Problem 92 - Algebra 1: Concepts and Skills

Question

Estimate the answer. Then evaluate the expression. $$ 2.1-0.2 $$

Step-by-Step Solution

Answer

The result of the subtraction 2.1 - 0.2 is 1.9

Step 1: Understand the problem

The task is to subtract 0.2 from 2.1. This involves being careful with decimal points.

Step 2: Perform the Subtraction

To subtract 0.2 from 2.1, line up the decimal points and perform the subtraction. In this case, 2.1 - 0.2 gives 1.9.

Step 3: Verify the Result

Check the result using a calculator or another method to ensure the answer is correct. Here, it can be seen that 1.9 + 0.2 gives the original 2.1, confirming the subtraction operation was done correctly.

Key Concepts

Decimal Subtraction

Subtracting decimals is an essential skill that requires careful alignment of numbers. It is similar to subtracting whole numbers, but you must line up the decimal points to ensure accuracy. Here's how you can master this skill:

First, write down the numbers one above the other with their decimal points aligned. For example, if we take the operation
\[ 2.1 - 0.2 \],
you place the '2.1' on top and '0.2' below it, making sure the decimal points are in a vertical line. Second, proceed to subtract as you would with whole numbers. You may add zeros to the right of the last digit after the decimal point for easier visualization. In our operation, this means subtracting the tenths place (1-0) and noting the result. Lastly, bring the decimal point straight down into your answer. The result of this subtraction will be
\[ 1.9 \].

With practice, subtracting decimals can become as straightforward as subtracting whole numbers.

Estimating Subtraction

Estimating is a useful technique to quickly determine a rough answer without needing the exact result. This can be helpful for checking work or setting expectations for what the answer should be. When estimating the subtraction of decimal numbers, you round each number to the nearest whole number or to a decimal place that is easier to work with.

For instance, with
\[ 2.1 - 0.2 \],
you could estimate by rounding '2.1' down to '2' and '0.2' approximately to '0', and then subtract to get an estimated result of '2'. While this estimated result is not the precise answer, it gives us a ballpark figure and is helpful for double-checking the subsequent exact calculation.

Arithmetic Operations

Arithmetic operations encompass the foundational calculations we use in math: addition, subtraction, multiplication, and division. These are the building blocks for more complex math concepts. Each operation has specific rules and properties that make numbers work in different ways.

In the context of subtraction, which is one of the four main arithmetic operations, it involves taking away one value from another to find the difference. As we've seen with decimal subtraction, following the proper alignment and subtraction rules is key. Mastery of these operations forms a strong basis for more advanced mathematics that students will encounter in the future.

Checking Math Results

Verifying your answers is a crucial step in the problem-solving process. One effective method to check subtraction is by adding the difference back to the subtracted amount. If the result matches the original number, your subtraction is likely correct.

In our example,
\[ 2.1 - 0.2 = 1.9 \],

we can add '0.2' back to '1.9'. Doing this check yields:
\[ 1.9 + 0.2 = 2.1 \],

which confirms our initial number, indicating that our subtraction was correct. This process not only provides confidence in your answer but also reinforces your understanding of the relationship between subtraction and addition.