Activity I Properties of whole Numbers b) \( 2(a-3)=(2 \times a)-(2 \times 3) \) D) \( 3+a=a+3 \) ㅁ) \( 2 \times(3 \times 4)=(2 \times 3) \times 4 \) d) \( 5(a+6)=(5 \times a)+(5 \times 6) \) e) \( \quad(7+c)+d=7+(c+d) \) fी \( 4 \times a=a \times 4 \)

Let's analyze each of the properties of whole numbers provided in your activity. These properties are related to the distributive property, commutative property, and associative property of addition and multiplication. ### b) \( 2(a-3)=(2 \times a)-(2 \times 3) \) This is an example of the **distributive property**. It states that multiplying a number by a sum (or difference) is the same as multiplying each addend (or subtrahend) separately and then adding (or subtracting) the results. **Step-by-step explanation:** 1. Start with the left side: \( 2(a - 3) \). 2. Distribute \( 2 \) to both \( a \) and \( -3 \): \[ 2(a - 3) = 2a - 6 \] 3. The right side is \( (2 \times a) - (2 \times 3) \): \[ (2 \times a) - (2 \times 3) = 2a - 6 \] 4. Both sides are equal, confirming the property. ### D) \( 3 + a = a + 3 \) This is an example of the **commutative property of addition**. It states that the order in which two numbers are added does not change the sum. **Step-by-step explanation:** 1. The left side is \( 3 + a \). 2. The right side is \( a + 3 \). 3. Both expressions represent the same sum, confirming the property. ### ㅁ) \( 2 \times (3 \times 4) = (2 \times 3) \times 4 \) This is an example of the **associative property of multiplication**. It states that the way in which numbers are grouped in multiplication does not change the product. **Step-by-step explanation:** 1. Calculate the left side: \( 2 \times (3 \times 4) \): \[ 3 \times 4 = 12 \quad \Rightarrow \quad 2 \times 12 = 24 \] 2. Calculate the right side: \( (2 \times 3) \times 4 \): \[ 2 \times 3 = 6 \quad \Rightarrow \quad 6 \times 4 = 24 \] 3. Both sides equal \( 24 \), confirming the property. ### d) \( 5(a + 6) = (5 \times a) + (5 \times 6) \) This is another example of the **distributive property**. **Step-by-step explanation:** 1. Start with the left side: \( 5(a + 6) \). 2. Distribute \( 5 \): \[ 5(a + 6) = 5a + 30 \] 3. The right side is \( (5 \times a) + (5 \times 6) \): \[ (5 \times a) + (5 \times 6) = 5a + 30 \] 4. Both sides are equal, confirming the property. ### e) \( (7 + c) + d = 7 + (c + d) \) This is an example of the **associative property of addition**. **Step-by-step explanation:** 1. The left side is \( (7 + c) + d \). 2. The right side is \( 7 + (c + d) \). 3. Both expressions represent the same sum, confirming the property. ### f) \( 4 \times a = a \times 4 \) This is an example of the **commutative property of multiplication**. **Step-by-step explanation:** 1. The left side is \( 4 \times a \). 2. The right side is \( a \times 4 \). 3. Both expressions represent the same product, confirming the property. ### Summary - **Distributive Property**: b), d) - **Commutative Property**: D), f) - **Associative Property**: ㅁ), e) All properties are correctly stated and verified.