Question

Verify the associative property of multiplication as well as addition for the numbers $13$, $7$ and $5$.

Answer 1

Hint: The given problem requires us to use and verify the associative property on addition and multiplication of the three numbers given to us in the question. There are various other algebraic properties such as the distributive property that help us to solve questions or problems involving algebraic operations and simplification. Associative property states that we can add or multiply the numbers in any order of our choice. We will rearrange the order to numbers using parentheses to verify the associative property for addition and multiplication for the three numbers.

Complete step by step answer:
So, we have to verify the associative property on addition and multiplication for the numbers $13$, $7$ and $5$. Now, according to the associative property, we know that we can use the parenthesis wherever required in between addition and multiplication. Now, in addition, we have,
$\left( {13 + 7} \right) + 5$
$ \Rightarrow 20 + 5$
$ \Rightarrow 25$
Also, $13 + \left( {7 + 5} \right)$
$ \Rightarrow 13 + 12$
$ \Rightarrow 25$
So, we get the same result in both the cases.Hence, the associative property is verified for addition.

Similarly, for multiplication, we have,
$\left( {13 \times 7} \right) \times 5$
$ \Rightarrow 91 \times 5$
$ \Rightarrow 455$
Also, $13 \times \left( {7 \times 5} \right)$
$ \Rightarrow 13 \times 35$
$ \Rightarrow 455$
We get the same answer in both cases. Hence, associative property is verified for multiplication as well.

Therefore, the associative property of multiplication and addition is verified for the numbers $13$, $7$ and $5$.

Note: There are many algebraic properties such as commutative property, distributive property, associative property and many more. Such properties are of significant use when we have to simplify an algebraic expression or an operation. In fact, these properties can be used to simplify trigonometric and calculus based problems and questions as well. Associative property holds true for addition and multiplication of real numbers.Associative property enables us to put parentheses in addition and multiplication wherever we like as the answer remains the same regardless of the order of these operations.