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

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

UpStudy AI · Accepted Answer

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.
The properties are: - **Distributive Property**: b) and d) - **Commutative Property**: D) and f) - **Associative Property**: ㅁ) and e) All properties are correctly applied.

Activity I Properties of whole Numbers
b)
D)

ㅁ)
d)
e)
fी

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Activity I Properties of whole Numbers b) D) ㅁ) d) e) fी