Evaluate
\frac{1294}{365}\approx 3.545205479
Factor
\frac{2 \cdot 647}{5 \cdot 73} = 3\frac{199}{365} = 3.5452054794520547
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\begin{array}{l}\phantom{365)}\phantom{1}\\365\overline{)1294}\\\end{array}
Use the 1^{st} digit 1 from dividend 1294
\begin{array}{l}\phantom{365)}0\phantom{2}\\365\overline{)1294}\\\end{array}
Since 1 is less than 365, use the next digit 2 from dividend 1294 and add 0 to the quotient
\begin{array}{l}\phantom{365)}0\phantom{3}\\365\overline{)1294}\\\end{array}
Use the 2^{nd} digit 2 from dividend 1294
\begin{array}{l}\phantom{365)}00\phantom{4}\\365\overline{)1294}\\\end{array}
Since 12 is less than 365, use the next digit 9 from dividend 1294 and add 0 to the quotient
\begin{array}{l}\phantom{365)}00\phantom{5}\\365\overline{)1294}\\\end{array}
Use the 3^{rd} digit 9 from dividend 1294
\begin{array}{l}\phantom{365)}000\phantom{6}\\365\overline{)1294}\\\end{array}
Since 129 is less than 365, use the next digit 4 from dividend 1294 and add 0 to the quotient
\begin{array}{l}\phantom{365)}000\phantom{7}\\365\overline{)1294}\\\end{array}
Use the 4^{th} digit 4 from dividend 1294
\begin{array}{l}\phantom{365)}0003\phantom{8}\\365\overline{)1294}\\\phantom{365)}\underline{\phantom{}1095\phantom{}}\\\phantom{365)9}199\\\end{array}
Find closest multiple of 365 to 1294. We see that 3 \times 365 = 1095 is the nearest. Now subtract 1095 from 1294 to get reminder 199. Add 3 to quotient.
\text{Quotient: }3 \text{Reminder: }199
Since 199 is less than 365, stop the division. The reminder is 199. The topmost line 0003 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 3.
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
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}