Question

Which expression is the same as \(54-30\) ? A. \(6(9-6)\) B. \(6(9+6)\) C. \(6(9+5)\) D. \(6(9-5)\)

Short answer

D. \(6(9 - 5)\)

Step-by-step solution

Evaluate the original expression

Start by calculating the value of the original expression given in the problem: \(54 - 30\).

Compute the difference

Subtract 30 from 54: \(54 - 30 = 24\).

Simplify each option

Calculate the value of each multiple-choice option to find the one that matches 24: A. \(6(9-6) = 6 \times 3 = 18\)B. \(6(9+6) = 6 \times 15 = 90\)C. \(6(9+5) = 6 \times 14 = 84\)D. \(6(9-5) = 6 \times 4 = 24\)

Select the correct answer

The expression that matches the computed value of the original expression (24) is:D. \(6(9 - 5)\)

Key concepts

Algebraic Expressions

Algebraic expressions form the backbone of algebra and are key to solving many math problems. An algebraic expression combines numbers, variables, and arithmetic operations. For example, if you have the expression \(54 - 30\), it contains only constants and the subtraction operation.

When dealing with algebraic expressions in a problem, you often need to simplify or evaluate them by performing the given operations. Simplifying an expression means reducing it to its simplest form.
For instance, \(6(9-5)\) simplifies to \(6 \times 4\). By practicing, you will get more comfortable with managing and manipulating these expressions.

Practice different kinds of algebraic expressions to build confidence and competence. Remember, any expression can be manipulated to find an equivalent version.

Basic Arithmetic

Basic arithmetic is crucial for solving mathematical reasoning problems, such as those found in the GED exam. It includes operations like addition, subtraction, multiplication, and division. In our example, we start with subtraction:
\(54 - 30\) which equals \(24\). This simple subtraction gives us the base value.

Once we have the base value, we explore options using multiplication and addition/subtraction:

• Option A: \(6(9-6) = 18\)
• Option B: \(6(9+6) = 90\)
• Option C: \(6(9+5) = 84\)
• Option D: \(6(9-5) = 24\)

In this example, understanding how to perform these operations correctly helps you verify which expression matches the original one. These basic arithmetic skills are essential in all math-related problems.

Problem-Solving

Problem-solving is the application of what you know to find an answer to a question. When faced with a problem like the one given, it's important to follow systematic steps:

First, evaluate the initial expression to understand its value. Here, calculating \(54 - 30\) tells us the value is \(24\). Next, assess each multiple-choice option to find an equivalent expression. This involves simplifying the given options:

This method involves critical thinking and logical reasoning to find the right match.

• Option A: \(6(9-6) = 18\)
• Option B: \(6(9+6) = 90\)
• Option C: \(6(9+5) = 84\)
• Option D: \(6(9-5) = 24\)

By comparing these results, you identify Option D as the equivalent expression.

Problem-solving can be practiced by working through various problems, ensuring you break down each step clearly and logically.