Problem 33 - Prealgebra

Question

Perform the following operations according to the rule for order of operations. $$2.02(0.03+2.5)$$

Step-by-Step Solution

Answer

The result of the operation \(2.02(0.03+2.5)\) is 5.1106.

Step 1: Identify the Operation Inside the Parentheses

The expression to solve is \(2.02(0.03 + 2.5)\). According to the order of operations, operations inside parentheses should be handled first. In this case, you should add 0.03 and 2.5 together.

Step 2: Calculate the Sum Inside the Parentheses

Add 0.03 and 2.5: \(0.03 + 2.5 = 2.53\). This simplifies the expression to \(2.02 \times 2.53\).

Step 3: Perform the Multiplication

Now multiply the values from the previous result: \(2.02 \times 2.53\). To multiply these numbers, you can use long multiplication or a calculator. The result is 5.1106.

Key Concepts

Parentheses Operations

When we see a mathematical expression, the first thing we need to do is look for any operations inside parentheses. Parentheses help to group certain numbers and operations together, telling us to solve these parts of the expression before anything else. This is critical because it ensures we follow the correct order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

In our expression, \(2.02(0.03 + 2.5)\), the parentheses around \(0.03 + 2.5\) tell us to focus on this addition first. Solving what is inside the parentheses makes the problem easier to manage as it reduces complexity step by step. By simplifying \(0.03 + 2.5\), we can transform the problem into something simpler for the next step.

Addition

Addition is one of the basic operations in mathematics where we combine numbers to find their total. It is important to perform addition carefully, especially when working with decimals, to ensure accurate results. Let's see this in action with our given expression.

Inside the parentheses of our problem \(2.02(0.03 + 2.5)\), we need to add \(0.03\) to \(2.5\). Adding these two numbers gives us \(2.53\).

• Start by lining up the decimals to ensure a clear and accurate addition process.
• Perform the addition from right to left, just like when adding whole numbers.
• Don’t forget to place the decimal point in the result—this is crucial in decimal addition.

Once you have the correct sum, you can move on to the next step in solving the expression.

Multiplication

After simplifying the expression inside the parentheses, the final step is to perform the multiplication. Multiplication is the operation of scaling one number by another. It is essential to understand it as repeated addition, but with more complex numbers and decimals, multiplication becomes necessary.

In our expression \(2.02 \times 2.53\), there are two numbers to multiply. Approaching this can be done in several ways:

• You can use a calculator for a quick and precise result, especially useful with decimals.
• Or, if doing it by hand, set up the long multiplication. Line up the numbers and multiply as you would with whole numbers, careful to account for the decimal places.

This step results in \(5.1106\).

Remember to always check the decimal places in your answer, ensuring they match the total number of decimal places from the numbers you multiplied. This ensures the final product is accurate, maintaining the integrity of your calculations.