We say the distributive property applies to multiplication over addition and subtraction. To distribute means to spread out. This property (or rule) allows us to redistribute numbers and still get the same answer.

Here are explanations for the mathematical topics shown in your image:

Topic 1: Distributive Property
The distributive property states that multiplying a number by a sum or difference is the same as multiplying that number by each term in the sum or difference and then adding or subtracting the products.

• Example 1 (Multiplication over Addition):

  $$15 \times 32 = 15 \times (30 + 2)$$ $$= (15 \times 30) + (15 \times 2)$$ $$= 450 + 30$$ $$= 480$$

• Example 2 (Multiplication over Subtraction):

  $$23 \times 18 = 23 \times (20 - 2)$$ $$= (23 \times 20) - (23 \times 2)$$ $$= 460 - 46$$ $$= 414$$

  You can also omit the multiplication sign before a bracket, for example, $2 \times (8+2)$ can be written as $2(8+2)$.

Topic 2: Identity Properties
Identity properties involve operations that leave a number unchanged. There are two main types:

• Additive Identity: Adding zero to any number leaves the number unchanged.

  • Example: $$310 + 0 = 310$$ $$310 - 0 = 310$$

• Multiplicative Identity: Multiplying any number by one leaves the number unchanged.

  • Example: $$739 \times 1 = 739$$ $$739 \div 1 = 739$$

Topic 3: Inverse Operations
Inverse operations are opposite operations that reverse the effect of another operation.

• Example (Addition and Subtraction): If you have an addition fact, you can derive related subtraction facts. If $460 + 340 = 800$, then: $$800 - 340 = 460$$ or $$800 - 460 = 340$$