Evaluate
\frac{105}{13}\approx 8.076923077
Factor
\frac{3 \cdot 5 \cdot 7}{13} = 8\frac{1}{13} = 8.076923076923077
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\begin{array}{l}\phantom{13)}\phantom{1}\\13\overline{)105}\\\end{array}
Use the 1^{st} digit 1 from dividend 105
\begin{array}{l}\phantom{13)}0\phantom{2}\\13\overline{)105}\\\end{array}
Since 1 is less than 13, use the next digit 0 from dividend 105 and add 0 to the quotient
\begin{array}{l}\phantom{13)}0\phantom{3}\\13\overline{)105}\\\end{array}
Use the 2^{nd} digit 0 from dividend 105
\begin{array}{l}\phantom{13)}00\phantom{4}\\13\overline{)105}\\\end{array}
Since 10 is less than 13, use the next digit 5 from dividend 105 and add 0 to the quotient
\begin{array}{l}\phantom{13)}00\phantom{5}\\13\overline{)105}\\\end{array}
Use the 3^{rd} digit 5 from dividend 105
\begin{array}{l}\phantom{13)}008\phantom{6}\\13\overline{)105}\\\phantom{13)}\underline{\phantom{}104\phantom{}}\\\phantom{13)99}1\\\end{array}
Find closest multiple of 13 to 105. We see that 8 \times 13 = 104 is the nearest. Now subtract 104 from 105 to get reminder 1. Add 8 to quotient.
\text{Quotient: }8 \text{Reminder: }1
Since 1 is less than 13, stop the division. The reminder is 1. The topmost line 008 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 8.
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}