Evaluate
75
Factor
3\times 5^{2}
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\begin{array}{l}\phantom{960)}\phantom{1}\\960\overline{)72000}\\\end{array}
Use the 1^{st} digit 7 from dividend 72000
\begin{array}{l}\phantom{960)}0\phantom{2}\\960\overline{)72000}\\\end{array}
Since 7 is less than 960, use the next digit 2 from dividend 72000 and add 0 to the quotient
\begin{array}{l}\phantom{960)}0\phantom{3}\\960\overline{)72000}\\\end{array}
Use the 2^{nd} digit 2 from dividend 72000
\begin{array}{l}\phantom{960)}00\phantom{4}\\960\overline{)72000}\\\end{array}
Since 72 is less than 960, use the next digit 0 from dividend 72000 and add 0 to the quotient
\begin{array}{l}\phantom{960)}00\phantom{5}\\960\overline{)72000}\\\end{array}
Use the 3^{rd} digit 0 from dividend 72000
\begin{array}{l}\phantom{960)}000\phantom{6}\\960\overline{)72000}\\\end{array}
Since 720 is less than 960, use the next digit 0 from dividend 72000 and add 0 to the quotient
\begin{array}{l}\phantom{960)}000\phantom{7}\\960\overline{)72000}\\\end{array}
Use the 4^{th} digit 0 from dividend 72000
\begin{array}{l}\phantom{960)}0007\phantom{8}\\960\overline{)72000}\\\phantom{960)}\underline{\phantom{}6720\phantom{9}}\\\phantom{960)9}480\\\end{array}
Find closest multiple of 960 to 7200. We see that 7 \times 960 = 6720 is the nearest. Now subtract 6720 from 7200 to get reminder 480. Add 7 to quotient.
\begin{array}{l}\phantom{960)}0007\phantom{9}\\960\overline{)72000}\\\phantom{960)}\underline{\phantom{}6720\phantom{9}}\\\phantom{960)9}4800\\\end{array}
Use the 5^{th} digit 0 from dividend 72000
\begin{array}{l}\phantom{960)}00075\phantom{10}\\960\overline{)72000}\\\phantom{960)}\underline{\phantom{}6720\phantom{9}}\\\phantom{960)9}4800\\\phantom{960)}\underline{\phantom{9}4800\phantom{}}\\\phantom{960)99999}0\\\end{array}
Find closest multiple of 960 to 4800. We see that 5 \times 960 = 4800 is the nearest. Now subtract 4800 from 4800 to get reminder 0. Add 5 to quotient.
\text{Quotient: }75 \text{Reminder: }0
Since 0 is less than 960, stop the division. The reminder is 0. The topmost line 00075 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 75.
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}