Evaluate
7
Factor
7
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\begin{array}{l}\phantom{42)}\phantom{1}\\42\overline{)294}\\\end{array}
Use the 1^{st} digit 2 from dividend 294
\begin{array}{l}\phantom{42)}0\phantom{2}\\42\overline{)294}\\\end{array}
Since 2 is less than 42, use the next digit 9 from dividend 294 and add 0 to the quotient
\begin{array}{l}\phantom{42)}0\phantom{3}\\42\overline{)294}\\\end{array}
Use the 2^{nd} digit 9 from dividend 294
\begin{array}{l}\phantom{42)}00\phantom{4}\\42\overline{)294}\\\end{array}
Since 29 is less than 42, use the next digit 4 from dividend 294 and add 0 to the quotient
\begin{array}{l}\phantom{42)}00\phantom{5}\\42\overline{)294}\\\end{array}
Use the 3^{rd} digit 4 from dividend 294
\begin{array}{l}\phantom{42)}007\phantom{6}\\42\overline{)294}\\\phantom{42)}\underline{\phantom{}294\phantom{}}\\\phantom{42)999}0\\\end{array}
Find closest multiple of 42 to 294. We see that 7 \times 42 = 294 is the nearest. Now subtract 294 from 294 to get reminder 0. Add 7 to quotient.
\text{Quotient: }7 \text{Reminder: }0
Since 0 is less than 42, stop the division. The reminder is 0. The topmost line 007 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 7.
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}