Evaluate
45
Factor
3^{2}\times 5
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\begin{array}{l}\phantom{15)}\phantom{1}\\15\overline{)675}\\\end{array}
Use the 1^{st} digit 6 from dividend 675
\begin{array}{l}\phantom{15)}0\phantom{2}\\15\overline{)675}\\\end{array}
Since 6 is less than 15, use the next digit 7 from dividend 675 and add 0 to the quotient
\begin{array}{l}\phantom{15)}0\phantom{3}\\15\overline{)675}\\\end{array}
Use the 2^{nd} digit 7 from dividend 675
\begin{array}{l}\phantom{15)}04\phantom{4}\\15\overline{)675}\\\phantom{15)}\underline{\phantom{}60\phantom{9}}\\\phantom{15)9}7\\\end{array}
Find closest multiple of 15 to 67. We see that 4 \times 15 = 60 is the nearest. Now subtract 60 from 67 to get reminder 7. Add 4 to quotient.
\begin{array}{l}\phantom{15)}04\phantom{5}\\15\overline{)675}\\\phantom{15)}\underline{\phantom{}60\phantom{9}}\\\phantom{15)9}75\\\end{array}
Use the 3^{rd} digit 5 from dividend 675
\begin{array}{l}\phantom{15)}045\phantom{6}\\15\overline{)675}\\\phantom{15)}\underline{\phantom{}60\phantom{9}}\\\phantom{15)9}75\\\phantom{15)}\underline{\phantom{9}75\phantom{}}\\\phantom{15)999}0\\\end{array}
Find closest multiple of 15 to 75. We see that 5 \times 15 = 75 is the nearest. Now subtract 75 from 75 to get reminder 0. Add 5 to quotient.
\text{Quotient: }45 \text{Reminder: }0
Since 0 is less than 15, stop the division. The reminder is 0. The topmost line 045 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 45.
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}