Problem 17 - Elementary Algebra

Question

Perform the operotions. Round dollar omounts to the nearest hundredth. $$ 55.611+7 \times 2 $$

Step-by-Step Solution

Answer

69.61

Step 1: Handle Multiplication

First, perform the multiplication operation in the expression. Multiply 7 by 2: \[7 \times 2 = 14\]

Step 2: Addition

Next, add the result of the multiplication to 55.611. So, the expression becomes: \[55.611 + 14 = 69.611\]

Step 3: Rounding

Round the sum to the nearest hundredth. Since the third decimal place is a '1', we round down: \[69.611 \approx 69.61\]

Key Concepts

Understanding the Order of Operations

In elementary algebra, the order of operations is crucial for solving equations correctly. It dictates the sequence in which operations are performed, ensuring consistency in the results.

The conventional order of operations can be memorized as PEMDAS:

• Parentheses
• Exponents (or powers and roots)
• Multiplication and Division (from left to right)
• Addition and Subtraction (from left to right)

In the given exercise, we apply this sequence by handling the multiplication before proceeding to addition. This approach prevents errors and guarantees that expressions, no matter how complex, are simplified correctly.

Always remember, solving equations without following this specific order could lead to misleading results, which is why mastering this concept is key in any mathematical undertaking.

Rounding Numbers to the Nearest Hundredth

Rounding numbers is an essential skill in both mathematics and everyday life, especially when dealing with decimals. When rounding to the nearest hundredth, focus on the digit in the thousandths place (the third digit to the right of the decimal point).

If this digit is 5 or greater, round the hundredths place up. If it is less than 5, keep the hundredths place as is. This rule ensures precision and clarity in numerical data.

In our exercise, we round 69.611 to 69.61 because the digit in the thousandths place is 1, which is less than 5. This technique helps in expressing numbers in a simpler form, particularly when dealing with money or measurements.

Mastering Multiplication and Addition

Multiplication and addition are foundational operations in elementary algebra. They form the building blocks for more advanced mathematical concepts and operations.

Multiplication can be thought of as repeated addition. For example, multiplying 7 by 2 means adding 7 to itself, resulting in 14. It allows for efficient calculations, especially with large numbers.

• Example: \[7 \times 2 = 14\]

Addition is the process of combining numbers to find their total. Once you have the result of any multiplication, as shown in our example, you can then add it to other numbers to compute the overall sum.

• Example: \[55.611 + 14 = 69.611\]

Understanding these operations and their real-life applications is vital as they are frequently used in everyday problem-solving, from budgeting to scientific calculations.