Evaluate
\frac{803}{42}\approx 19.119047619
Factor
\frac{11 \cdot 73}{2 \cdot 3 \cdot 7} = 19\frac{5}{42} = 19.11904761904762
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\begin{array}{l}\phantom{42)}\phantom{1}\\42\overline{)803}\\\end{array}
Use the 1^{st} digit 8 from dividend 803
\begin{array}{l}\phantom{42)}0\phantom{2}\\42\overline{)803}\\\end{array}
Since 8 is less than 42, use the next digit 0 from dividend 803 and add 0 to the quotient
\begin{array}{l}\phantom{42)}0\phantom{3}\\42\overline{)803}\\\end{array}
Use the 2^{nd} digit 0 from dividend 803
\begin{array}{l}\phantom{42)}01\phantom{4}\\42\overline{)803}\\\phantom{42)}\underline{\phantom{}42\phantom{9}}\\\phantom{42)}38\\\end{array}
Find closest multiple of 42 to 80. We see that 1 \times 42 = 42 is the nearest. Now subtract 42 from 80 to get reminder 38. Add 1 to quotient.
\begin{array}{l}\phantom{42)}01\phantom{5}\\42\overline{)803}\\\phantom{42)}\underline{\phantom{}42\phantom{9}}\\\phantom{42)}383\\\end{array}
Use the 3^{rd} digit 3 from dividend 803
\begin{array}{l}\phantom{42)}019\phantom{6}\\42\overline{)803}\\\phantom{42)}\underline{\phantom{}42\phantom{9}}\\\phantom{42)}383\\\phantom{42)}\underline{\phantom{}378\phantom{}}\\\phantom{42)99}5\\\end{array}
Find closest multiple of 42 to 383. We see that 9 \times 42 = 378 is the nearest. Now subtract 378 from 383 to get reminder 5. Add 9 to quotient.
\text{Quotient: }19 \text{Reminder: }5
Since 5 is less than 42, stop the division. The reminder is 5. The topmost line 019 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 19.
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}