Lesson 3 Homeworl Practice Properties of Operations Name the property shown by each statement. \( \begin{array}{l}\text { 1. } 1 \cdot(a+3)=a+3 \\ \begin{array}{l}\text { 3. }(a b)_{c}=c(a b) \\ \text { 5. } m(n r)=(m n) r\end{array} \\ \text { 2. } 2 p+(3 q+2)=(2 p+3 q)+2 \\ \text { state whether the following conjectures are true or false. If false, } \\ \text { 7. The product of an odd number and an even number is always odd. } \\ \text { 8. The sum of two whole numbers is always larger than either whole number. } \\ \text { 4. } 2 t \cdot 0=0\end{array} \) Simplify each expression. Justify each step. 9. \( 2 d(3) \)
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First, let's dive into some fascinating historical context. Did you know that the properties of operations we study today have their roots in ancient civilizations? The Babylonians and Egyptians were some of the first known civilizations to use basic arithmetic and algebraic principles. Their mathematical advancements laid the groundwork for the properties we now use, such as the distributive and associative properties, which help streamline calculations! Now, let's talk real-world applications! These properties of operations are not just academic; they are integral in various fields. For example, engineers use these properties when designing structures to ensure calculations are precise. Similarly, computer programmers rely on these properties to create algorithms that efficiently handle data. Understanding how to apply these mathematical properties in real-world scenarios makes problem-solving both effective and exciting!
