Evaluate
372567
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\begin{array}{c}\phantom{\times999}699\\\underline{\times\phantom{999}533}\\\end{array}
First line up the numbers vertically and match the places from the right like this.
\begin{array}{c}\phantom{\times999}699\\\underline{\times\phantom{999}533}\\\phantom{\times99}2097\\\end{array}
Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 699 with 3. Write the result 2097 at the end leaving 0 spaces to the right like this.
\begin{array}{c}\phantom{\times999}699\\\underline{\times\phantom{999}533}\\\phantom{\times99}2097\\\phantom{\times9}2097\phantom{9}\\\end{array}
Now multiply the first number with the 2^{nd} digit in 2^{nd} number to get intermediate results. That is Multiply 699 with 3. Write the result 2097 at the end leaving 1 spaces to the right like this.
\begin{array}{c}\phantom{\times999}699\\\underline{\times\phantom{999}533}\\\phantom{\times99}2097\\\phantom{\times9}2097\phantom{9}\\\underline{\phantom{\times}3495\phantom{99}}\\\end{array}
Now multiply the first number with the 3^{rd} digit in 2^{nd} number to get intermediate results. That is Multiply 699 with 5. Write the result 3495 at the end leaving 2 spaces to the right like this.
\begin{array}{c}\phantom{\times999}699\\\underline{\times\phantom{999}533}\\\phantom{\times99}2097\\\phantom{\times9}2097\phantom{9}\\\underline{\phantom{\times}3495\phantom{99}}\\\phantom{\times}372567\end{array}
Now add the intermediate results to get final answer.
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}