Evaluate
35
Factor
5\times 7
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\begin{array}{l}\phantom{13)}\phantom{1}\\13\overline{)455}\\\end{array}
Use the 1^{st} digit 4 from dividend 455
\begin{array}{l}\phantom{13)}0\phantom{2}\\13\overline{)455}\\\end{array}
Since 4 is less than 13, use the next digit 5 from dividend 455 and add 0 to the quotient
\begin{array}{l}\phantom{13)}0\phantom{3}\\13\overline{)455}\\\end{array}
Use the 2^{nd} digit 5 from dividend 455
\begin{array}{l}\phantom{13)}03\phantom{4}\\13\overline{)455}\\\phantom{13)}\underline{\phantom{}39\phantom{9}}\\\phantom{13)9}6\\\end{array}
Find closest multiple of 13 to 45. We see that 3 \times 13 = 39 is the nearest. Now subtract 39 from 45 to get reminder 6. Add 3 to quotient.
\begin{array}{l}\phantom{13)}03\phantom{5}\\13\overline{)455}\\\phantom{13)}\underline{\phantom{}39\phantom{9}}\\\phantom{13)9}65\\\end{array}
Use the 3^{rd} digit 5 from dividend 455
\begin{array}{l}\phantom{13)}035\phantom{6}\\13\overline{)455}\\\phantom{13)}\underline{\phantom{}39\phantom{9}}\\\phantom{13)9}65\\\phantom{13)}\underline{\phantom{9}65\phantom{}}\\\phantom{13)999}0\\\end{array}
Find closest multiple of 13 to 65. We see that 5 \times 13 = 65 is the nearest. Now subtract 65 from 65 to get reminder 0. Add 5 to quotient.
\text{Quotient: }35 \text{Reminder: }0
Since 0 is less than 13, stop the division. The reminder is 0. The topmost line 035 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 35.
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}