Problem 80 - Prealgebra

Question

Multiply. $$6 \cdot 6 \cdot 2$$

Step-by-Step Solution

Answer

The product is 72.

Step 1: Multiply the First Two Numbers

Begin by multiplying the first two numbers in the expression: \[ 6 \times 6 = 36 \]

Step 2: Multiply the Result by the Last Number

Take the result from Step 1 and multiply it by the last number in the expression:\[ 36 \times 2 = 72 \]

Key Concepts

Step-by-step solution

A step-by-step solution is crucial for making complex problems easier to understand, especially in mathematics. This approach helps break down the process into manageable parts, guiding students through each stage with simplicity.
Let's take a look at the exercise: multiplying the numbers 6, 6, and 2.

• Step 1: Focus on the first two numbers, 6 and 6. Multiply them together to get 36.
• Step 2: Take the result from Step 1, which is 36, and multiply it by the next number, 2. This gives you the final result of 72.

Following such detailed steps not only ensures accuracy but also boosts confidence in solving similar problems. Each stage is designed to reinforce understanding and familiarity with basic operations.

Multiplication of numbers

Multiplication is one of the core operations in mathematics, allowing you to find the total number of items in groups of the same size. It's essentially a faster way of adding the same number multiple times.
In our problem, we are asked to multiply 6, 6, and 2. Let's understand what that means:

• When you multiply 6 by 6, you're adding the number 6, six times (6 + 6 + 6 + 6 + 6 + 6 = 36).
• Next, multiply this result (36) by 2. This means you are doubling the group size, which can be thought of as adding 36 plus 36 to get 72.

This operation highlights how multiplication simplifies repetitive addition tasks, making it an efficient tool for problem-solving. Understanding its basic principles is essential for tackling more complex mathematical challenges.

Order of operations

The order of operations is a set of rules that determines the sequence in which operations should be carried out in a mathematical expression. It's crucial to ensure consistent and correct results.
Consider the order of operations, often remembered by the acronym PEMDAS:

• P for Parentheses
• E for Exponents
• M for Multiplication
• D for Division
• A for Addition
• S for Subtraction

In our particular exercise, 6 multiplied by 6, then multiplied by 2, you only deal with multiplication, so you simply perform it from left to right according to PEMDAS. No need to worry about other operations, since they are not present here.
By following these rules, you can be sure your calculations are free of mistakes, leading to the correct answer every time.