How does one can simplify $\dfrac{2}{9}\times \dfrac{3}{5}/\left( {\dfrac{1}{2} + \dfrac{2}{3}} \right)$ ?

Hint: For solving this particular question , we have to simplify the expression by using algebraic identities and by performing arithmetic operations such as addition , subtraction , multiplication, and division . We have to convert numbers into its equivalent exponential form where required.

Complete step-by-step solution:
We have to simplify the given expression that is $\dfrac{2}{9}\times \dfrac{3}{5}/\left( {\dfrac{1}{2} + \dfrac{2}{3}} \right)$ ,
Now, we have to multiply the numerator and add the denominator ,
When we have to multiply two fractions , we multiply numerator by numerator and denominator by denominator ,
$
   \Rightarrow \dfrac{{2 \times 3}}{{9 \times 5}}/\left( {\dfrac{1}{2} + \dfrac{2}{3}} \right) \\
   \Rightarrow \dfrac{6}{{45}}/\left( {\dfrac{1}{2} + \dfrac{2}{3}} \right) \\
 $
When we have to add two fractions with different denominator , we have to find the least common multiple of the denominator then rename the numerator with common denominator ,
$
   \Rightarrow \dfrac{6}{{45}}/\left( {\dfrac{{1 \times 3 + 2 \times 2}}{6}} \right) \\
   \Rightarrow \dfrac{6}{{45}}/\left( {\dfrac{7}{6}} \right) \\
 $
When we divide two fractions , we first find the reciprocal of the denominator then multiply it with the numerator as show ,
$
   \Rightarrow \dfrac{6}{{45}} \times \dfrac{6}{7} \\
   \Rightarrow \dfrac{2}{5} \times \dfrac{2}{7} \\
   \Rightarrow \dfrac{4}{{35}} \\
 $
Hence we have the required solution.


Note: Before you evaluate an algebraic expression as given the question , your aim is to simplify it as much as possible . Simplifying an expression can make all of your calculations much easier and simpler. Here we are having some of the fundamental steps needed to simplify an algebraic expression: Step I. Always try to remove the parentheses given in the expression by multiplying with its corresponding factors. Step II. Simplify the given expression by using exponent rules to get rid of parentheses in terms of exponents. Step III. Try to make it less complex by combining like terms , do operations on like terms first in order to combine them. Step IV. Lastly try to combine all the constant by doing so you will get you desired result