Evaluate
\frac{1512}{5}=302.4
Factor
\frac{2 ^ {3} \cdot 3 ^ {3} \cdot 7}{5} = 302\frac{2}{5} = 302.4
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\begin{array}{l}\phantom{25)}\phantom{1}\\25\overline{)7560}\\\end{array}
Use the 1^{st} digit 7 from dividend 7560
\begin{array}{l}\phantom{25)}0\phantom{2}\\25\overline{)7560}\\\end{array}
Since 7 is less than 25, use the next digit 5 from dividend 7560 and add 0 to the quotient
\begin{array}{l}\phantom{25)}0\phantom{3}\\25\overline{)7560}\\\end{array}
Use the 2^{nd} digit 5 from dividend 7560
\begin{array}{l}\phantom{25)}03\phantom{4}\\25\overline{)7560}\\\phantom{25)}\underline{\phantom{}75\phantom{99}}\\\phantom{25)99}0\\\end{array}
Find closest multiple of 25 to 75. We see that 3 \times 25 = 75 is the nearest. Now subtract 75 from 75 to get reminder 0. Add 3 to quotient.
\begin{array}{l}\phantom{25)}03\phantom{5}\\25\overline{)7560}\\\phantom{25)}\underline{\phantom{}75\phantom{99}}\\\phantom{25)99}6\\\end{array}
Use the 3^{rd} digit 6 from dividend 7560
\begin{array}{l}\phantom{25)}030\phantom{6}\\25\overline{)7560}\\\phantom{25)}\underline{\phantom{}75\phantom{99}}\\\phantom{25)99}6\\\end{array}
Since 6 is less than 25, use the next digit 0 from dividend 7560 and add 0 to the quotient
\begin{array}{l}\phantom{25)}030\phantom{7}\\25\overline{)7560}\\\phantom{25)}\underline{\phantom{}75\phantom{99}}\\\phantom{25)99}60\\\end{array}
Use the 4^{th} digit 0 from dividend 7560
\begin{array}{l}\phantom{25)}0302\phantom{8}\\25\overline{)7560}\\\phantom{25)}\underline{\phantom{}75\phantom{99}}\\\phantom{25)99}60\\\phantom{25)}\underline{\phantom{99}50\phantom{}}\\\phantom{25)99}10\\\end{array}
Find closest multiple of 25 to 60. We see that 2 \times 25 = 50 is the nearest. Now subtract 50 from 60 to get reminder 10. Add 2 to quotient.
\text{Quotient: }302 \text{Reminder: }10
Since 10 is less than 25, stop the division. The reminder is 10. The topmost line 0302 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 302.
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}