Evaluate
65
Factor
5\times 13
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\begin{array}{l}\phantom{95)}\phantom{1}\\95\overline{)6175}\\\end{array}
Use the 1^{st} digit 6 from dividend 6175
\begin{array}{l}\phantom{95)}0\phantom{2}\\95\overline{)6175}\\\end{array}
Since 6 is less than 95, use the next digit 1 from dividend 6175 and add 0 to the quotient
\begin{array}{l}\phantom{95)}0\phantom{3}\\95\overline{)6175}\\\end{array}
Use the 2^{nd} digit 1 from dividend 6175
\begin{array}{l}\phantom{95)}00\phantom{4}\\95\overline{)6175}\\\end{array}
Since 61 is less than 95, use the next digit 7 from dividend 6175 and add 0 to the quotient
\begin{array}{l}\phantom{95)}00\phantom{5}\\95\overline{)6175}\\\end{array}
Use the 3^{rd} digit 7 from dividend 6175
\begin{array}{l}\phantom{95)}006\phantom{6}\\95\overline{)6175}\\\phantom{95)}\underline{\phantom{}570\phantom{9}}\\\phantom{95)9}47\\\end{array}
Find closest multiple of 95 to 617. We see that 6 \times 95 = 570 is the nearest. Now subtract 570 from 617 to get reminder 47. Add 6 to quotient.
\begin{array}{l}\phantom{95)}006\phantom{7}\\95\overline{)6175}\\\phantom{95)}\underline{\phantom{}570\phantom{9}}\\\phantom{95)9}475\\\end{array}
Use the 4^{th} digit 5 from dividend 6175
\begin{array}{l}\phantom{95)}0065\phantom{8}\\95\overline{)6175}\\\phantom{95)}\underline{\phantom{}570\phantom{9}}\\\phantom{95)9}475\\\phantom{95)}\underline{\phantom{9}475\phantom{}}\\\phantom{95)9999}0\\\end{array}
Find closest multiple of 95 to 475. We see that 5 \times 95 = 475 is the nearest. Now subtract 475 from 475 to get reminder 0. Add 5 to quotient.
\text{Quotient: }65 \text{Reminder: }0
Since 0 is less than 95, stop the division. The reminder is 0. The topmost line 0065 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 65.
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}