Evaluate
\frac{30179}{1345}\approx 22.437918216
Factor
\frac{103 \cdot 293}{5 \cdot 269} = 22\frac{589}{1345} = 22.437918215613383
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\begin{array}{l}\phantom{1345)}\phantom{1}\\1345\overline{)30179}\\\end{array}
Use the 1^{st} digit 3 from dividend 30179
\begin{array}{l}\phantom{1345)}0\phantom{2}\\1345\overline{)30179}\\\end{array}
Since 3 is less than 1345, use the next digit 0 from dividend 30179 and add 0 to the quotient
\begin{array}{l}\phantom{1345)}0\phantom{3}\\1345\overline{)30179}\\\end{array}
Use the 2^{nd} digit 0 from dividend 30179
\begin{array}{l}\phantom{1345)}00\phantom{4}\\1345\overline{)30179}\\\end{array}
Since 30 is less than 1345, use the next digit 1 from dividend 30179 and add 0 to the quotient
\begin{array}{l}\phantom{1345)}00\phantom{5}\\1345\overline{)30179}\\\end{array}
Use the 3^{rd} digit 1 from dividend 30179
\begin{array}{l}\phantom{1345)}000\phantom{6}\\1345\overline{)30179}\\\end{array}
Since 301 is less than 1345, use the next digit 7 from dividend 30179 and add 0 to the quotient
\begin{array}{l}\phantom{1345)}000\phantom{7}\\1345\overline{)30179}\\\end{array}
Use the 4^{th} digit 7 from dividend 30179
\begin{array}{l}\phantom{1345)}0002\phantom{8}\\1345\overline{)30179}\\\phantom{1345)}\underline{\phantom{}2690\phantom{9}}\\\phantom{1345)9}327\\\end{array}
Find closest multiple of 1345 to 3017. We see that 2 \times 1345 = 2690 is the nearest. Now subtract 2690 from 3017 to get reminder 327. Add 2 to quotient.
\begin{array}{l}\phantom{1345)}0002\phantom{9}\\1345\overline{)30179}\\\phantom{1345)}\underline{\phantom{}2690\phantom{9}}\\\phantom{1345)9}3279\\\end{array}
Use the 5^{th} digit 9 from dividend 30179
\begin{array}{l}\phantom{1345)}00022\phantom{10}\\1345\overline{)30179}\\\phantom{1345)}\underline{\phantom{}2690\phantom{9}}\\\phantom{1345)9}3279\\\phantom{1345)}\underline{\phantom{9}2690\phantom{}}\\\phantom{1345)99}589\\\end{array}
Find closest multiple of 1345 to 3279. We see that 2 \times 1345 = 2690 is the nearest. Now subtract 2690 from 3279 to get reminder 589. Add 2 to quotient.
\text{Quotient: }22 \text{Reminder: }589
Since 589 is less than 1345, stop the division. The reminder is 589. The topmost line 00022 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 22.
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}