Evaluate
\frac{347}{42}\approx 8.261904762
Factor
\frac{347}{2 \cdot 3 \cdot 7} = 8\frac{11}{42} = 8.261904761904763
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\begin{array}{l}\phantom{42)}\phantom{1}\\42\overline{)347}\\\end{array}
Use the 1^{st} digit 3 from dividend 347
\begin{array}{l}\phantom{42)}0\phantom{2}\\42\overline{)347}\\\end{array}
Since 3 is less than 42, use the next digit 4 from dividend 347 and add 0 to the quotient
\begin{array}{l}\phantom{42)}0\phantom{3}\\42\overline{)347}\\\end{array}
Use the 2^{nd} digit 4 from dividend 347
\begin{array}{l}\phantom{42)}00\phantom{4}\\42\overline{)347}\\\end{array}
Since 34 is less than 42, use the next digit 7 from dividend 347 and add 0 to the quotient
\begin{array}{l}\phantom{42)}00\phantom{5}\\42\overline{)347}\\\end{array}
Use the 3^{rd} digit 7 from dividend 347
\begin{array}{l}\phantom{42)}008\phantom{6}\\42\overline{)347}\\\phantom{42)}\underline{\phantom{}336\phantom{}}\\\phantom{42)9}11\\\end{array}
Find closest multiple of 42 to 347. We see that 8 \times 42 = 336 is the nearest. Now subtract 336 from 347 to get reminder 11. Add 8 to quotient.
\text{Quotient: }8 \text{Reminder: }11
Since 11 is less than 42, stop the division. The reminder is 11. The topmost line 008 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 8.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
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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}