Evaluate
\frac{520}{11}\approx 47.272727273
Factor
\frac{2 ^ {3} \cdot 5 \cdot 13}{11} = 47\frac{3}{11} = 47.27272727272727
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\begin{array}{l}\phantom{22)}\phantom{1}\\22\overline{)1040}\\\end{array}
Use the 1^{st} digit 1 from dividend 1040
\begin{array}{l}\phantom{22)}0\phantom{2}\\22\overline{)1040}\\\end{array}
Since 1 is less than 22, use the next digit 0 from dividend 1040 and add 0 to the quotient
\begin{array}{l}\phantom{22)}0\phantom{3}\\22\overline{)1040}\\\end{array}
Use the 2^{nd} digit 0 from dividend 1040
\begin{array}{l}\phantom{22)}00\phantom{4}\\22\overline{)1040}\\\end{array}
Since 10 is less than 22, use the next digit 4 from dividend 1040 and add 0 to the quotient
\begin{array}{l}\phantom{22)}00\phantom{5}\\22\overline{)1040}\\\end{array}
Use the 3^{rd} digit 4 from dividend 1040
\begin{array}{l}\phantom{22)}004\phantom{6}\\22\overline{)1040}\\\phantom{22)}\underline{\phantom{9}88\phantom{9}}\\\phantom{22)9}16\\\end{array}
Find closest multiple of 22 to 104. We see that 4 \times 22 = 88 is the nearest. Now subtract 88 from 104 to get reminder 16. Add 4 to quotient.
\begin{array}{l}\phantom{22)}004\phantom{7}\\22\overline{)1040}\\\phantom{22)}\underline{\phantom{9}88\phantom{9}}\\\phantom{22)9}160\\\end{array}
Use the 4^{th} digit 0 from dividend 1040
\begin{array}{l}\phantom{22)}0047\phantom{8}\\22\overline{)1040}\\\phantom{22)}\underline{\phantom{9}88\phantom{9}}\\\phantom{22)9}160\\\phantom{22)}\underline{\phantom{9}154\phantom{}}\\\phantom{22)999}6\\\end{array}
Find closest multiple of 22 to 160. We see that 7 \times 22 = 154 is the nearest. Now subtract 154 from 160 to get reminder 6. Add 7 to quotient.
\text{Quotient: }47 \text{Reminder: }6
Since 6 is less than 22, stop the division. The reminder is 6. The topmost line 0047 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 47.
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}