Evaluate
\frac{180}{7}\approx 25.714285714
Factor
\frac{2 ^ {2} \cdot 3 ^ {2} \cdot 5}{7} = 25\frac{5}{7} = 25.714285714285715
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\begin{array}{l}\phantom{7000)}\phantom{1}\\7000\overline{)180000}\\\end{array}
Use the 1^{st} digit 1 from dividend 180000
\begin{array}{l}\phantom{7000)}0\phantom{2}\\7000\overline{)180000}\\\end{array}
Since 1 is less than 7000, use the next digit 8 from dividend 180000 and add 0 to the quotient
\begin{array}{l}\phantom{7000)}0\phantom{3}\\7000\overline{)180000}\\\end{array}
Use the 2^{nd} digit 8 from dividend 180000
\begin{array}{l}\phantom{7000)}00\phantom{4}\\7000\overline{)180000}\\\end{array}
Since 18 is less than 7000, use the next digit 0 from dividend 180000 and add 0 to the quotient
\begin{array}{l}\phantom{7000)}00\phantom{5}\\7000\overline{)180000}\\\end{array}
Use the 3^{rd} digit 0 from dividend 180000
\begin{array}{l}\phantom{7000)}000\phantom{6}\\7000\overline{)180000}\\\end{array}
Since 180 is less than 7000, use the next digit 0 from dividend 180000 and add 0 to the quotient
\begin{array}{l}\phantom{7000)}000\phantom{7}\\7000\overline{)180000}\\\end{array}
Use the 4^{th} digit 0 from dividend 180000
\begin{array}{l}\phantom{7000)}0000\phantom{8}\\7000\overline{)180000}\\\end{array}
Since 1800 is less than 7000, use the next digit 0 from dividend 180000 and add 0 to the quotient
\begin{array}{l}\phantom{7000)}0000\phantom{9}\\7000\overline{)180000}\\\end{array}
Use the 5^{th} digit 0 from dividend 180000
\begin{array}{l}\phantom{7000)}00002\phantom{10}\\7000\overline{)180000}\\\phantom{7000)}\underline{\phantom{}14000\phantom{9}}\\\phantom{7000)9}4000\\\end{array}
Find closest multiple of 7000 to 18000. We see that 2 \times 7000 = 14000 is the nearest. Now subtract 14000 from 18000 to get reminder 4000. Add 2 to quotient.
\begin{array}{l}\phantom{7000)}00002\phantom{11}\\7000\overline{)180000}\\\phantom{7000)}\underline{\phantom{}14000\phantom{9}}\\\phantom{7000)9}40000\\\end{array}
Use the 6^{th} digit 0 from dividend 180000
\begin{array}{l}\phantom{7000)}000025\phantom{12}\\7000\overline{)180000}\\\phantom{7000)}\underline{\phantom{}14000\phantom{9}}\\\phantom{7000)9}40000\\\phantom{7000)}\underline{\phantom{9}35000\phantom{}}\\\phantom{7000)99}5000\\\end{array}
Find closest multiple of 7000 to 40000. We see that 5 \times 7000 = 35000 is the nearest. Now subtract 35000 from 40000 to get reminder 5000. Add 5 to quotient.
\text{Quotient: }25 \text{Reminder: }5000
Since 5000 is less than 7000, stop the division. The reminder is 5000. The topmost line 000025 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 25.
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}