Problem 31 - Prealgebra

Question

Perform the following operations according to the rule for order of operations. $$0.05(0.02+0.03)$$

Step-by-Step Solution

Answer

The result is 0.0025.

Step 1: Solve Parenthesis

According to the order of operations, we start with calculations inside parentheses. We have \(0.02 + 0.03\). Add these two numbers together: \(0.02 + 0.03 = 0.05\).

Step 2: Multiply

Now, multiply the result from Step 1 by \(0.05\). So, we have \(0.05 \times 0.05\). Perform the multiplication: \(0.05 \times 0.05 = 0.0025\).

Key Concepts

Parentheses

When you encounter an equation with parentheses, it's a signal to solve whatever is inside them first. In math, this is a rule we call the "order of operations". It's like following a recipe step by step to get the intended dish. If we solve things out of order, we might get different results!

The equation in our exercise starts with a parentheses: \(0.02 + 0.03\). By handling this first, we simplify the equation. Think of parentheses as deal-makers in math—they bring terms together, ensuring they are solved before other operations. In our example, once we solve \(0.02 + 0.03\) to get \(0.05\), we can then proceed with the next step.

Multiplication

Once you have solved what's inside the parentheses, you move to multiplication. This operation is one of the main building blocks of math, allowing us to combine equal groups into a total sum. Multiplication is often faster and more efficient than repeated addition.

• Multiplication can represent repeated addition.
• It is used to find the total number of items in equal-sized groups.

In this exercise, we multiply the result from the parentheses \(0.05\) by \(0.05\). Multiplication is straight forward but requires careful handling of decimals, as it can affect the entire solution.

Decimals

Decimals are special types of numbers used to express parts of a whole, similar to fractions. They are important because they allow for more precision. When multiplying decimals, you must keep track of the decimal places to ensure accuracy.

In our problem, both numbers involved in the multiplication are decimals—\(0.05\) and \(0.05\). The trick is to first pretend they are whole numbers and multiply them, ignoring the decimal points temporarily. Then, count how many decimal places there are in both original numbers.

• Each number \(0.05\) has two decimal places (00's).
• Thus, the answer should have four decimal places (0000).

As a result, the final product is \(0.0025\). Handling decimals correctly ensures consistent results, especially in calculations that demand precision!