Question

Translate the statement “the product of a number and $3$” into a mathematical expression.

Answer 1

The term “product” indicates multiplication of two numbers.

Complete step by step solution:
To write any statement in the form of a mathematical expression, first, understand each term of the statement. Here the term product is mentioned. It indicates the multiplication of two terms.
Multiplication means to add quantities that are similar i.e. have the same unit.
So, the product of a number and $3$ means $3$ is multiplied by any number. Let the number be $a$. Hence the mathematical expression will be:
$3 \times a$

Additional information:
Multiplication is commutative. It means that terms when multiplied give the same result irrespective of their order. For example, the statement “$5$ multiplied by $3$” is the same as the statement “$3$ multiplied by $5$”, which means $3 \times 5$ is the same as $5 \times 3$.
The symbol, “$\cdot$” can also be used in place of ” for denoting the product of two numbers.

Note:
The operation is termed as multiplication and the result of a multiplication is termed as the product of the numbers multiplied. Students must be aware of the various mathematical operations and their symbols. The order of the terms must be noted for operations that are non-commutative like subtraction, i.e. one must note that $a - b$ is not equal to $b - a$. Addition and multiplication are commutative, while subtraction and division are non-commutative.