Evaluate
\frac{1350}{7}\approx 192.857142857
Factor
\frac{2 \cdot 3 ^ {3} \cdot 5 ^ {2}}{7} = 192\frac{6}{7} = 192.85714285714286
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\begin{array}{l}\phantom{700)}\phantom{1}\\700\overline{)135000}\\\end{array}
Use the 1^{st} digit 1 from dividend 135000
\begin{array}{l}\phantom{700)}0\phantom{2}\\700\overline{)135000}\\\end{array}
Since 1 is less than 700, use the next digit 3 from dividend 135000 and add 0 to the quotient
\begin{array}{l}\phantom{700)}0\phantom{3}\\700\overline{)135000}\\\end{array}
Use the 2^{nd} digit 3 from dividend 135000
\begin{array}{l}\phantom{700)}00\phantom{4}\\700\overline{)135000}\\\end{array}
Since 13 is less than 700, use the next digit 5 from dividend 135000 and add 0 to the quotient
\begin{array}{l}\phantom{700)}00\phantom{5}\\700\overline{)135000}\\\end{array}
Use the 3^{rd} digit 5 from dividend 135000
\begin{array}{l}\phantom{700)}000\phantom{6}\\700\overline{)135000}\\\end{array}
Since 135 is less than 700, use the next digit 0 from dividend 135000 and add 0 to the quotient
\begin{array}{l}\phantom{700)}000\phantom{7}\\700\overline{)135000}\\\end{array}
Use the 4^{th} digit 0 from dividend 135000
\begin{array}{l}\phantom{700)}0001\phantom{8}\\700\overline{)135000}\\\phantom{700)}\underline{\phantom{9}700\phantom{99}}\\\phantom{700)9}650\\\end{array}
Find closest multiple of 700 to 1350. We see that 1 \times 700 = 700 is the nearest. Now subtract 700 from 1350 to get reminder 650. Add 1 to quotient.
\begin{array}{l}\phantom{700)}0001\phantom{9}\\700\overline{)135000}\\\phantom{700)}\underline{\phantom{9}700\phantom{99}}\\\phantom{700)9}6500\\\end{array}
Use the 5^{th} digit 0 from dividend 135000
\begin{array}{l}\phantom{700)}00019\phantom{10}\\700\overline{)135000}\\\phantom{700)}\underline{\phantom{9}700\phantom{99}}\\\phantom{700)9}6500\\\phantom{700)}\underline{\phantom{9}6300\phantom{9}}\\\phantom{700)99}200\\\end{array}
Find closest multiple of 700 to 6500. We see that 9 \times 700 = 6300 is the nearest. Now subtract 6300 from 6500 to get reminder 200. Add 9 to quotient.
\begin{array}{l}\phantom{700)}00019\phantom{11}\\700\overline{)135000}\\\phantom{700)}\underline{\phantom{9}700\phantom{99}}\\\phantom{700)9}6500\\\phantom{700)}\underline{\phantom{9}6300\phantom{9}}\\\phantom{700)99}2000\\\end{array}
Use the 6^{th} digit 0 from dividend 135000
\begin{array}{l}\phantom{700)}000192\phantom{12}\\700\overline{)135000}\\\phantom{700)}\underline{\phantom{9}700\phantom{99}}\\\phantom{700)9}6500\\\phantom{700)}\underline{\phantom{9}6300\phantom{9}}\\\phantom{700)99}2000\\\phantom{700)}\underline{\phantom{99}1400\phantom{}}\\\phantom{700)999}600\\\end{array}
Find closest multiple of 700 to 2000. We see that 2 \times 700 = 1400 is the nearest. Now subtract 1400 from 2000 to get reminder 600. Add 2 to quotient.
\text{Quotient: }192 \text{Reminder: }600
Since 600 is less than 700, stop the division. The reminder is 600. The topmost line 000192 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 192.
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}