Evaluate
\frac{675}{4}=168.75
Factor
\frac{3 ^ {3} \cdot 5 ^ {2}}{2 ^ {2}} = 168\frac{3}{4} = 168.75
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\begin{array}{l}\phantom{1000)}\phantom{1}\\1000\overline{)168750}\\\end{array}
Use the 1^{st} digit 1 from dividend 168750
\begin{array}{l}\phantom{1000)}0\phantom{2}\\1000\overline{)168750}\\\end{array}
Since 1 is less than 1000, use the next digit 6 from dividend 168750 and add 0 to the quotient
\begin{array}{l}\phantom{1000)}0\phantom{3}\\1000\overline{)168750}\\\end{array}
Use the 2^{nd} digit 6 from dividend 168750
\begin{array}{l}\phantom{1000)}00\phantom{4}\\1000\overline{)168750}\\\end{array}
Since 16 is less than 1000, use the next digit 8 from dividend 168750 and add 0 to the quotient
\begin{array}{l}\phantom{1000)}00\phantom{5}\\1000\overline{)168750}\\\end{array}
Use the 3^{rd} digit 8 from dividend 168750
\begin{array}{l}\phantom{1000)}000\phantom{6}\\1000\overline{)168750}\\\end{array}
Since 168 is less than 1000, use the next digit 7 from dividend 168750 and add 0 to the quotient
\begin{array}{l}\phantom{1000)}000\phantom{7}\\1000\overline{)168750}\\\end{array}
Use the 4^{th} digit 7 from dividend 168750
\begin{array}{l}\phantom{1000)}0001\phantom{8}\\1000\overline{)168750}\\\phantom{1000)}\underline{\phantom{}1000\phantom{99}}\\\phantom{1000)9}687\\\end{array}
Find closest multiple of 1000 to 1687. We see that 1 \times 1000 = 1000 is the nearest. Now subtract 1000 from 1687 to get reminder 687. Add 1 to quotient.
\begin{array}{l}\phantom{1000)}0001\phantom{9}\\1000\overline{)168750}\\\phantom{1000)}\underline{\phantom{}1000\phantom{99}}\\\phantom{1000)9}6875\\\end{array}
Use the 5^{th} digit 5 from dividend 168750
\begin{array}{l}\phantom{1000)}00016\phantom{10}\\1000\overline{)168750}\\\phantom{1000)}\underline{\phantom{}1000\phantom{99}}\\\phantom{1000)9}6875\\\phantom{1000)}\underline{\phantom{9}6000\phantom{9}}\\\phantom{1000)99}875\\\end{array}
Find closest multiple of 1000 to 6875. We see that 6 \times 1000 = 6000 is the nearest. Now subtract 6000 from 6875 to get reminder 875. Add 6 to quotient.
\begin{array}{l}\phantom{1000)}00016\phantom{11}\\1000\overline{)168750}\\\phantom{1000)}\underline{\phantom{}1000\phantom{99}}\\\phantom{1000)9}6875\\\phantom{1000)}\underline{\phantom{9}6000\phantom{9}}\\\phantom{1000)99}8750\\\end{array}
Use the 6^{th} digit 0 from dividend 168750
\begin{array}{l}\phantom{1000)}000168\phantom{12}\\1000\overline{)168750}\\\phantom{1000)}\underline{\phantom{}1000\phantom{99}}\\\phantom{1000)9}6875\\\phantom{1000)}\underline{\phantom{9}6000\phantom{9}}\\\phantom{1000)99}8750\\\phantom{1000)}\underline{\phantom{99}8000\phantom{}}\\\phantom{1000)999}750\\\end{array}
Find closest multiple of 1000 to 8750. We see that 8 \times 1000 = 8000 is the nearest. Now subtract 8000 from 8750 to get reminder 750. Add 8 to quotient.
\text{Quotient: }168 \text{Reminder: }750
Since 750 is less than 1000, stop the division. The reminder is 750. The topmost line 000168 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 168.
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}