Evaluate
\frac{324}{37}\approx 8.756756757
Factor
\frac{2 ^ {2} \cdot 3 ^ {4}}{37} = 8\frac{28}{37} = 8.756756756756756
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\begin{array}{l}\phantom{37)}\phantom{1}\\37\overline{)324}\\\end{array}
Use the 1^{st} digit 3 from dividend 324
\begin{array}{l}\phantom{37)}0\phantom{2}\\37\overline{)324}\\\end{array}
Since 3 is less than 37, use the next digit 2 from dividend 324 and add 0 to the quotient
\begin{array}{l}\phantom{37)}0\phantom{3}\\37\overline{)324}\\\end{array}
Use the 2^{nd} digit 2 from dividend 324
\begin{array}{l}\phantom{37)}00\phantom{4}\\37\overline{)324}\\\end{array}
Since 32 is less than 37, use the next digit 4 from dividend 324 and add 0 to the quotient
\begin{array}{l}\phantom{37)}00\phantom{5}\\37\overline{)324}\\\end{array}
Use the 3^{rd} digit 4 from dividend 324
\begin{array}{l}\phantom{37)}008\phantom{6}\\37\overline{)324}\\\phantom{37)}\underline{\phantom{}296\phantom{}}\\\phantom{37)9}28\\\end{array}
Find closest multiple of 37 to 324. We see that 8 \times 37 = 296 is the nearest. Now subtract 296 from 324 to get reminder 28. Add 8 to quotient.
\text{Quotient: }8 \text{Reminder: }28
Since 28 is less than 37, stop the division. The reminder is 28. The topmost line 008 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 8.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
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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}