Evaluate
7
Factor
7
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\begin{array}{l}\phantom{60)}\phantom{1}\\60\overline{)420}\\\end{array}
Use the 1^{st} digit 4 from dividend 420
\begin{array}{l}\phantom{60)}0\phantom{2}\\60\overline{)420}\\\end{array}
Since 4 is less than 60, use the next digit 2 from dividend 420 and add 0 to the quotient
\begin{array}{l}\phantom{60)}0\phantom{3}\\60\overline{)420}\\\end{array}
Use the 2^{nd} digit 2 from dividend 420
\begin{array}{l}\phantom{60)}00\phantom{4}\\60\overline{)420}\\\end{array}
Since 42 is less than 60, use the next digit 0 from dividend 420 and add 0 to the quotient
\begin{array}{l}\phantom{60)}00\phantom{5}\\60\overline{)420}\\\end{array}
Use the 3^{rd} digit 0 from dividend 420
\begin{array}{l}\phantom{60)}007\phantom{6}\\60\overline{)420}\\\phantom{60)}\underline{\phantom{}420\phantom{}}\\\phantom{60)999}0\\\end{array}
Find closest multiple of 60 to 420. We see that 7 \times 60 = 420 is the nearest. Now subtract 420 from 420 to get reminder 0. Add 7 to quotient.
\text{Quotient: }7 \text{Reminder: }0
Since 0 is less than 60, 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}