Problem 34 - Prealgebra

Question

Perform the following operations according to the rule for order of operations. $$4.04(0.05+6.6)$$

Step-by-Step Solution

Answer

The result is 26.866.

Step 1: Solve Inside Parentheses

First, we need to perform the operation inside the parentheses. Add 0.05 and 6.6: \[ 0.05 + 6.6 = 6.65 \]

Step 2: Multiply with the Coefficient

Next, we multiply the result from Step 1 by the coefficient (4.04). So, calculate: \[ 4.04 imes 6.65 = 26.866 \]

Key Concepts

Parentheses

In the world of mathematics, parentheses are like the guardians of operations, making sure that the expressions enclosed within them are handled first. When you see parentheses in an expression, always prioritize solving what is inside them before moving on to other operations. These brackets help clarify which part of an equation should be addressed first, ensuring calculations follow the correct order.

Consider a situation similar to our exercise, where we have an expression like \(4.04(0.05+6.6)\). Here, the operation inside the parentheses—adding 0.05 and 6.6—must be completed first to simplify and correctly resolve the larger expression. So, always remember when parentheses are there, they demand the first slice of attention!

• Identify operations inside parentheses.
• Perform all operations within them before moving further.
• Once simplified, consider the parentheses done and move to the next steps.

Addition

Addition is one of the fundamental operations in math, asking us to find the total by combining numbers. The process of adding numbers is quite straightforward, yet it's crucial to ensure accuracy and follow the order of operations.

In our original exercise, the addition occurs within the parentheses. We have to add 0.05 and 6.6. This results in 6.65. Simplifying within the parentheses helps us narrow down the equation, making it easier to proceed with further calculations. Always make sure to:

• Ensure all numbers are properly lined up, especially while dealing with decimals.
• Double-check your additions to avoid small mistakes.
• Carry over any values as necessary when working with multi-digit numbers.

By following these steps, you can efficiently navigate through addition challenges, particularly in larger expressions.

Multiplication

After taking care of tasks within parentheses and simplifying addition, the next step in many expressions is multiplication. This operation builds products through the combination of numbers. When multiple operations are involved, like in our example \(4.04 \times 6.65\), multiplication takes center stage next.

This step involves multiplying the number outside the parentheses by the sum we calculated earlier, 6.65. Multiplication requires precision:

• Ensure numbers align correctly, paying special attention to decimal places.
• Multiply each digit systematically, taking one step at a time.
• Sum up each part of the product for an accurate result.

By carefully executing multiplication, you ensure that the final value reflects the accurate total of the earlier additions and parenthesis simplifications. This method lays a solid finish to processing expressions, reflecting sound mathematical reasoning.