91Ó°ÊÓ

Arithmetic operations are the basic building blocks of mathematics. These include addition, subtraction, multiplication, and division. In our exercise, we see an example of how multiple arithmetic operations interact with each other:
- Addition: We see the expression ‘567 + 874’.
- Multiplication: The term ‘-2 ⋅ 4’.
- Subtraction: Notice how multiplication and addition results lead to possible implicit subtraction.
Understanding how to perform each of these operations individually and then combining them correctly is essential for solving more complex arithmetic problems.

When solving a mathematical expression, it is crucial to follow the order of operations. This ensures we get the correct result. The common acronym to remember is PEMDAS:
- Parentheses: Simplify expressions inside parentheses first.
- Exponents: Next, solve exponents and powers.
- Multiplication and Division: These are done from left to right.
- Addition and Subtraction: Finally, perform these operations from left to right.
In our exercise:
Step 1: Simplify inside the parentheses first: $$(-2 \times 4 + 8)$$
Step 2: Perform the multiplication inside: $$-2 \times 4 = -8$$
Step 3: Then, add 8: $$-8 + 8 = 0$$
Lastly, anything multiplied by 0 results in 0.

Multiplication has several important properties that help us simplify and solve mathematical expressions. Here are a few key properties:
- Commutative Property: Changing the order of the multiplied numbers does not change the result, i.e., $$a \times b = b \times a$$.
- Associative Property: The way numbers are grouped when multiplying does not change the product, i.e., $$(a \times b) \times c = a \times (b \times c)$$.
- Distributive Property: Multiplication distributes over addition, i.e., $$a \times (b + c) = (a \times b) + (a \times c)$$.
- Multiplicative Identity: Any number multiplied by 1 remains unchanged, i.e., $$a \times 1 = a$$.
- Multiplicative Property of Zero: Any number multiplied by 0 equals 0, i.e., $$a \times 0 = 0$$.
In our exercise, we leverage the multiplicative property of zero: $$(567 + 874) \times 0 = 0$$.