Properties of Numbers Quiz Questions

1. Which property does the following expression represent? 8 * 1 = 8

Distributive Property

Identity Property of Multiplication

Commutative Property of Multiplication

Identity Property of Addition

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.

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 of addition is demonstrated by the equation: 3+5=5+3?

Commutative Property

Associative Property

Distributive Property

Identity Property

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.

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.

3. Which property does the following expression represent? (4+7)+3=4+(7+3)

Distributive Property

Associative Property of Multiplication

Associative Property of Addition

Commutative Property of Addition

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.

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.

4. Which one of the following is the correct answer for 3(x+2)?

3x+2

3x+6

X+6

3

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.

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. Which one of the following is the identify property for addition?

3 + 0 = 3

3 * 1 = 3

3 + 7 = 7 + 3

3 + -3 = 0

3 * 0 = 0

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.

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.

6. What is the result of applying the distributive property to the expression 4 (2+6)

4 x 8

8 + 8

8 + 24

2 + 24

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.

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.

7. Which property of multiplication is shown by the equation: 5 m (3 m 2) = (5 m 3) m 2?

Commutative Property

Associative Property

Distributive Property

Identity Property

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.

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.

8. The following expression represents the Identity Property of Multiplication. 3 * 0 = 0

True

False

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).

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).

9. Find the perimeter of the rectangle shown in the following picture.

4x

12x

6x

8x

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.

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.

10. What property is this an example of : 8 + (9 + 6) = 8 + ( 6 + 9)?

Commutative

Associative

Distributive

Inverse

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.

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.

Properties Of Numbers Quiz Questions