Problem 76 - Prealgebra

Question

Multiply. $$2 \cdot 4 \cdot 5$$

Step-by-Step Solution

Answer

40

Step 1: Multiply the First Two Numbers

Start by multiplying the first two numbers in the list. We have 2 and 4, so compute the product: \( 2 \times 4 = 8 \).

Step 2: Multiply the Result with the Third Number

Take the result from the first step, which is 8, and multiply it by the third number, which is 5. Perform the multiplication: \( 8 \times 5 = 40 \).

Key Concepts

Understanding Arithmetic Operations

Arithmetic operations are the basic computations we perform in mathematics to manipulate numbers. These operations include addition, subtraction, multiplication, and division. In this particular exercise, we focus on multiplication. Multiplication is essentially a shortcut for repeated addition. For example, when we say "2 times 4," it means we are adding four twice, so it's the same as 4 + 4.
These operations are fundamental because they allow us to perform more complex calculations. By understanding how to multiply numbers, you develop a skill that is foundational for advanced math concepts.

• Basic Properties: Multiplication is commutative, meaning \( a \times b = b \times a \).
• Associative Property: It allows you to change the grouping of numbers, such as \((a \times b) \times c = a \times (b \times c)\).

Effective Sequential Calculation

Sequential calculation refers to the step-by-step process of solving a math problem. Instead of attempting to solve everything at once, break the problem into smaller, more manageable steps. This method is particularly useful in complex calculations involving multiple operations.
In our exercise, we first multiply the first two numbers, 2 and 4, to get 8. Then we take this result and multiply it by the next number, which is 5. By processing the calculation in steps, it reduces the risk of making errors and makes it easier to follow the logic of the operations.

• Step-by-Step Framework: Breaking down problems into steps provides clarity.
• Reduces Complexity: Tackling a problem stage-by-stage simplifies complex tasks.

Strategies for Math Problem-Solving

Math problem-solving is not just about getting the right answer; it's about the process of understanding the problem, planning a strategy, and executing it effectively. For arithmetic tasks like multiplication, recognizing patterns and relationships between numbers can be very beneficial.
Consider the exercise of multiplying three numbers: it's helpful to apply properties such as commutative or associative to make calculations easier. Knowing that multiplication is associative allows us to group numbers differently if it simplifies calculations.

• Identify the Problem Type: Understand whether dealing with multiplication, division, etc.
• Plan a Strategy: Decide whether to use properties like distribution or simplification.
• Verify Your Results: Always double-check the operations, ensuring accuracy.