Question

17x + $\frac{15}{2}$ + 25x - 4

Use the following steps to compress the above statement:

Step 1: 17x + 25x + $\frac{15}{2}$ + (-4)

Step 2 : {17x + 25x} + {$\frac{15}{2}$ +(-4)} = 42x + $\frac{7}{2}$.

Choose the correct property used for the given steps?

• A. Step 1 represents commutative property whereas Step 2 represents associative property.
• B. Both Step 1 and Step 2 represent associative property.
• C. Both Step 1 and Step 2 represent commutative property.
• D. Step 1 represents associative property whereas Step 2 represents commutative property.

Answer 1

The correct option is A Step 1 represents commutative property whereas Step 2 represents associative property.

When numbers are grouped together, they represent associative property, whereas when numbers are rearranged in an expression, they represent commutative property.

For the expression, 17x + $\frac{15}{2}$ + 25x - 4, the following steps are given:

Step 1: 17x + 25x + $\frac{15}{2}$ + (-4)

Step 2: {17x + 25x} + {$\frac{15}{2}$ + (-4)} = 42x + $\frac{7}{2}$

In Step 1, the numbers are rearranged, hence they represent commutative property.

In Step 2, the numbers are grouped, hence they represent associative property.

Hence, Step 1 represents commutative property and Step 2 represents assosiative property.