{23)}\underline{\phantom{}23\phantom{99}}\\\phantom{23)}126\\\phantom{23)}\underline{\phantom{}115\phantom{9}}\\\phantom{23)9}114\\\end{array}
Use the 4^{th} digit 4 from dividend 3564
\begin{array}{l}\phantom{23)}0154\phantom{8}\\23\overline{)3564}\\\phantom{23)}\underline{\phantom{}23\phantom{99}}\\\phantom{23)}126\\\phantom{23)}\underline{\phantom{}115\phantom{9}}\\\phantom{23)9}114\\\phantom{23)}\underline{\phantom{99}92\phantom{}}\\\phantom{23)99}22\\\end{array}
Find closest multiple of 23 to 114. We see that 4 \times 23 = 92 is the nearest. Now subtract 92 from 114 to get reminder 22. Add 4 to quotient.
\text{Quotient: }154 \text{Reminder: }22
Since 22 is less than 23, stop the division. The reminder is 22. The topmost line 0154 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 154.
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}