91Ó°ÊÓ

When we convert a verbal phrase into math language, it results in a variable expression. This process involves identifying and translating words into mathematical symbols and values. In the exercise, we encounter the phrase "some number." This indicates a variable. Variables are symbols, often letters like \( x \), \( y \), or \( z \), that stand in for unknown values. They are essential for writing expressions that can be used in a wide range of scenarios. Variables allow us to create a formula or equation that can change when different values are substituted for "some number." When you see a variable in an expression, imagine it as a placeholder for any potential number. This flexibility is what makes algebra so powerful—it allows for generalized solutions and representations.

Mathematical operations are actions that manipulate numbers and variables to transform expressions. The main operations are addition, subtraction, multiplication, and division.

• Addition: Symbolized by a plus sign (+), it combines two quantities to yield a sum.
• Subtraction: Represented by a minus sign (-), it finds the difference between two numbers.
• Multiplication: Shown with an asterisk (\(*\)) or parentheses, it scales one number by another, producing a product.
• Division: Denoted by a forward slash (/) or fraction, it partitions one number by another to obtain a quotient.

In the exercise, we specifically deal with addition and multiplication. "Negative five plus" indicates that we will add to a number, and "product of seven and some number" tells us to multiply 7 by a variable. Understanding these operations allows us to read and write expressions correctly, ensuring they perform the intended calculations.

The order of operations is a set of rules that define the sequence in which operations should be performed to accurately evaluate an expression. You might remember this rule from the acronym PEMDAS:

• Parentheses: Do operations inside parentheses first.
• Exponents: Calculate powers and square roots next.
• Multiplication and Division: Perform these from left to right.
• Addition and Subtraction: Finally, handle these operations from left to right.

In our task, the phrase "negative five plus the product of seven and some number" needs to follow these rules. First, we handle the multiplication, as "the product of seven and some number" is 7 multiplied by \( x \), resulting in \( 7x \). Then, we can add the negative five, forming the expression \( -5 + 7x \). Adhering to the order of operations ensures that expressions are evaluated correctly and uniformly, providing consistent results every time.