Problem 19 - Algebra 1: Concepts and Skills

Question

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

Step-by-Step Solution

Answer

The variable expression \(\frac{y}{8}\) matches with option B '\(y\) divided by 8'.

Step 1: Analyze the expression

The expression provided is \(\frac{y}{8}\). The slash (/) in the expression denotes division operation. It means that the variable \(y\) is divided by the number 8.

Step 2: Match with appropriate meaning

Considering the nature of the operation in the expression, we need to look for an option that implies 'division by 8'. Looking at the provided options, option B, which states '\(y\) divided by 8' corresponds exactly to the mathematical operation of the expression \(\frac{y}{8}\).

Key Concepts

Division in Variable Expressions

In mathematics, a variable expression is a combination of numbers, variables, and operations that describe a particular calculation. The expression \( \frac{y}{8} \) is an example of a variable expression, where division is the operation performed.
Division is signified by the slash (\(/\)), indicating that the variable \( y \) is being divided by the number 8. Understanding the role of division in expressions helps break down mathematical problems into smaller, manageable parts.
In any expression involving division, it's crucial to identify the dividend and the divisor:

• The dividend is the number or variable being divided, which in this case is \( y \).
• The divisor is the number by which the dividend is divided, here being 8.

Recognizing this setup is essential for interpreting and solving mathematical problems involving division.

Interpreting Mathematical Expressions

Mathematical expressions are the foundation of algebra and calculus, serving as a representation of relationships between numbers and variables. Learning how to interpret these expressions is crucial for solving equations and understanding concepts in mathematics.
For example, in the variable expression \( \frac{y}{8} \), we interpret it by analyzing each component:

• Understand what operation is being indicated, which here is division.
• Identify the terms involved, the variable \( y \), and the constant 8.

Understanding that \( \frac{y}{8} \) translates to \( y \) being divided into 8 parts is key. When interpreting expressions, it’s also important to consider context, which guides the meaning and application of an expression.
Using clear steps to decode expressions enhances comprehension and allows students to apply their mathematical reasoning more effectively in various situations.

Matching Expressions to Meanings

Matching mathematical expressions to their meanings is a vital skill in mathematics. It involves interpreting the structure and operations in an expression and linking them to the corresponding description. This skill enhances a student's ability to solve problems and communicate mathematical ideas accurately.
When given the expression \( \frac{y}{8} \), students should:

• First, identify the operation. Here, it’s division, as indicated by the division sign \(/\).
• Then, match this operation with the correct verbal expression from provided options. For this exercise, the correct match is ' \( y \) divided by 8'.

Practicing this exercise helps solidify understanding of how mathematical expressions translate to real-world descriptions. It also enhances logical reasoning skills as students learn to connect abstract symbols with concrete meanings, a crucial ability for tackling more advanced mathematical challenges.