Evaluate
\frac{105}{23}\approx 4.565217391
Factor
\frac{3 \cdot 5 \cdot 7}{23} = 4\frac{13}{23} = 4.565217391304348
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\begin{array}{l}\phantom{460)}\phantom{1}\\460\overline{)2100}\\\end{array}
Use the 1^{st} digit 2 from dividend 2100
\begin{array}{l}\phantom{460)}0\phantom{2}\\460\overline{)2100}\\\end{array}
Since 2 is less than 460, use the next digit 1 from dividend 2100 and add 0 to the quotient
\begin{array}{l}\phantom{460)}0\phantom{3}\\460\overline{)2100}\\\end{array}
Use the 2^{nd} digit 1 from dividend 2100
\begin{array}{l}\phantom{460)}00\phantom{4}\\460\overline{)2100}\\\end{array}
Since 21 is less than 460, use the next digit 0 from dividend 2100 and add 0 to the quotient
\begin{array}{l}\phantom{460)}00\phantom{5}\\460\overline{)2100}\\\end{array}
Use the 3^{rd} digit 0 from dividend 2100
\begin{array}{l}\phantom{460)}000\phantom{6}\\460\overline{)2100}\\\end{array}
Since 210 is less than 460, use the next digit 0 from dividend 2100 and add 0 to the quotient
\begin{array}{l}\phantom{460)}000\phantom{7}\\460\overline{)2100}\\\end{array}
Use the 4^{th} digit 0 from dividend 2100
\begin{array}{l}\phantom{460)}0004\phantom{8}\\460\overline{)2100}\\\phantom{460)}\underline{\phantom{}1840\phantom{}}\\\phantom{460)9}260\\\end{array}
Find closest multiple of 460 to 2100. We see that 4 \times 460 = 1840 is the nearest. Now subtract 1840 from 2100 to get reminder 260. Add 4 to quotient.
\text{Quotient: }4 \text{Reminder: }260
Since 260 is less than 460, stop the division. The reminder is 260. The topmost line 0004 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 4.
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}