Evaluate
15
Factor
3\times 5
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\begin{array}{l}\phantom{300)}\phantom{1}\\300\overline{)4500}\\\end{array}
Use the 1^{st} digit 4 from dividend 4500
\begin{array}{l}\phantom{300)}0\phantom{2}\\300\overline{)4500}\\\end{array}
Since 4 is less than 300, use the next digit 5 from dividend 4500 and add 0 to the quotient
\begin{array}{l}\phantom{300)}0\phantom{3}\\300\overline{)4500}\\\end{array}
Use the 2^{nd} digit 5 from dividend 4500
\begin{array}{l}\phantom{300)}00\phantom{4}\\300\overline{)4500}\\\end{array}
Since 45 is less than 300, use the next digit 0 from dividend 4500 and add 0 to the quotient
\begin{array}{l}\phantom{300)}00\phantom{5}\\300\overline{)4500}\\\end{array}
Use the 3^{rd} digit 0 from dividend 4500
\begin{array}{l}\phantom{300)}001\phantom{6}\\300\overline{)4500}\\\phantom{300)}\underline{\phantom{}300\phantom{9}}\\\phantom{300)}150\\\end{array}
Find closest multiple of 300 to 450. We see that 1 \times 300 = 300 is the nearest. Now subtract 300 from 450 to get reminder 150. Add 1 to quotient.
\begin{array}{l}\phantom{300)}001\phantom{7}\\300\overline{)4500}\\\phantom{300)}\underline{\phantom{}300\phantom{9}}\\\phantom{300)}1500\\\end{array}
Use the 4^{th} digit 0 from dividend 4500
\begin{array}{l}\phantom{300)}0015\phantom{8}\\300\overline{)4500}\\\phantom{300)}\underline{\phantom{}300\phantom{9}}\\\phantom{300)}1500\\\phantom{300)}\underline{\phantom{}1500\phantom{}}\\\phantom{300)9999}0\\\end{array}
Find closest multiple of 300 to 1500. We see that 5 \times 300 = 1500 is the nearest. Now subtract 1500 from 1500 to get reminder 0. Add 5 to quotient.
\text{Quotient: }15 \text{Reminder: }0
Since 0 is less than 300, stop the division. The reminder is 0. The topmost line 0015 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 15.
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}