91Ó°ÊÓ

Substitution is the process of replacing variables in an expression with their assigned values. In our example, we are given two variables: \(b\) and \(c\). The values provided are \(b = 2\) and \(c = 6\).
Firstly, replace every instance of \(b\) and \(c\) in the expression \(2c \div 3b\) with their respective values:
\[2c \div 3b = 2 \times 6 \div 3 \times 2\].
This step transforms the original algebraic expression into a numerical one, making it easier to handle in subsequent steps.

After substituting the variables with their numerical values, we need to perform multiplication and division.
Looking at our substituted expression \(2 \times 6 \div 3 \times 2\), observe the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). In our case, multiplication and division are performed from left to right.
First, multiply the numbers as follows:
\[2 \times 6 = 12\].
Next, perform the division:
\[12 \div 3 \times 2\] can be separated into two parts: first\[12 \div 3 = 4\].
Then, we can perform the final multiplication step:
\[4 \div 2 = 2\].
At the end of this section, we reduce the extended expression step by step into a simpler numeric value.

Simplification is the final step where we convert our computed values into the easiest possible form.
After substituting, multiplying, and dividing, our problem reduces to the value 1. Following the calculations:
\[2 \times 6 \div 3 \times 2 = 2\],
you simplify it further if possible. Here, simplifying \[2 = 2\] is unnecessary.
Thus, the final simplified value of the expression \(2c \div 3b\) for \(b = 2\) and \(c = 6\) is simply 1.
The overall process may look complex but breaking it down into substitution, multiplication & division, and simplification makes it much more manageable.