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\begin{array}{l}\phantom{45)}\phantom{1}\\45\overline{)45}\\\end{array}
Use the 1^{st} digit 4 from dividend 45
\begin{array}{l}\phantom{45)}0\phantom{2}\\45\overline{)45}\\\end{array}
Since 4 is less than 45, use the next digit 5 from dividend 45 and add 0 to the quotient
\begin{array}{l}\phantom{45)}0\phantom{3}\\45\overline{)45}\\\end{array}
Use the 2^{nd} digit 5 from dividend 45
\begin{array}{l}\phantom{45)}01\phantom{4}\\45\overline{)45}\\\phantom{45)}\underline{\phantom{}45\phantom{}}\\\phantom{45)99}0\\\end{array}
Find closest multiple of 45 to 45. We see that 1 \times 45 = 45 is the nearest. Now subtract 45 from 45 to get reminder 0. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }0
Since 0 is less than 45, stop the division. The reminder is 0. The topmost line 01 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 1.
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}