Arlene is showing her work in simplifying −7.9 + 8.2 − 3.4 + 2.1. identify any errors in her work or in her reasoning. write feedback to arlene explaining the mistake she made and how to correct her work. step work reasoning −7.9 + 8.2 − 3.4 + 2.1 original problem 1 −7.9 + 8.2 + (−3.4) + 2.1 additive inverse 2 −7.9 + (−3.4) + 8.2 + 2.1 associative property 3 (−7.9 + (−3.4)) + (8.2 + 2.1 commutative property 4 −11.3 + 10.3 simplify 5 −1 simplify

There is nothing wrong with Arlene's math. Her answer is correct. The mistake is that she has cited the "associative property" where the "commutative property" should have been cited, and vice versa.

The associative property has to do with where you put parentheses. The commutative property has to do with what order the operands are in.

In step 2 and step 3 reasoning mistakes

Step-by-step explanation:

We are given that Arlene is showing her work in simplifying -7.9+8.2-3.4+2.1

We have to find error and correct the error made by Arlene in her work

Original problem : -7.9+8.2-3.4+2.1

Step 1: -7.9+8.2+(-3.4)+2.1

Additive inverse property

Step 2:-7.9+(-3.4)+8.2+2.1

Using Commutative property   (commutative property a+b=b+a)

Step 3:(-7.9+(-3.4))+(8.2+2.1)

Using associative  property   (Associative property a+(b+c)=(a+b)+c))

Step 4: -11.3+10.3

By Simplification

Step 5:-1

By simplification

Arlene simplify in correct way but she is doing mistake in reasoning in step 2 and step 3.

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.