Evaluate
95
Factor
5\times 19
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\begin{array}{l}\phantom{85)}\phantom{1}\\85\overline{)8075}\\\end{array}
Use the 1^{st} digit 8 from dividend 8075
\begin{array}{l}\phantom{85)}0\phantom{2}\\85\overline{)8075}\\\end{array}
Since 8 is less than 85, use the next digit 0 from dividend 8075 and add 0 to the quotient
\begin{array}{l}\phantom{85)}0\phantom{3}\\85\overline{)8075}\\\end{array}
Use the 2^{nd} digit 0 from dividend 8075
\begin{array}{l}\phantom{85)}00\phantom{4}\\85\overline{)8075}\\\end{array}
Since 80 is less than 85, use the next digit 7 from dividend 8075 and add 0 to the quotient
\begin{array}{l}\phantom{85)}00\phantom{5}\\85\overline{)8075}\\\end{array}
Use the 3^{rd} digit 7 from dividend 8075
\begin{array}{l}\phantom{85)}009\phantom{6}\\85\overline{)8075}\\\phantom{85)}\underline{\phantom{}765\phantom{9}}\\\phantom{85)9}42\\\end{array}
Find closest multiple of 85 to 807. We see that 9 \times 85 = 765 is the nearest. Now subtract 765 from 807 to get reminder 42. Add 9 to quotient.
\begin{array}{l}\phantom{85)}009\phantom{7}\\85\overline{)8075}\\\phantom{85)}\underline{\phantom{}765\phantom{9}}\\\phantom{85)9}425\\\end{array}
Use the 4^{th} digit 5 from dividend 8075
\begin{array}{l}\phantom{85)}0095\phantom{8}\\85\overline{)8075}\\\phantom{85)}\underline{\phantom{}765\phantom{9}}\\\phantom{85)9}425\\\phantom{85)}\underline{\phantom{9}425\phantom{}}\\\phantom{85)9999}0\\\end{array}
Find closest multiple of 85 to 425. We see that 5 \times 85 = 425 is the nearest. Now subtract 425 from 425 to get reminder 0. Add 5 to quotient.
\text{Quotient: }95 \text{Reminder: }0
Since 0 is less than 85, stop the division. The reminder is 0. The topmost line 0095 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 95.
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}