Problem 49 - Prealgebra

Question

Perform the indicated operations. \(3 \times 1.06 \times 2\)

Step-by-Step Solution

Answer

The result of the multiplication is 6.36.

Step 1: Perform the first multiplication

Multiply the first two numbers in the expression. Here, you need to calculate \(3 \times 1.06\). To do this, multiply 3 by 1.06 giving an intermediate result of 3.18.

Step 2: Perform the second multiplication

Now, take the result from Step 1 and multiply it by the third number in the expression. Thus, compute \(3.18 \times 2\), which results in 6.36.

Key Concepts

Step-by-step multiplication

When approaching multiplication problems involving several numbers, a step-by-step approach is beneficial for avoiding mistakes and ensuring each multiplication is performed accurately. Here is how you can effectively tackle a problem with successive multiplications:

• Identify the set of numbers to be multiplied. In our exercise, these are 3, 1.06, and 2.
• Break down the problem, tackling one multiplication at a time. This means that instead of multiplying three numbers at once, begin by multiplying the first two numbers.
• Multiply these initial numbers fully to get an intermediate result. For the exercise, multiplying 3 by 1.06 gave us 3.18.
• Use the intermediate result for the next multiplication step. Here, we multiply 3.18 by the third number (2) to get the final result.

This methodical approach ensures clarity and accuracy at each stage, helping to prevent errors in calculation.

Decimal multiplication

Decimal multiplication requires careful attention to the placement of the decimal point. The process is similar to whole number multiplication, but there are specific steps to follow to ensure accuracy.

• Ignore the decimal point at first and multiply the numbers as if they were whole numbers. In our example, you multiply 3 by 106 (ignoring the decimal), resulting in 318.
• Count the total number of decimal places in the factors. Here, the number 1.06 has two decimal places.
• Apply this count to the product. Thus, you place the decimal point two spaces from the right in 318, resulting in 3.18.

It’s crucial always to revisit the placement of the decimal point post-calculation to avoid misplacing it and ending up with an incorrect result.

Arithmetic operations

Arithmetic operations form the foundation of mathematics, encompassing addition, subtraction, multiplication, and division. Multiplication, particularly, is a method for combining equal groups. When dealing with decimals and several factors at once, there are some key considerations:

• Successive multiplication, such as multiplying three numbers, involves combining several products. Each multiplication should be approached stepwise.
• Focus on order and precision, especially with decimals, to maintain the correct placement of numbers and decimal points.
• The commutative property states that the order in which numbers are multiplied does not affect the final product. Therefore, choosing which two numbers to multiply first can sometimes simplify calculations.

Understanding how multiplication integrates into the broader world of arithmetic operations is essential for solving complex problems with confidence and precision.