Evaluate
\frac{2213}{42}\approx 52.69047619
Factor
\frac{2213}{2 \cdot 3 \cdot 7} = 52\frac{29}{42} = 52.69047619047619
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\begin{array}{l}\phantom{84)}\phantom{1}\\84\overline{)4426}\\\end{array}
Use the 1^{st} digit 4 from dividend 4426
\begin{array}{l}\phantom{84)}0\phantom{2}\\84\overline{)4426}\\\end{array}
Since 4 is less than 84, use the next digit 4 from dividend 4426 and add 0 to the quotient
\begin{array}{l}\phantom{84)}0\phantom{3}\\84\overline{)4426}\\\end{array}
Use the 2^{nd} digit 4 from dividend 4426
\begin{array}{l}\phantom{84)}00\phantom{4}\\84\overline{)4426}\\\end{array}
Since 44 is less than 84, use the next digit 2 from dividend 4426 and add 0 to the quotient
\begin{array}{l}\phantom{84)}00\phantom{5}\\84\overline{)4426}\\\end{array}
Use the 3^{rd} digit 2 from dividend 4426
\begin{array}{l}\phantom{84)}005\phantom{6}\\84\overline{)4426}\\\phantom{84)}\underline{\phantom{}420\phantom{9}}\\\phantom{84)9}22\\\end{array}
Find closest multiple of 84 to 442. We see that 5 \times 84 = 420 is the nearest. Now subtract 420 from 442 to get reminder 22. Add 5 to quotient.
\begin{array}{l}\phantom{84)}005\phantom{7}\\84\overline{)4426}\\\phantom{84)}\underline{\phantom{}420\phantom{9}}\\\phantom{84)9}226\\\end{array}
Use the 4^{th} digit 6 from dividend 4426
\begin{array}{l}\phantom{84)}0052\phantom{8}\\84\overline{)4426}\\\phantom{84)}\underline{\phantom{}420\phantom{9}}\\\phantom{84)9}226\\\phantom{84)}\underline{\phantom{9}168\phantom{}}\\\phantom{84)99}58\\\end{array}
Find closest multiple of 84 to 226. We see that 2 \times 84 = 168 is the nearest. Now subtract 168 from 226 to get reminder 58. Add 2 to quotient.
\text{Quotient: }52 \text{Reminder: }58
Since 58 is less than 84, stop the division. The reminder is 58. The topmost line 0052 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 52.
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}