Problem 1 - Prealgebra

Question

Evaluate each expression if \(a=5, b=12,\) and \(c=4\) $$b+6$$

Step-by-Step Solution

Answer

The expression evaluates to 18.

Step 1: Identify the Expression and Inputs

The expression given is \(b + 6\). The values provided are \(a = 5\), \(b = 12\), and \(c = 4\). We only need the value of \(b\) for this expression.

Step 2: Substitute the Value of b

Substitute \(b = 12\) into the expression. The expression becomes \(12 + 6\).

Step 3: Perform the Arithmetic Operation

Add 12 and 6 together. \(12 + 6 = 18\).

Key Concepts

Variable Substitution

One of the first steps when working with algebraic expressions is variable substitution. In simpler terms, this means replacing a variable in an expression with its given value.

• Start by identifying the expression and the variable you need to substitute. Here, the expression is \(b + 6\).
• Next, determine what value the variable holds. For this exercise, the variable \(b\) has a value of \(12\).
• Perform the substitution by replacing \(b\) in the expression with \(12\). Your expression now reads: \(12 + 6\).

Substituting variables is crucial because it allows us to simplify and evaluate expressions, transforming them from abstract representations into something concrete that we can calculate.

Expression Evaluation

Once you have substituted the variable with its value, the next step is expression evaluation. This means calculating or simplifying the expression to find its numerical value.

• The initial step involves ensuring all variables have been replaced with their designated values. For instance, in the expression \(b + 6\), after substitution, becomes \(12 + 6\).
• Once substitution is done, you proceed with evaluating the expression by performing the indicated arithmetic operation, which in this case is addition.

Evaluating expressions is essential as it helps to solve mathematical problems, providing clear and precise answers to queries formed as algebraic expressions. It’s a simple yet profound skill that is foundational in many areas of math and science.

Addition

Addition is a fundamental arithmetic operation that involves combining two numbers to get a total. In the context of this exercise, addition comes into play after substituting the variable.

• With the expression now \(12 + 6\), you simply add the numbers step-by-step, starting from the leftmost digit to the right.
• Begin by adding the units: \(12\) has two in the unit's place, and \(6\) is entirely units. Adding these gives \(8\) in the units place.
• Once you ignore the units, notice that there's a tens digit \(1\) in \(12\), making the sum \(18\).

Addition like this appears everywhere, from simple calculations to more complex problem-solving situations. By mastering addition, you enhance your capability to tackle a wide array of mathematical challenges.