Problem 18 - Algebra 1: Concepts and Skills

Question

Match the variable expression with its meaning. $$ y-8 $$ A. 8 times \(y\) B. \(y\) divided by 8 C. y plus 8 D. \(y\) minus 8

Step-by-Step Solution

Answer

The correct match for the expression \(y - 8\) is D. \(y\) minus 8.

Step 1: Identify the Operation

Looking at the expression \(y - 8\), the operation taking place between the variable \(y\) and the number 8 is subtraction.

Step 2: Match the Operation

Now, review the options provided and find the one that correctly describes the expression. The expression represents \(y\) minus 8.

Key Concepts

Variable Expressions

Variable expressions are algebraic expressions that contain variables, numbers, and mathematical operations. Variables are symbols that represent unknown values and are often denoted by letters like \(x\), \(y\), or \(z\). These expressions are fundamental in expressing mathematical relationships and equations.
For example:

• \(y + 5\) where \(y\) is the variable and 5 is a constant added to \(y\).
• \(3x - 2\) implies 3 times \(x\), reduced by 2.

Variable expressions can simplify problem-solving, allowing you to manipulate equations to find a value or check relationships. Understanding how variables interact with numbers through different operations is crucial in algebra.

Subtraction in Algebra

Subtraction in algebra involves taking a value away from another, which is symbolized by the minus sign \(-\). In the context of variable expressions, subtraction decreases the value of the variable by a given amount. For example, with \(y - 8\), 8 is subtracted from the value represented by \(y\).
Subtraction can be visualized as:

• Starting with an original amount or number.
• Removing or cutting down by a specific value.

If you encounter an expression like \(a - b\), it represents the number \(a\) reduced by \(b\). Understanding subtraction is key to balancing equations and solving algebra problems, including solving for unknown variables.

Translating Expressions

Translating expressions involves changing verbal phrases or descriptions into algebraic expressions. This skill is vital when solving word problems, as it helps in converting the situation described into an expression or equation that can be solved mathematically.
Some common phrases and their algebraic counterparts include:

• "The difference of something" translates to using subtraction (e.g., \("y - 8"\) means \("y" minus 8\)).
• "The sum of something" translates to using addition.
• "A product of something" involves multiplication.
• "A quotient of something" involves division.

By correlating natural language phrases to algebraic symbols, you can systematically approach and solve various types of problems in mathematics. Mastery in translating expressions equips you to transition seamlessly between problems and solutions.