These are 18 questions and 18 answers. Each with its justification.
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I leave here some of the answers (less than 5,000 characters) but the document contain all the answers.
Question 1 (Multiple Choice Worth 1 points)
Which expression is equivalent to 5x − 2x + 6 and why?
Third option: 6 + 3x, because (5x − 2x) + 6 = 3x + 6 = 6 + 3x
Justification:
These are the steps that proove the equivalence:
Given: 5x - 2x + 6
Associative property: (5x - 2x) + 6 ← grouping the first two terms
Combine like terms: 3x + 6 ← subtract the terms with common literal part
Conmutative property: 6 + 3x ← change the order of the summands
Question 2(Multiple Choice Worth 1 points)
Four expressions are shown:
6(5x + 3)
6(6x + 2)
36x + 12
30x + 18
Which two expressions are equivalent to 6(5x + 2 + x)?
B and C
Justification:
Given: 6 (5x + 2 + x)
Combine like terms (add 5x and x): 6 (6x + 2)
That is the option B.
Use distributive property: 6(6x) + 6(2)
Due the operations: 36x + 12
That is the option C.
Question 3(Multiple Choice Worth 1 points)
Which expression is equal to p + (m + n)?
(p + m) + n
Justification:
This is a direct application of the associative property of the addiction, which states that you can group the addends in any order. So given p + (m + n) you can regroup moving the parenthesis to (p + m) + n.
This numerical example will help you:
assume p = 1, m = 2, n = 3, then:
1 + (2 + 3) = ( 1 + 2) + 3
1 + (5) = (3) + 3
1+ 5 = 3 + 3
6 = 6
Question 4(Multiple Choice Worth 1 points)
Which of the following best describes the expression 11(x + 7)?
The product of a constant factor 11 and a 2-term factor x + 7
Justification:
A number or a letter preceding a parenthesis indicates that the former is being multiplied by the amount that is in parentheses.
The amounts being multiplied are called factors
11 as a number is a constant factor
The amount in the parentheses is other factor. In this case, x and 7 each is a term. So, it is a two-term factor.
Question 5(Multiple Choice Worth 1 points)
The equation below shows the total volume (V), in cubic units, of 6 identical boxes with each side equal to s units:
V = 6s³
If s = 3.1 units, what is the value of V?
178.746 cubic units
Justification:
Given: V = 6s³
Substitue s = 3.1 units: V = 6(3.1 units)³
Do the operation indicated by the parentheses: V = 6(29.791 unit³)
Do the operation 6×29.791 unit³: 178.746
Question 6(Multiple Choice Worth 1 points)
A student attempted to generate an equivalent expression using the distributive property, as shown below:
7(y − 5) = y − 35
What was the mistake made?
7 was not multiplied by y
Justification:
The distributive property states that you must multiply the factor that preceeds the parentheses by all the terms inside the parentheses. this is: 7 (y - 5) = 7y - 7(5) = 7y - 35
So, in the correct product 7 must appear as a coefficient of the variable y.
Question 7(Multiple Choice Worth 1 points)
Which expression represents "5 times the sum of 4 and y?"
5(4 + y)
Justification:
The factor 4 + y represents the sum of 4 and y.
The statement indicate 5 times such sum, so you have to multiply the factor 4 + y by the constant factor 5. Mathematically you must use the parentheses to show that 4 and y must be added before the multiplication is performed.
Question 8 (Fill-In-The-Blank Worth 1 points)
If s = 1/2 unit and A = 16s², what is the value of A, in square units? square unit(s). (Input whole number only.)
Answer for Blank 1: 4
Justification:
Given: A = 16s²
Substitute s = 1/2: A = 16 (1/2)²
(1/2)² = (1/4)
A = 16(1/4) = 16 / 4 = 4
Question 9(Multiple Choice Worth 1 points)
Which of these shows 2s + 8 rewritten using the commutative property of addition?
8 + 2s
Justification:
The conmutative property of addition states that the order of the addends do not modificy the sum.
This is represented by: a + b = b + c.
Hence, 2s + 8 = 8 + 2s
Finally a numerical example may help you:
8 + 2(5) = 2(5) + 8
8 + 10 = 10 + 8
18 = 18
Which shows how the sum is not modified when you change the order of the addends.
Question 10(Multiple Choice Worth 1 points)
What is the value of fraction 1/2 x³ + 5.3y, when x = 2 and y = 3?
19.9
Justification:
Given: 1/2 x³ + 5.3y and x = 2 and y = 3
Substitute: 1/2 (2³) + 5.3(3) = 1/2 (8) + 15.9 = 8/2 + 15.9 = 4 + 15.9 = 19.9
