Question

Given below are the steps to simplify the following expression:

[-$\frac{1}{7}$ × -$\frac{4}{3}$] x (-7) × $\frac{3}{2}$

Step 1: (-7) × [-$\frac{1}{7}$ × -$\frac{4}{3}$] × $\frac{3}{2}$

Step 2: [-7 × -$\frac{1}{7}$ ] × (-$\frac{4}{3}$) × ($\frac{3}{2}$)

Step 3: 1 × (-$\frac{4}{3}$) × ($\frac{3}{2}$)

Which solution step represents the property of 'multiplicative inverse'?

• A. Step 1
• B. Step 2
• C. Step 3
  
• D. None of the above

Answer 1

The correct option is C Step 3


Given the expression:
[-$\frac{1}{7}$ × -$\frac{4}{3}$] × (-7) × $\frac{3}{2}$

Step 1: (-7) × [-$\frac{1}{7}$ × -$\frac{4}{3}$] × $\frac{3}{2}$
Since in Step 1 only the order of multiplication is changed, it represents commutative property.

Step 2: [-7 × -$\frac{1}{7}$ ] × (-$\frac{4}{3}$) × ($\frac{3}{2}$)
In Step 2, the similar rational numbers are grouped together, hence it represents associative property.

Step 3: 1 × (-$\frac{4}{3}$) × ($\frac{3}{2}$) = -2
When we multiply a number with its reciprocal, we get 1 as the answer and this property is known as multiplicative inverse.