Problem 60 - Algebra 1: Concepts and Skills

Question

Evaluate the expression for the given value of the variable. $$ \frac{x}{4} \text { when } x=56 $$

Step-by-Step Solution

Answer

The evaluated expression is \(14\).

Step 1: Identify the variable in the expression

The expression \(\frac{x}{4}\) contains the variable \(x\). The value given for this variable is \(56\).

Step 2: Substitute the value of the variable into the expression

Replace \(x\) with \(56\) in the expression \(\frac{x}{4}\). So, the new expression becomes \(\frac{56}{4}\).

Step 3: Evaluate the expression

After substitution, evaluate the expression. The result of the expression \(\frac{56}{4}\) is \(14\).

Key Concepts

Substitution

Substitution in algebra is a fundamental concept where you replace a variable with its given value in an expression. It's like filling in the blanks with the correct numbers to make calculations possible. In the exercise, we have the variable \(x\) present in the expression \(\frac{x}{4}\). We are told \(x = 56\). This means we need to substitute 56 wherever we see \(x\) in the expression. When substitution is done correctly, it simplifies the expression down to numbers, making it easier to solve.

• Find the part of the expression containing the variable.
• Replace it with its given value.
• Re-calculate the expression.

Substitution is a tool that allows you to translate a problem into a simpler form that you know how to deal with, thus making it a crucial step in evaluating algebraic expressions.

Variable Identification

Identifying variables in an expression is crucial in algebra as it allows us to understand the role they play. A variable, often represented by letters like \(x\), \(y\), or \(z\), stands in for numbers we don't know yet or that can change. In our expression, \(\frac{x}{4}\), the variable is \(x\). Recognizing this:

• Helps in knowing what values need to be substituted.
• Ensures that each step in solving the expression is clear.
• Guides us on how calculations should proceed.

Being able to pinpoint variables quickly ensures that you can approach the problem with confidence, and it's a skill that will undoubtedly make working with algebra more straightforward.

Division in Algebra

Division in algebra works similarly to division in arithmetic, but it involves variables as well as numbers. Evaluating expressions that include division means you're breaking down a value by another number. In our specific expression \(\frac{x}{4}\), division is occurring with \(x\) as the numerator and 4 as the divisor. After substituting \(x = 56\), the expression becomes \(\frac{56}{4}\). The steps to perform division in algebra are:

• Ensure the variable has been substituted with a number, if necessary.
• Calculate the result of dividing the numerator by the divisor.
• Simplify to the lowest terms, if possible.

Here, \(56 \div 4\) simplifies nicely to 14, illustrating that even when variables and numbers are involved, basic division rules apply, making algebra feel familiar and manageable.