The Commutative Property can be used to rewrite the expression
3 x 5 2/3 as 3(5) + 3(2/3).
Looks like the distributive property.
Distributive property: The sum of two numbers times a third number is equal to the sum of each addend times the third number. For example 4 * (6 + 3) = 4*6 + 4*3
thank you
To understand how the Commutative Property can be used to rewrite the expression 3 x 5 2/3 as 3(5) + 3(2/3), we first need to clarify what the Commutative Property is.
The Commutative Property is a fundamental property in mathematics that applies to addition and multiplication. For addition, it states that changing the order of the numbers being added does not affect the sum. In other words, a + b = b + a. For multiplication, it states that changing the order of the numbers being multiplied does not affect the product. In other words, a * b = b * a.
Now, let's apply the Commutative Property to the given expression, 3 x 5 2/3.
We can rewrite 3 x 5 2/3 using the Commutative Property of multiplication. Since multiplication is commutative, we can switch the order of the factors:
3 x 5 2/3 = 5 2/3 x 3
This is an important step because it allows us to break down the expression into two separate multiplications.
Next, we can simplify each multiplication separately:
5 2/3 x 3 = 5 x 3 + 2/3 x 3
Here, we have used the Distributive Property of multiplication over addition to split the multiplication into two separate parts.
Now, we can simplify each part:
5 x 3 = 15
2/3 x 3 = 2/3 * 3 = 6/3 = 2
Finally, we can substitute the simplified values back into the previous expression:
5 2/3 x 3 = 5 x 3 + 2/3 x 3 = 15 + 2 = 17
Therefore, the expression 3 x 5 2/3 can be rewritten using the Commutative Property as 3(5) + 3(2/3), which simplifies to 17.