Evaluate
\frac{613}{184}\approx 3.331521739
Factor
\frac{613}{2 ^ {3} \cdot 23} = 3\frac{61}{184} = 3.3315217391304346
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\begin{array}{l}\phantom{184)}\phantom{1}\\184\overline{)613}\\\end{array}
Use the 1^{st} digit 6 from dividend 613
\begin{array}{l}\phantom{184)}0\phantom{2}\\184\overline{)613}\\\end{array}
Since 6 is less than 184, use the next digit 1 from dividend 613 and add 0 to the quotient
\begin{array}{l}\phantom{184)}0\phantom{3}\\184\overline{)613}\\\end{array}
Use the 2^{nd} digit 1 from dividend 613
\begin{array}{l}\phantom{184)}00\phantom{4}\\184\overline{)613}\\\end{array}
Since 61 is less than 184, use the next digit 3 from dividend 613 and add 0 to the quotient
\begin{array}{l}\phantom{184)}00\phantom{5}\\184\overline{)613}\\\end{array}
Use the 3^{rd} digit 3 from dividend 613
\begin{array}{l}\phantom{184)}003\phantom{6}\\184\overline{)613}\\\phantom{184)}\underline{\phantom{}552\phantom{}}\\\phantom{184)9}61\\\end{array}
Find closest multiple of 184 to 613. We see that 3 \times 184 = 552 is the nearest. Now subtract 552 from 613 to get reminder 61. Add 3 to quotient.
\text{Quotient: }3 \text{Reminder: }61
Since 61 is less than 184, stop the division. The reminder is 61. The topmost line 003 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 3.
Examples
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Linear equation
y = 3x + 4
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Matrix
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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}