Evaluate
7
Factor
7
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\begin{array}{l}\phantom{45)}\phantom{1}\\45\overline{)315}\\\end{array}
Use the 1^{st} digit 3 from dividend 315
\begin{array}{l}\phantom{45)}0\phantom{2}\\45\overline{)315}\\\end{array}
Since 3 is less than 45, use the next digit 1 from dividend 315 and add 0 to the quotient
\begin{array}{l}\phantom{45)}0\phantom{3}\\45\overline{)315}\\\end{array}
Use the 2^{nd} digit 1 from dividend 315
\begin{array}{l}\phantom{45)}00\phantom{4}\\45\overline{)315}\\\end{array}
Since 31 is less than 45, use the next digit 5 from dividend 315 and add 0 to the quotient
\begin{array}{l}\phantom{45)}00\phantom{5}\\45\overline{)315}\\\end{array}
Use the 3^{rd} digit 5 from dividend 315
\begin{array}{l}\phantom{45)}007\phantom{6}\\45\overline{)315}\\\phantom{45)}\underline{\phantom{}315\phantom{}}\\\phantom{45)999}0\\\end{array}
Find closest multiple of 45 to 315. We see that 7 \times 45 = 315 is the nearest. Now subtract 315 from 315 to get reminder 0. Add 7 to quotient.
\text{Quotient: }7 \text{Reminder: }0
Since 0 is less than 45, stop the division. The reminder is 0. The topmost line 007 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 7.
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}