Question

Use numbers 2,5 and 10 to illustrate associative property of multiplication​

Answer 1

`(2 * 5) * 10 = 100 = 2 * (5 * 10)`

Explanation:

The multiplication of numbers is associative. The result does not depend on the way the multiplications are grouped. In other words, as long as only multiplication is involved (no addition, subtraction, etc,) adding parentheses to the expression won't change the result.

In this question, there are more than one ways to find the value of
`2 * 5 * 10`.

One way is to calculate
`2* 5`, and then multiply the output by
`10`.

`2 * 5 = 10`.

`\underbrace{10}_{\text{from}\atop 2* 5} * 10 = 100`.

That's the same as adding parentheses to
`(2 * 5)` in the original expression:
`(2 * 5) * 10 = \underbrace{10}_{\text{from}\atop 2 * 5} * 10 = 100`.

Alternatively, calculate
`5 * 10` first, then multiply
`2` to the output.

`5 * 10 = 50`.

`2 * \underbrace{50}_{\text{from}\atop 5 * 10} = 100`.

That's the same as adding parentheses to
`(5 * 10)` in the original expression:
`2 * (5 * 10) = 2 * \underbrace{50}_{\text{from}\atop 5 * 10} = 100`.

By the associative property of multiplication, these two results shall be the same. Keep in mind that the order of the numbers shall stay the same. For example, in
`2 * (5 * 10)` make sure you place
`2` before
`50`. Indeed, by the commutative property of multiplication,
`2* 50 = 50 * 2`. However, that doesn't really help illustrate the associative property of multiplication.