Problem 36 - Prealgebra

Question

Perform the following operations according to the rule for order of operations. $$(9.2+0.01)(3.5+0.03)$$

Step-by-Step Solution

Answer

The result of the operation is 32.5113.

Step 1: Simplify Inside Parentheses

First, simplify inside the parentheses by performing the additions: \(9.2 + 0.01 = 9.21\) and \(3.5 + 0.03 = 3.53\).

Step 2: Multiply the Results

Now multiply the results from the simplified expressions:\(9.21 \times 3.53\).

Step 3: Calculate the Product

To find the product of \(9.21\) and \(3.53\), multiply them: \(9.21 \times 3.53 = 32.5113\).

Key Concepts

Addition

Addition is one of the fundamental operations in arithmetic. It is the process of finding the total or sum by combining two or more numbers. In the given problem, you are tasked with adding numbers inside parentheses first, according to the rule of order of operations. This is important because doing addition before other operations, like multiplication, can greatly affect the final result.

When adding numbers like in the expression \(9.2 + 0.01\), you simply align the decimal points and add each corresponding digit. In this case:

• Align the numbers by their decimal point
• Start adding from the rightmost digit
• For 9.2 and 0.01, the sum is 9.21

This shows how small numbers, like a hundredth, can influence the result. Double check your additions to ensure accuracy in subsequent operations.

Multiplication

Once you've simplified the expressions inside the parentheses, the next step involves multiplication. Multiplication is essentially repeated addition but follows its pattern of operation rules. In our exercise, you multiply two results from inside the parentheses: \(9.21 \times 3.53 \).

Here's how to tackle it:

• Write the numbers vertically with 9.21 on top over 3.53
• Multiply each digit in 3.53 by each in 9.21, remembering to keep decimal places in line
• Add up these products according to their place value
• Make sure to include decimal places in the final result

This gives us a multiplication result, which, when done accurately, yields a final answer of 32.5113. You might find it helpful to use a calculator to verify if your manual computations match this result.

Simplifying Expressions

Simplifying expressions is about making calculations easier to handle by performing operations in a structured way. This involves following the "PEMDAS/BODMAS" rule, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). It's crucial in ensuring the accuracy of mathematical operations.

In our example, the problem starts with simplifying expressions inside parentheses. This means doing the additions first before multiplying. This step-by-step approach not only reduces errors but also simplifies the problem into smaller, more manageable parts.

• Always simplify expressions inside parentheses first
• Follow the order of operations strictly
• Recheck each calculation at each step for consistency

Once each part is simplified, you can combine them to get the final simplified product. By practicing this process, you train yourself to see complex expressions as a series of simpler problems. This is a vital skill in mathematics and everyday calculations.