Evaluate
\frac{7315}{12}\approx 609.583333333
Factor
\frac{5 \cdot 7 \cdot 11 \cdot 19}{2 ^ {2} \cdot 3} = 609\frac{7}{12} = 609.5833333333334
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\begin{array}{l}\phantom{12)}\phantom{1}\\12\overline{)7315}\\\end{array}
Use the 1^{st} digit 7 from dividend 7315
\begin{array}{l}\phantom{12)}0\phantom{2}\\12\overline{)7315}\\\end{array}
Since 7 is less than 12, use the next digit 3 from dividend 7315 and add 0 to the quotient
\begin{array}{l}\phantom{12)}0\phantom{3}\\12\overline{)7315}\\\end{array}
Use the 2^{nd} digit 3 from dividend 7315
\begin{array}{l}\phantom{12)}06\phantom{4}\\12\overline{)7315}\\\phantom{12)}\underline{\phantom{}72\phantom{99}}\\\phantom{12)9}1\\\end{array}
Find closest multiple of 12 to 73. We see that 6 \times 12 = 72 is the nearest. Now subtract 72 from 73 to get reminder 1. Add 6 to quotient.
\begin{array}{l}\phantom{12)}06\phantom{5}\\12\overline{)7315}\\\phantom{12)}\underline{\phantom{}72\phantom{99}}\\\phantom{12)9}11\\\end{array}
Use the 3^{rd} digit 1 from dividend 7315
\begin{array}{l}\phantom{12)}060\phantom{6}\\12\overline{)7315}\\\phantom{12)}\underline{\phantom{}72\phantom{99}}\\\phantom{12)9}11\\\end{array}
Since 11 is less than 12, use the next digit 5 from dividend 7315 and add 0 to the quotient
\begin{array}{l}\phantom{12)}060\phantom{7}\\12\overline{)7315}\\\phantom{12)}\underline{\phantom{}72\phantom{99}}\\\phantom{12)9}115\\\end{array}
Use the 4^{th} digit 5 from dividend 7315
\begin{array}{l}\phantom{12)}0609\phantom{8}\\12\overline{)7315}\\\phantom{12)}\underline{\phantom{}72\phantom{99}}\\\phantom{12)9}115\\\phantom{12)}\underline{\phantom{9}108\phantom{}}\\\phantom{12)999}7\\\end{array}
Find closest multiple of 12 to 115. We see that 9 \times 12 = 108 is the nearest. Now subtract 108 from 115 to get reminder 7. Add 9 to quotient.
\text{Quotient: }609 \text{Reminder: }7
Since 7 is less than 12, stop the division. The reminder is 7. The topmost line 0609 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 609.
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}