Question

How do you use the distributive property to rewrite and evaluate: $9 \times 499$?

Answer 1

Hint: The given problem requires us to use the distributive property to evaluate the product of the numbers given to us. Distributive law is applicable for various scenarios and situations including multiplication over addition. There are various other algebraic properties just like the distributive property that help us to solve questions or problems involving algebraic operations and simplification.

Complete step by step answer:
Distributing something with someone means to share or give a part of a specific thing to them. According to the distributive property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.
The distributive property of binary operations generalizes the distributive law from Boolean algebra and elementary algebra. In general, the distributive property can be represented as follows: \[\left( {a + b} \right)c = \left( {ac + bc} \right)\] .
So, we have, $9 \times 499$
We break down the number $9$ as $\left( {10 - 1} \right)$. So, we get,
$9 \times 499 = \left( {10 - 1} \right) \times 499$
Using the distributive property for evaluating the product given to us, we get,
$ \Rightarrow 9 \times 499 = 10 \times 499 - 499 \times 1$
$ \Rightarrow 9 \times 499 = 4990 - 499 \times 1$
$ \Rightarrow 9 \times 499 = 4491$
Hence, the answer for the given question $9 \times 499$ can be calculated using the distributive law, and comes out to be $4491$.

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. These properties can be also used to simplify trigonometric and calculus-based problems and questions as well. We have to first break down one of the numbers into two parts so as to find the product easily using the distributive property.