Evaluate
\frac{85}{69}\approx 1.231884058
Factor
\frac{5 \cdot 17}{3 \cdot 23} = 1\frac{16}{69} = 1.2318840579710144
Share
Copied to clipboard
\begin{array}{l}\phantom{69)}\phantom{1}\\69\overline{)85}\\\end{array}
Use the 1^{st} digit 8 from dividend 85
\begin{array}{l}\phantom{69)}0\phantom{2}\\69\overline{)85}\\\end{array}
Since 8 is less than 69, use the next digit 5 from dividend 85 and add 0 to the quotient
\begin{array}{l}\phantom{69)}0\phantom{3}\\69\overline{)85}\\\end{array}
Use the 2^{nd} digit 5 from dividend 85
\begin{array}{l}\phantom{69)}01\phantom{4}\\69\overline{)85}\\\phantom{69)}\underline{\phantom{}69\phantom{}}\\\phantom{69)}16\\\end{array}
Find closest multiple of 69 to 85. We see that 1 \times 69 = 69 is the nearest. Now subtract 69 from 85 to get reminder 16. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }16
Since 16 is less than 69, stop the division. The reminder is 16. The topmost line 01 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 1.
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}