Answer:
[tex](2 \times 5) \times 10 = 100 = 2 \times (5 \times 10)[/tex]
Step-by-step 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 [tex]2 \times 5 \times 10[/tex].
One way is to calculate [tex]2\times 5[/tex], and then multiply the output by [tex]10[/tex].
[tex]2 \times 5 = 10[/tex].
[tex]\underbrace{10}_{\text{from}\atop 2\times 5} \times 10 = 100[/tex].
That's the same as adding parentheses to [tex](2 \times 5)[/tex] in the original expression: [tex](2 \times 5) \times 10 = \underbrace{10}_{\text{from}\atop 2 \times 5} \times 10 = 100[/tex].
Alternatively, calculate [tex]5 \times 10[/tex] first, then multiply [tex]2[/tex] to the output.
[tex]5 \times 10 = 50[/tex].
[tex]2 \times \underbrace{50}_{\text{from}\atop 5 \times 10} = 100[/tex].
That's the same as adding parentheses to [tex](5 \times 10)[/tex] in the original expression: [tex]2 \times (5 \times 10) = 2 \times \underbrace{50}_{\text{from}\atop 5 \times 10} = 100[/tex].
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 [tex]2 \times (5 \times 10)[/tex] make sure you place [tex]2[/tex] before [tex]50[/tex]. Indeed, by the commutative property of multiplication, [tex]2\times 50 = 50 \times 2[/tex]. However, that doesn't really help illustrate the associative property of multiplication.
