Problem 6 - Algebra 1

Question

Evaluate the expression when \(y=6\). $$ \frac{24}{y} $$

Step-by-Step Solution

Answer

Therefore, the evaluated expression when \(y=6\) is 4.

Step 1: Identify and Substitute Variable Y into Expression

First, identify the variable \(y\) in the given expression \(\frac{24}{y}\). Substitution means replacing the variable with the provided value. Here, the value for \(y\) is 6. So we replace \(y\) in the given expression with 6. This results in \(\frac{24}{6}\).

Step 2: Perform Division

After the substitution, perform the division operation. 24 divided by 6 equals 4.

Key Concepts

Substitution

In mathematics, substitution is a technique used to simplify expressions by replacing variables with specific values. This process helps to solve equations or evaluate expressions, making it easier to understand and manage. For example, when evaluating the expression \(\frac{24}{y}\) given \(y = 6\), substitution requires us to replace the variable \(y\) with 6.

• Locate the variable in the expression.
• Replace it with the given value.

This turns the expression into \(\frac{24}{6}\), which can then be easily calculated. Substitution is a powerful tool because it helps bridge the gap between abstract algebraic expressions and concrete numbers.

Division

Division is a fundamental operation in mathematics, often used to find out how many times a number, called the divisor, is contained within another number, known as the dividend. The result of the division is termed the quotient. In our example, the expression \(\frac{24}{6}\) means we need to determine how many times 6 fits into 24.

• Identify the dividend (24) and the divisor (6).
• Calculate the quotient, which in this case is 4.

Understanding division is crucial not only in arithmetic but also in solving more complex algebraic equations and expressions.

Variables

Variables are symbols, often letters, used to represent unknown or changeable values in mathematical expressions and equations. They serve as placeholders that can stand for actual numbers. In algebra, variables allow us to work with expressions abstractly until given specific values, like in the problem \(\frac{24}{y}\).

• Variables can change depending on the context or problem.
• Substitution involves assigning a specific number to a variable.

Using variables helps to model real-world situations and solve problems systematically. Variables are a cornerstone in developing algebraic thinking, which further models relationships and changes.

Algebraic Expressions

Algebraic expressions are mathematical phrases that can include numbers, variables, and operation symbols. They can be simple or complex, depending on the number of elements and operations involved. For instance, the expression \(\frac{24}{y}\) is an algebraic expression that includes a division operation and a variable \(y\).

• They don't contain an equality sign, hence not making them equations.
• They can be evaluated by substituting variables with numbers.

Understanding algebraic expressions is essential in algebra as they form the basis from which equations and functions are built. They represent and solve many real-life situations by expressing relationships between quantities.