Problem 88 - Algebra 1: Concepts and Skills

Question

Estimate the answer. Then evaluate the expression. $$ 2.5-0.5 $$

Step-by-Step Solution

Answer

The evaluated result of the expression is 2.0

Step 1: Evaluate the Expression

To evaluate the expression \(2.5 - 0.5\), subtract 0.5 from 2.5. It's a normal subtraction, just keep in mind that you're working with decimal numbers.

Step 2: Effective Subtraction

On subtracting 0.5 from 2.5, we get \(2.0\)

Key Concepts

Estimating Differences

When learning to subtract decimal numbers, estimating differences is a helpful strategy. Estimation allows you to quickly find an approximate result which can serve as a useful comparison to check the accuracy of your actual computation later on. For instance, with the original expression, you have 2.5 and 0.5.

To estimate this, consider rounding each decimal number to the nearest whole number. In this case, 2.5 rounds to 3, and 0.5 rounds to 1. Subtracting these rounded numbers gives an estimated difference:

• 3 minus 1 equals approximately 2.

Thus, even before doing any precise calculation, we can guess that the result should be around 2. Estimation doesn't only make calculations easier, but it provides a quick check to ensure your final answer is reasonable.

Decimal Numbers

Decimal numbers are numbers that include a decimal point to represent a fraction of a whole. They are a vital aspect of everyday math because they help represent values that are not whole, like amounts of money or measurements. Understanding how to work with them involves knowing their structure and how to perform operations like subtraction.
In the case of the expression we are working with, 2.5 and 0.5 are both decimal numbers. Here, the digit before the decimal point represents the whole part, while the digit after represents parts of a whole. For instance:

• In 2.5, the "2" is the whole number part or the ones place.
• The ".5" is the decimal part, meaning five-tenths.

So when subtracting 0.5, it involves using these components properly to maintain precision. It’s often best approached by aligning the decimal points, which helps to subtract correctly as if it was whole numbers.

Evaluating Expressions

Evaluating expressions requires executing the operations like addition, subtraction, multiplication, or division to find the value of an expression. Here, the expression is a simple subtraction for decimal numbers: 2.5 - 0.5. This involves understanding how to operate on decimals, as we do with whole numbers.
When we subtract 0.5 from 2.5, it requires these steps:

• Align the decimal points of both numbers: 2.5 and 0.5.
• Subtract each digit starting from the rightmost side (tenths place in this case) like regular subtraction.
• Here, 5 subtracts from 5 resulting in 0 in the tenths place.
• Next, subtract the whole number parts: 2 minus 0 giving us 2.0.

Hence, the evaluated expression ends up being 2.0, demonstrating that dealing with decimal subtraction closely follows fundamental subtraction rules, just with additional consideration for the decimal point alignment.