Problem 30 - Prealgebra

Question

Perform the following operations according to the rule for order of operations. $$5.4(9.9-6.6)$$

Step-by-Step Solution

Answer

The result of the operation is 17.82.

Step 1: Identify the Operation

First, identify what operations need to be performed inside the parentheses. The expression is \(5.4(9.9-6.6)\). The operation within the parentheses is subtraction: \(9.9 - 6.6\).

Step 2: Perform the Subtraction inside the Parentheses

Subtract the numbers inside the parentheses: \(9.9 - 6.6 = 3.3\). The expression now simplifies to \(5.4 \times 3.3\).

Step 3: Multiply the Result by 5.4

Multiply the result from the subtraction by 5.4: \(5.4 \times 3.3 = 17.82\).

Step 4: Conclusion

The complete operations give us the final answer: \(5.4(9.9-6.6) = 17.82\).

Key Concepts

Understanding Parentheses

When dealing with mathematical expressions, order is key. Parentheses are used to group together parts of an expression that need to be solved first. By doing so, they indicate which operations should be prioritized. This ensures that the calculations are done in a correct and logical manner. Here's what you need to know about working with parentheses:

• When you see parentheses in an expression, always perform the operations inside them first.
• They take precedence over other operations, including subtraction and multiplication.

In our example, the expression is given as \(5.4(9.9-6.6)\). This means we need to deal with the subtraction inside the parentheses right away. Parentheses effectively "protect" this part of the expression, making sure that nothing outside them is addressed until the interior operation is complete.
Therefore, it simplifies the process by breaking it down into more manageable pieces, ultimately leading to accurate results.

Subtraction within Parentheses

Subtraction inside parentheses must be handled carefully to ensure proper results. This operation involves taking one number away from another, which is foundational but can be tricky if not approached methodically. Here are some tips:

• Ensure that the numbers are lined up correctly, especially when working with decimals.
• Remember that subtraction signifies the difference between two numbers.

In the given expression \(5.4(9.9-6.6)\), we first focus on \(9.9 - 6.6\). Solve this by simply subtracting 6.6 from 9.9. This calculation results in 3.3. Completing this step reduces the complexity of the original expression and allows us to move onto the next phase, which is multiplication. It emphasizes the orderly approach taken when dealing with expressions.

Combining with Multiplication

After dealing with the parentheses and performing the subtraction, the next operation is multiplication. This arithmetic operation is fundamental, involving the scaling of one number by another. Here’s what to keep in mind when multiplying:

• Multiplication can simplify expressions by producing a single result from combining terms.
• It's important to multiply the numbers exactly as recalculated in previous steps.

Once you've determined the result from the parentheses, such as \(3.3\) from \(9.9-6.6\), it's time to combine it with the outside term of the expression, which in this case is \(5.4\).
Multiply \(5.4\) by \(3.3\), resulting in \(17.82\). It's crucial to perform multiplication with precision to ensure the accuracy and validity of the result, especially when decimals are involved. This step concludes the entire operation, illustrating how each part plays an essential role in reaching the final answer.