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In the following practice activity, you will determine how the properties of equality are used. This practice is aligned with Lesson 5.

Which of the following properties could be used to rewrite the expression [tex]\left(\frac{1}{3} \cdot \frac{2}{3}\right) \cdot \frac{5}{2}=\frac{2}{3} \cdot\left(\frac{1}{3} \cdot \frac{5}{2}\right)[/tex]?

A. The commutative property followed by the associative property
B. The associative property used once
C. The associative property followed by the commutative property
D. The commutative property used twice, once on each of the two multiplications

Rewrite [tex]35 \cdot y[/tex] in a different way, using the commutative property of multiplication. Note that [tex]y[/tex] represents [tex]a[/tex].



Answer :

GinnyAnswer
To solve this, we will use the commutative property of multiplication. The commutative property of multiplication states that for any two numbers or variables, their product remains the same even if the order in which they are multiplied changes. In other words, [tex]\( a \cdot b = b \cdot a \)[/tex].

Given the expression [tex]\( 35 \cdot y \)[/tex], we need to rewrite this expression using the commutative property of multiplication.

Step-by-step solution:

1. Identify the two factors in the multiplication expression. In this case, the factors are [tex]\( 35 \)[/tex] and [tex]\( y \)[/tex].
2. According to the commutative property, we can swap the order of these factors, and the product will remain the same. Therefore, we can rewrite [tex]\( 35 \cdot y \)[/tex] as [tex]\( y \cdot 35 \)[/tex].

Thus, using the commutative property of multiplication, the expression [tex]\( 35 \cdot y \)[/tex] can be rewritten as [tex]\( y \cdot 35 \)[/tex].

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