Question

How do you evaluate \[\dfrac{4ab}{8c}\] where \[a=8,\] \[b=4\] and \[c=\dfrac{1}{2}\]?

Answer 1

Hint: In order to find the solution of this question, put the given values of the variables \[a\], \[b\]and \[c\] that is \[a=8,\] \[b=4\] and \[c=\dfrac{1}{2}\] in the given expression which needs to be evaluated that is \[\dfrac{4ab}{8c}\] and solve the expression using multiplication and subtraction to get the final answer. Here a “variable” is a symbol which functions as a placeholder for varying expression or quantities and an “expression” is a sentence with a minimum of two numbers and at least one math operation. This math operation can be addition, subtraction, multiplication, and division.

Complete step by step solution:
We have been given expression in the question as:
\[\dfrac{4ab}{8c}...\left( 1 \right)\]
According to the question, we have been given the values of \[a\], \[b\] and \[c\] for the expression as:
\[a=8,\] \[b=4\] and \[c=\dfrac{1}{2}\]
Now substituting these values of \[a\], \[b\] and \[c\] in expression $\left( 1 \right)$ as mentioned in the question, we get:
\[\Rightarrow \dfrac{4\times 8\times 4}{8\times \left( \dfrac{1}{2} \right)}\]
Now, we will open the brackets and simplify. Therefore, we get:
\[\Rightarrow \dfrac{4\times 8\times 4}{4}\]
As we can see \[4\] is in both numerator and denominator. Therefore, it’s gets cancelled and we get:
\[\Rightarrow 4\times 8\]
After simplifying the above expression further with the help of multiplication we get the final answer as:
\[\Rightarrow 32\]

Therefore, the value of the given expression \[\dfrac{4ab} {8c} \] where \[a=8,\] \[b=4\] and \[c=\dfrac{1}{2}\] is \[32\].

Note: Students can go wrong by substituting wrong values that is putting \[a=4,b=8\] and \[c=\dfrac{1}{2}\]instead of \[a=8,\] \[b=4\] and \[c=\dfrac{1}{2}\] which can further lead to the incorrect answer. Therefore, students’ needs to be really careful when they substitute the value of the variable in the expression and crosscheck if they are putting it right or not. Also, students might end up making calculation mistakes that are wrong multiplication or wrong division between the numbers. It's better to cross check and recheck the calculation after completing the answer.