Evaluate
\frac{2154}{125}=17.232
Factor
\frac{2 \cdot 3 \cdot 359}{5 ^ {3}} = 17\frac{29}{125} = 17.232
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\begin{array}{l}\phantom{1000)}\phantom{1}\\1000\overline{)17232}\\\end{array}
Use the 1^{st} digit 1 from dividend 17232
\begin{array}{l}\phantom{1000)}0\phantom{2}\\1000\overline{)17232}\\\end{array}
Since 1 is less than 1000, use the next digit 7 from dividend 17232 and add 0 to the quotient
\begin{array}{l}\phantom{1000)}0\phantom{3}\\1000\overline{)17232}\\\end{array}
Use the 2^{nd} digit 7 from dividend 17232
\begin{array}{l}\phantom{1000)}00\phantom{4}\\1000\overline{)17232}\\\end{array}
Since 17 is less than 1000, use the next digit 2 from dividend 17232 and add 0 to the quotient
\begin{array}{l}\phantom{1000)}00\phantom{5}\\1000\overline{)17232}\\\end{array}
Use the 3^{rd} digit 2 from dividend 17232
\begin{array}{l}\phantom{1000)}000\phantom{6}\\1000\overline{)17232}\\\end{array}
Since 172 is less than 1000, use the next digit 3 from dividend 17232 and add 0 to the quotient
\begin{array}{l}\phantom{1000)}000\phantom{7}\\1000\overline{)17232}\\\end{array}
Use the 4^{th} digit 3 from dividend 17232
\begin{array}{l}\phantom{1000)}0001\phantom{8}\\1000\overline{)17232}\\\phantom{1000)}\underline{\phantom{}1000\phantom{9}}\\\phantom{1000)9}723\\\end{array}
Find closest multiple of 1000 to 1723. We see that 1 \times 1000 = 1000 is the nearest. Now subtract 1000 from 1723 to get reminder 723. Add 1 to quotient.
\begin{array}{l}\phantom{1000)}0001\phantom{9}\\1000\overline{)17232}\\\phantom{1000)}\underline{\phantom{}1000\phantom{9}}\\\phantom{1000)9}7232\\\end{array}
Use the 5^{th} digit 2 from dividend 17232
\begin{array}{l}\phantom{1000)}00017\phantom{10}\\1000\overline{)17232}\\\phantom{1000)}\underline{\phantom{}1000\phantom{9}}\\\phantom{1000)9}7232\\\phantom{1000)}\underline{\phantom{9}7000\phantom{}}\\\phantom{1000)99}232\\\end{array}
Find closest multiple of 1000 to 7232. We see that 7 \times 1000 = 7000 is the nearest. Now subtract 7000 from 7232 to get reminder 232. Add 7 to quotient.
\text{Quotient: }17 \text{Reminder: }232
Since 232 is less than 1000, stop the division. The reminder is 232. The topmost line 00017 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 17.
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}