1.
Which property does the following expression represent?
8 * 1 = 8
Correct Answer
B. Identity Property of Multiplication
Explanation
The expression 8 * 1 = 8 represents the Identity Property of Multiplication. This property states that when any number is multiplied by 1, the result is the original number. In this case, when 8 is multiplied by 1, the product is 8, which is the same as the original number.
2.
Which property does the following expression represent?
(4+7)+3=4+(7+3)
Correct Answer
C. Associative Property of Addition
Explanation
The given expression represents the Associative Property of Addition. This property states that when adding three or more numbers, the grouping of the numbers does not affect the sum. In the given expression, the numbers 4, 7, and 3 are added together. The expression shows that whether we group (4+7) first and then add 3, or group 7 and 3 first and then add 4, the result will be the same. This demonstrates the Associative Property of Addition.
3.
The following expression represents the Identity Property of Multiplication.
3 * 0 = 0
Correct Answer
B. False
Explanation
The expression 3 * 0 = 0 represents the Zero Property of Multiplication, which states that any number multiplied by zero equals zero. The Identity Property of Multiplication states that any number multiplied by one equals itself (e.g., 3 * 1 = 3).
4.
Which one of the following is the correct answer for 3(x+2)?
Correct Answer
B. 3x+6
Explanation
The correct answer is 3x+6 because when we distribute the 3 to both terms inside the parentheses, we get 3 times x which is 3x, and 3 times 2 which is 6. Therefore, the expression simplifies to 3x+6.
5.
Find the perimeter of the rectangle shown in the following picture.
Correct Answer
B. 12x
Explanation
To find the perimeter of the rectangle shown in the picture, we use the formula for the perimeter of a rectangle:
Perimeter = 2 × (Length + Width)
From the picture:
Length = 4x
Width = 2x
Step-by-step Solution:
Apply the Formula:
Perimeter = 2 × (4x + 2x)
Simplify the Expression:
Perimeter = 2 × 6x
Perimeter = 12x
Final Answer:
The perimeter of the rectangle is 12x.
6.
Which property of addition is demonstrated by the equation: 3+5=5+3?
Correct Answer
A. Commutative Property
Explanation
The commutative property of addition states that the order in which two numbers are added does not affect the sum. In other words, a+b=b+a. In the given equation, 3+5=5+3, the numbers 3 and 5 are added in different orders, but the result is the same (8). This demonstrates the commutative property.
7.
Which one of the following is the identify property for addition?
Correct Answer
A. 3 + 0 = 3
Explanation
The identity property for addition states that when any number is added to zero, the result is the original number. In the given options, the equation 3 + 0 = 3 satisfies this property. Adding 0 to 3 does not change the value of 3, making it the identity element for addition.
8.
What property is this an example of : 8 + (9 + 6) = 8 + ( 6 + 9)?
Correct Answer
B. Associative
Explanation
8 + (9 + 6) = 8 + (6 + 9)
is the associative property of addition.
According to the associative property of addition, the grouping of numbers in addition does not affect the sum. In other words, you can change the grouping of the numbers being added, and the result will remain the same. This property holds true for addition because the order in which numbers are added does not change the total sum.
9.
What is the result of applying the distributive property to the expression 4 (2+6)
Correct Answer
C. 8 + 24
Explanation
The distributive property states that multiplying a number by a sum is the same as multiplying the number by each addend separately and then adding the results. Mathematically, it is represented as a(b+c)=ab+ac In the expression 4(2+6), applying the distributive property means multiplying 4 by 2 and 4 by 6, then adding the results:
4(2+6)=(4⋅2)+(4⋅6)=8+24.
10.
Which property of multiplication is shown by the equation: 5 × (3 × 2) = (5 × 3) × 2?
Correct Answer
B. Associative Property
Explanation
The associative property of multiplication states that the way in which numbers are grouped in a multiplication problem does not change the product. This property is shown in the equation 5 × (3 × 2) = (5 × 3) × 2, where the grouping of the numbers changes, but the result remains the same.