Problem 5 - Prealgebra

Question

Find the value of each expression. $$6(15-4)$$

Step-by-Step Solution

Answer

The value of the expression is 66.

Step 1: Evaluate the Expression Inside the Parentheses

Start by solving the expression inside the parentheses. Subtract 4 from 15, which is inside the parentheses: \[ 15 - 4 = 11 \]

Step 2: Multiply the Result by 6

Now that you have solved the expression inside the parentheses, you multiply the result by 6:\[ 6 \times 11 = 66 \]

Key Concepts

Understanding Parentheses in Mathematics

Parentheses play an essential role in mathematics, especially when solving arithmetic expressions. They allow us to modify the natural order of operations and ensure that certain operations are performed first. This is crucial when expressions include various operators such as addition, subtraction, multiplication, and division.

In the exercise "6(15-4)", the first step is to focus on the part of the expression inside the parentheses: "15-4". By performing this operation first, one gets the correct intermediate result. After calculating "15-4", which equals 11, we can proceed with the remainder of the expression.

Using parentheses correctly ensures accuracy in calculations. When solving math problems, always think of parentheses as priority flags—they tell you which part of the equation to tackle first. Prioritizing what's inside the parentheses helps keep calculations organized and avoids mistakes.

The Role of Multiplication in Order of Operations

Multiplication is a foundational arithmetic operation that we often encounter in various math expressions. In expressions like "6(15-4)", multiplication follows the evaluation of the expression within the parentheses. Following the order of operations, multiplication comes after parentheses and exponents but before addition and subtraction. This order is sometimes remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

In the given problem, once we simplify the expression inside the parentheses to "11", the next step involves multiplying "6" by this simplified value. This step is crucial because multiplication determines the scaling factor of the result from the simplified operation inside the parentheses. In other words, the number outside the parentheses multiplies everything within the parentheses once it has been simplified to a single value.

Remember, when you see a number outside parentheses directly adjacent to them, it implies multiplication. Approach multiplication methodically to ensure accuracy and clarity in your results.

Solving Arithmetic Expressions with Ease

Arithmetic expressions can seem intimidating at first glance, but breaking them down into simpler components can make them much more manageable. An arithmetic expression, like "6(15-4)", involves numbers and operations, including addition, subtraction, multiplication, and division. Solving these expressions requires understanding and applying the order of operations properly.

In our example, we first handle the operation inside the parentheses ("15-4"), which is a subtraction operation. Once simplified to "11", we move on to the multiplication step to solve the expression fully. This results in the final answer as "66".

When tackling arithmetic expressions, it's helpful to:

• Identify and solve operations inside parentheses first.
• Follow the correct order of operations (PEMDAS).
• Work step-by-step to avoid mistakes and ensure accuracy.

By practicing systematically, you'll gain confidence and improve your ability to solve even the most complex arithmetic expressions efficiently!