91Ó°ÊÓ

Negative numbers are a fundamental part of the number system. They are numbers less than zero and are usually denoted with a minus sign (-). When you see a negative number, it simply means you're looking at a value below zero. For instance, if you have –5, it means you're five units below zero on a number line.

• In mathematical operations, the negative sign can affect results significantly. For example, adding a negative number is like subtracting its positive counterpart.
• When a negative sign is applied to a number already positive, it flips the number to become negative. This operation is shown in our exercise, where the square root of 100 is 10, and the negative sign changes it to –10.

Understanding how negative numbers work is crucial for more advanced mathematical operations. They often appear in real life, such as in temperature readings below zero or bank account overdrafts.

Multiplication involves finding the product when a number is added to itself a certain number of times. In simpler terms, it’s a repeated addition. For example, 3 multiplied by 4 (denoted as 3×4) is the same as adding 3 four times: 3 + 3 + 3 + 3 = 12.

• When multiplying, the result is known as the product. Thus, the product of 3 and 4 is 12.
• Multiplication is commutative, which means that changing the order of the numbers does not change the product (e.g., 3×4 is the same as 4×3).
• In our exercise, we use multiplication when we compute the square root, because \(\sqrt{100} = 10\) means 10 times 10 gives 100.

Multiplication is a key operation that often lays the foundation for solving more complex problems in mathematics, and understanding its properties helps with evaluating various expressions.

Evaluating mathematical expressions involves performing operations according to the rules of arithmetic to find a value. To effectively evaluate expressions, follow algebraic principles and order of operations. This ensures accuracy in calculations.
The order of operations is crucial and can be remembered by the acronym PEMDAS:

• Parentheses first
• Exponents (or roots, like square roots)
• Multiplication and Division (left to right)
• Addition and Subtraction (left to right)

In the given exercise, you first calculate the square root of 100 under the guidelines of PEMDAS, which is an exponent operation. You then apply the negative sign to the result, as stated in step 2 of our solution.
Evaluating expressions accurately ensures you determine the correct value, an essential skill not just in mathematics but also in various real-world applications.