Question

How do you write the algebraic expression given: the product of $8$ and z plus the product of $6.5$ and y?

Answer 1

Hint: We have been given a statement in the above question which involves the two unknown numbers z and y, and their product with $8$ and $6.5$ respectively. In mathematics, the product between an unknown number, represented by a letter, and a number is shown by writing the number before the letter. Therefore, the two products will be $8z$ and $6.5y$. Since the term “plus” is used between these two products, we will add these two products so as to obtain the final required algebraic expression.

Complete step by step answer:
According to the statement given in the above question, we have two products, the first product of $8$ and z, and the second product of $6.5$ and y. So the mathematical expression or the algebraic expression for these two will be $8z$ and $6.5y$ respectively. Now, the given statement, which is “the product of $8$ and z plus the product of $6.5$ and y” connects these two products using the term “plus”. We know that “plus” refers to the addition in mathematics. Therefore, we have to add the two products $8z$ and $6.5y$ to obtain the algebraic expression of the given statement. Thus, the algebraic expression will be written as
$\Rightarrow 8z+6.5y$
Hence, we have finally obtained the required algebraic expression as $8z+6.5y$.

Note:
The statement given in the above question does not refer to any mathematical equation. We must understand the difference between a mathematical expression and a mathematical equation. A mathematical expression can be any constant, variable, a combination of constants and variables, or even a mathematical equation. But a mathematical equation is essentially an expression which equates two constants, variables, or their combination.