Question

Given are the steps to simplify the following expression:
[-$\frac{1}{5}$ × -$\frac{1}{3}$] × (-5) × $\frac{5}{2}$

Step 1: (-5) × [-$\frac{1}{5}$ × -$\frac{1}{3}$] × $\frac{5}{2}$

Step 2: [-5 × $-\frac{1}{5}$ ] × (-$\frac{1}{3}$) × ($\frac{5}{2}$)

Step 3: 1 × (-$\frac{1}{3}$) × ($\frac{5}{2}$)

Identify the steps representing the right properties from the following:

• A. Step 2 represents associative property.
• B. Step 1 represents multiplicative inverse.
• C. Step 3 represents commutative property.
• D. Step 1 represents associative property.

Answer 1

The correct option is A Step 2 represents associative property.

Given expression: [-$\frac{1}{5}$ × -$\frac{1}{3}$] × (-5) × $\frac{5}{2}$

Step 1: (-5) × [-$\frac{1}{5}$ × -$\frac{1}{3}$] × $\frac{5}{2}$

Since in Step 1, only the order of multiplication is changed, it represents commutative property.

Step 2: [-5 × -$\frac{1}{5}$ ] × (-$\frac{1}{3}$) × ($\frac{5}{2}$)
In Step 2, the similar rational numbers are grouped together, hence it represents associative property.

Step 3: 1 × (-$\frac{1}{3}$) × ($\frac{5}{2}$)
When we multiply a number with its reciprocal, we get 1 as the answer and this property is known as multiplicative inverse.