Problem 5 - Algebra 1

Question

Evaluate the expression when \(y=6\). \(5 y\)

Step-by-Step Solution

Answer

The evaluated result of the expression when \(y = 6\) is 30.

Step 1: Substitute the given value

The first step involves substituting the given value of y, which is 6, into the expression. So the expression \(5 y\) becomes \(5 * 6\).

Step 2: Perform the multiplication

Now, the next step is to carry out the multiplication. \(5 * 6 = 30\).

Key Concepts

Substitution in Algebra

Understanding substitution in algebra is a fundamental skill for evaluating expressions. It involves replacing a variable with its given value. For instance, consider the problem where you need to evaluate the expression when \(y=6\). The expression given is \(5y\). Here, the variable \(y\) does not have a numerical value until we substitute it with the number 6.

Let's break down the substitution process:

• Identify the variable: In the expression \(5y\), \(y\) is the variable.
• Determine the value of the variable: In this case, we are told that \(y=6\).
• Replace the variable: Substitute 6 for \(y\) in the expression, making it \(5*6\).

Substitution is like giving a placeholder – the variable – a real value so you can work with it in a tangible way. This is a critical step in solving not just simple evaluations but also complex functions and equations in algebra.

Multiplication in Algebra

After substituting the value into the expression, the next step in the evaluation process usually involves some arithmetic, like multiplication. In our example, after substituting 6 for \(y\), we get the new expression \(5*6\). The asterisk symbol (*) signifies multiplication between 5 and 6.

Some key points about multiplication in algebra:

• Symbols: Multiplication in algebra can be represented by the asterisk (*), a centered dot (\(\cdot\)), or even without a symbol, as in \(5y\) or \(5(6)\).
• Order of Operations: Remember to follow the order of operations (PEMDAS/BODMAS) where multiplication comes after parentheses/exponents and before addition/subtraction.
• Performing the Operation: With the value substituted, multiply 5 by 6 to get 30 (\(5*6=30\)). This step is fundamental in simplifying algebraic expressions to find the value of expressions.

Being proficient in applying multiplication is essential not only in algebra but virtually in all areas of mathematics.

Algebraic Expressions

An algebraic expression is a combination of constants, variables, and arithmetic operations. Expressions, unlike equations, don't have an equal sign and are not solved but simplified or evaluated. For example, the expression \(5y\) is algebraic; it contains a constant (5) and a variable (y).

These expressions can be evaluated when the variables have known values, as demonstrated in our example where \(y=6\). Some features of algebraic expressions include:

• Terms: Expressions are made of terms, which are the building blocks separated by plus (+) or minus (-) signs. In \(5y\), there is only one term.
• Variables and Constants: Variables are symbols that represent unknown values (e.g., \(y\)), and constants are fixed values (e.g., 5).
• Coefficients: In terms like \(5y\), the number before the variable (5) is the coefficient, which indicates how many times the variable is multiplied.

Grasping the fundamentals of algebraic expressions is crucial as they are at the heart of algebra and form the foundation of more complex mathematical ideas.