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 × 32 = 15 × (30 + 2) = (15 × 30) + (15 × 2) = 450 + 30 = 480 Example 2 (Multiplication over Subtraction): 23 × 18 = 23 × (20 - 2) = (23 × 20) - (23 × 2) = 460 - 46 = 414 You can also omit the multiplication sign before a bracket, for example, 2 × (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 × 1 = 739 739 ÷ 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 That's 2 down. 3 left today — send the next one.