Question

PART D

Three students evaluated three different expressions using the real number properties and the order of operations. Answer each question based on the processes they used and their results.
Student 1:
5 - 2(4 + 9) - 11
5 - 2(4) - 2(9) -11
5 - 8 - 18 -11
5 + (-8) + (-18) + (-11)
-3 + (-18) + (-11)
-21 + (-11)
-32
Student 2:
-9 + (6 + 9) - 42
-9 + (9 + 6) - 42
(-9 + 9) + 6 - 42
0 + 6 - 42
0 + 6 - 16
0 + 6 + (-16)
6 + (-16)
-10
Student 3:
-4(14) - 32 - 2 ∙ 0
-4(10 + 4) - 32 - 2 ∙ 0
-4(10) - 4(4) - 32 - 2 ∙ 0
-40 - 16 - 32 - 2 ∙ 0
-40 - 16 - 9 - 2 ∙ 0
-56 - 9 - 2 ∙ 0
-65 - 2 ∙ 0
-67 ∙ 0
0

Questions: All Questions are Multiple Answers

Question 1: Which of the students used the commutative property to simplify their expression? Select all that are true.
Student 1
Student 2
Student 3
None of the students


Question 2:Which of the students used the associative property to simplify their expression? Select all that are true.
Student 1
Student 2
Student 3
None of the students


Question 3: Which of the students used the distributive property to simplify their expression? Select all that are true.
Student 1
Student 2
Student 3
None of the students


Question 4: Which of the students used the identity property to simplify their expression? Select all that are true.
Student 1
Student 2
Student 3
None of the students


Question 5: Which of the students found the correct value of their expression? Select all that are true.
Student 1
Student 2
Student 3
None of the students

Answer 1

1.
None

2.
Student 2

Know the answer? Add it here!3.
Student 1 and student 3

4.
None

5.
Student 1

Disclaimer: I'm not 100percent sure, but I'm pretty sure

Hope this helps!

Answer 2

1. Student 2

2. Student 2

3. Student 1 and Student 3

4. Student 2

5. Student 1

Explanation:

In order to answer the questions, you have to know the real number properties. These are:

Let A,B and C represent real numbers

Conmutative Properties:

A+B = B+A

A.B = B.A

Associative Properties:

(A+B) + C = A + (B+C)

(A.B).C = A. (B.C)

Distributive Property:

A. (B+C)= A.B + B.C

Identity Properties:

1.A=A

0+A=A

Hence, you have to identify the use of the properties in the processes of the three students.

For question 1:

The student 2 used the conmutative property A+ B = B+A because he wrote (6+9) as (9+6)

For question 2:

The student 2 used the associative property (A+B) + C = A + (B+C) because he wrote -9 + (9 + 6) - 42 as (-9 + 9) + 6 - 42

For question 3:

The student 1 used the distributive property because he wrote 5 - 2(4 + 9) - 11 as 5 - 2(4) - 2(9) -11. Also the student 3 because he wrote -4(10 + 4) - 32 - 2 ∙ 0 as -4(10) - 4(4) - 32 - 2 ∙ 0

For question 4:

The student 2 used the identity property 0+A=A because he wrote 0 + 6 + (-16) as 6 + (-16)

For question 5:

Just student 1, because the correct value of the expression of student 2 is:

-9 + (6+9) -42 = -9 + 15 -42 = -36

The correct value of the expression of student 3 is:

-4(14) - 32 - 2 ∙ 0 = -56 -32 = -88