Evaluate
\frac{326}{45}\approx 7.244444444
Factor
\frac{2 \cdot 163}{3 ^ {2} \cdot 5} = 7\frac{11}{45} = 7.2444444444444445
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\begin{array}{l}\phantom{45)}\phantom{1}\\45\overline{)326}\\\end{array}
Use the 1^{st} digit 3 from dividend 326
\begin{array}{l}\phantom{45)}0\phantom{2}\\45\overline{)326}\\\end{array}
Since 3 is less than 45, use the next digit 2 from dividend 326 and add 0 to the quotient
\begin{array}{l}\phantom{45)}0\phantom{3}\\45\overline{)326}\\\end{array}
Use the 2^{nd} digit 2 from dividend 326
\begin{array}{l}\phantom{45)}00\phantom{4}\\45\overline{)326}\\\end{array}
Since 32 is less than 45, use the next digit 6 from dividend 326 and add 0 to the quotient
\begin{array}{l}\phantom{45)}00\phantom{5}\\45\overline{)326}\\\end{array}
Use the 3^{rd} digit 6 from dividend 326
\begin{array}{l}\phantom{45)}007\phantom{6}\\45\overline{)326}\\\phantom{45)}\underline{\phantom{}315\phantom{}}\\\phantom{45)9}11\\\end{array}
Find closest multiple of 45 to 326. We see that 7 \times 45 = 315 is the nearest. Now subtract 315 from 326 to get reminder 11. Add 7 to quotient.
\text{Quotient: }7 \text{Reminder: }11
Since 11 is less than 45, stop the division. The reminder is 11. The topmost line 007 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 7.
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}