Question

Matt is showing his work in simplifying (6.2 − 1.6) − 4.4 + 7.8. Identify any error in his work or reasoning. Step 1: (6.2 − 1.6) − 4.4 + 7.8 Step 2: 6.2 + (− 1.6 − 4.4) + 7.8 (commutative property) Step 3: 6.2 − 6 + 7.8 Step 4: −14 − 6 = 8 (commutative property) Step 5: 14 − 6 = 8

(a)-He wrote commutative instead of distributive in Step 4.
(b)-He wrote commutative instead of distributive in Step 2.
(c)-He wrote commutative instead of associative in Step 4.
(d)-He wrote commutative instead of associative in Step 2.

Answer 1

in a shorter explanation it’s D: he wrote commutative instead of associative in step 2

Answer 2

The correct option is (d)-He wrote commutative instead of associative in Step 2.

Explanation:

Commutative property:
`a+b=b+a`

Associative property:
`(a+b)+c=a+(b+c)`

Now consider the provided expression.

(6.2 − 1.6) − 4.4 + 7.8

Step 1

(6.2 − 1.6) − 4.4 + 7.8

Step 2 Use Associative property

6.2 + (−1.6 − 4.4) + 7.8

Step 3: Simplify

6.2 − 6 + 7.8

Step 4: Use commutative property

14 − 6

Step 5: Simplify

14 − 6 = 8

Hence, the wrong step is step 2. He wrote commutative instead of associative in Step 2.

Therefore, the correct option is (d)-He wrote commutative instead of associative in Step 2.