Problem 17 - 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 choice is 'C. y plus 8'

Step 1: Identifying the Operation

Examine the expression is \( y + 8 \). The operation symbol present here is '+', which corresponds to the mathematical operation of addition.

Step 2: Matching the Expression

Find the option that correctly describes 'y plus 8'. The options are: 'A. 8 times y', 'B. y divided by 8', 'C. y plus 8', and 'D. y minus 8'. Going through the options, it is clear that option 'C. y plus 8' correctly corresponds to the expression.

Step 3: Confirming the Matching

Confirm the matching of the expression to its meaning. In this case, 'y plus 8' is the accurate reflection of the variable expression \( y + 8 \). So, the answer is correct.

Key Concepts

Variable Expressions

Variable expressions are mathematical phrases that use numbers, variables, and operators. Variables, like the letter "y" in our expression, represent quantities that can change or vary. They are placeholders for unknown or changing values.
A variable expression can be as simple as "y + 8" or more complex with multiple variables and operations.
Understanding variable expressions is crucial in algebra because they form the foundation for creating equations and inequalities. These expressions help in modeling real-world situations where quantities are not fixed, and we need a flexible way to represent them.

Mathematical Operations

Mathematical operations are the actions we perform on numbers or variables. The basic operations include:

• Addition ('+'), adding quantities together.
• Subtraction ('-'), taking one quantity away from another.
• Multiplication ('×' or '*'), finding the total of adding a number a certain number of times.
• Division ('÷' or '/'), distributing a number into equal parts.

In the expression "y + 8," the operation used is addition. It involves combining or adding the variable "y" with the number 8. Identifying the correct operation is essential to understand and solve algebraic problems accurately.
Each operation has its symbol, and recognizing these symbols helps in translating the expression correctly into verbal explanations.

Addition in Algebra

Addition in algebra involves the process of combining quantities represented by variables and numbers. It follows the same principles as regular addition but includes variable terms.
When you see an expression like "y + 8," it means you are adding 8 to the variable y.
This kind of expression is read as 'y plus 8.' It is important to note that addition is commutative, which means "y + 8" is the same as "8 + y."
Recognizing addition in algebra is crucial for solving equations, simplifying expressions, and understanding relationships between quantities. Practicing with variable expressions helps you grasp how addition works within algebraic contexts.