Evaluate
\frac{1919}{17}\approx 112.882352941
Factor
\frac{19 \cdot 101}{17} = 112\frac{15}{17} = 112.88235294117646
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\begin{array}{l}\phantom{68)}\phantom{1}\\68\overline{)7676}\\\end{array}
Use the 1^{st} digit 7 from dividend 7676
\begin{array}{l}\phantom{68)}0\phantom{2}\\68\overline{)7676}\\\end{array}
Since 7 is less than 68, use the next digit 6 from dividend 7676 and add 0 to the quotient
\begin{array}{l}\phantom{68)}0\phantom{3}\\68\overline{)7676}\\\end{array}
Use the 2^{nd} digit 6 from dividend 7676
\begin{array}{l}\phantom{68)}01\phantom{4}\\68\overline{)7676}\\\phantom{68)}\underline{\phantom{}68\phantom{99}}\\\phantom{68)9}8\\\end{array}
Find closest multiple of 68 to 76. We see that 1 \times 68 = 68 is the nearest. Now subtract 68 from 76 to get reminder 8. Add 1 to quotient.
\begin{array}{l}\phantom{68)}01\phantom{5}\\68\overline{)7676}\\\phantom{68)}\underline{\phantom{}68\phantom{99}}\\\phantom{68)9}87\\\end{array}
Use the 3^{rd} digit 7 from dividend 7676
\begin{array}{l}\phantom{68)}011\phantom{6}\\68\overline{)7676}\\\phantom{68)}\underline{\phantom{}68\phantom{99}}\\\phantom{68)9}87\\\phantom{68)}\underline{\phantom{9}68\phantom{9}}\\\phantom{68)9}19\\\end{array}
Find closest multiple of 68 to 87. We see that 1 \times 68 = 68 is the nearest. Now subtract 68 from 87 to get reminder 19. Add 1 to quotient.
\begin{array}{l}\phantom{68)}011\phantom{7}\\68\overline{)7676}\\\phantom{68)}\underline{\phantom{}68\phantom{99}}\\\phantom{68)9}87\\\phantom{68)}\underline{\phantom{9}68\phantom{9}}\\\phantom{68)9}196\\\end{array}
Use the 4^{th} digit 6 from dividend 7676
\begin{array}{l}\phantom{68)}0112\phantom{8}\\68\overline{)7676}\\\phantom{68)}\underline{\phantom{}68\phantom{99}}\\\phantom{68)9}87\\\phantom{68)}\underline{\phantom{9}68\phantom{9}}\\\phantom{68)9}196\\\phantom{68)}\underline{\phantom{9}136\phantom{}}\\\phantom{68)99}60\\\end{array}
Find closest multiple of 68 to 196. We see that 2 \times 68 = 136 is the nearest. Now subtract 136 from 196 to get reminder 60. Add 2 to quotient.
\text{Quotient: }112 \text{Reminder: }60
Since 60 is less than 68, stop the division. The reminder is 60. The topmost line 0112 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 112.
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}