Problem 3 - Algebra 1: Concepts and Skills

Question

Evaluate the expression. $$5 \cdot 6 \cdot 2$$

Step-by-Step Solution

Answer

The evaluated result of the expression \(5 \cdot 6 \cdot 2\) is 60.

Step 1: Understand The Operation

The operation to be performed here is multiplication. The given expression is \(5 \cdot 6 \cdot 2\), which means multiply 5 by 6, and then multiply the result by 2.

Step 2: Perform The First Multiplication

Perform multiplication of the first two numbers. The result of multiplying 5 by 6 equals 30.

Step 3: Perform The Second Multiplication

Now, multiply the result of the first multiplication, which is 30, by the third number in the expression, which is 2. The result of multiplying 30 by 2 equals 60.

Key Concepts

Multiplication

Multiplication is one of the fundamental arithmetic operations and an essential part of mathematics. In multiplication, you take one number, referred to as the multiplicand, and multiply it by another number called the multiplier. The result is known as the product.
For example, in the expression \(5 \cdot 6\), 5 is the multiplicand, 6 is the multiplier, and 30 is the product.

• The symbol for multiplication can vary but is often represented as \( \cdot \) or \( \times \).
• Multiplication can be thought of as repeated addition. For example, multiplying 5 by 6 is the same as adding 5 six times (5 + 5 + 5 + 5 + 5 + 5).
• The multiplication operation is commutative, which means \(5 \cdot 6 = 6 \cdot 5\), and associative, meaning \((5 \cdot 6) \cdot 2 = 5 \cdot (6 \cdot 2)\).

Understanding multiplication is crucial for solving more complex mathematical problems and forms the basis for algebra and calculus.

Order of Operations

The order of operations is a set of rules that determines the sequence in which operations should be performed in a mathematical expression. It ensures clarity and consistency in solving expressions.
An easy way to remember the order of operations is the acronym PEMDAS:

• P for Parentheses: Solve anything in parentheses first.
• E for Exponents: Next, calculate any powers or square roots.
• MD for Multiplication and Division: From left to right as they appear in the expression.
• AS for Addition and Subtraction: Finally, handle these operations from left to right.

In the expression \(5 \cdot 6 \cdot 2\), multiplication is performed first because it is the only operation. There is no need to consider anything else like parentheses or addition. By following these rules, everyone can solve expressions accurately and efficiently, avoiding confusion or errors.

Arithmetic Operations

Arithmetic operations include basic functions such as addition, subtraction, multiplication, and division. They are the building blocks of mathematics and are used to create more complex equations and solve problems.
Here's a brief explanation of each:

• Addition: Combining two numbers to get a sum. For instance, \(3 + 4 = 7\).
• Subtraction: Taking one number away from another to get a difference. For example, \(9 - 5 = 4\).
• Multiplication: As previously discussed, it involves multiplying two numbers to get a product, as in \(5 \cdot 6 = 30\).
• Division: Splitting a number into equal parts, like \(12 \div 4 = 3\).

These operations are essential for daily math tasks and understanding higher-level mathematics. They help us to simplify complex problems and find solutions efficiently, making them a vital part of math education.