Question

Perform the indicated operations. Give exact answers. \(3.8-1.3=\) ______

Short answer

The exact answer is 2.5.

Step-by-step solution

Understand the Operation

The exercise is asking us to perform a subtraction operation. We have the numbers 3.8 and 1.3, and we need to subtract 1.3 from 3.8.

Align the Decimals

To make the subtraction easier, align the two numbers by their decimal points:\[\begin{align*}3.8 \-1.3 \end{align*}\]

Perform the Subtraction

Starting from the rightmost digit (tenths place), subtract 3 from 8, which gives 5.\[\begin{align*}3.8 \-1.3 \\hline2.5 \end{align*}\]

Verify the Calculation

Quickly verify the subtraction by performing the reverse operation: add 2.5 and 1.3. If the result is 3.8, then the subtraction is correct: \[2.5 + 1.3 = 3.8\]This confirms the subtraction was done correctly.

Key concepts

Subtraction

Subtraction is a fundamental arithmetic operation where you take away a value from another value. In essence, it answers the question: "How much is left if I remove a certain amount?" When we subtract, we perform a simple operation that reduces the number we start with. For example, subtracting 1.3 from 3.8 tells us how much remains if we have 3.8 and remove 1.3 from it.

Keep in mind that subtraction, like all arithmetic operations, has specific rules you need to follow to get the right answer. These rules include controlling how you carry out the operation and verifying your answer to ensure its correctness.

Place Value Alignment

Aligning decimal numbers by their place value is crucial for carrying out subtraction accurately. When you're subtracting numbers, especially those with decimals like 3.8 and 1.3, aligning the digits according to the decimal point ensures you're subtracting equivalent place values.

Here's how to align the numbers for our example:

• Write the first number (3.8) above the second number (1.3).
• Ensure the decimal points are directly above one another.
• Fill in any empty spaces with zero if needed to keep digits lined up correctly.

With proper alignment, each digit in one number aligns with the corresponding digit in the other number, allowing for a smooth and error-free subtraction.

Basic Math Skills

Developing strong basic math skills can make tasks like subtraction much simpler. These skills include understanding how numbers work and how basic operations like addition, subtraction, multiplication, and division relate to each other.

When subtracting numbers such as 3.8 and 1.3, start by understanding the individual digits' values and how they contribute to the whole number. For instance, recognizing that in 3.8, the digit 3 is in the 'ones' place and 8 is in the 'tenths' place.

By practicing these basic skills, you'll learn to tackle subtraction problems more confidently and know how to check your answers, as in our example, by verifying the subtraction with the inverse operation—addition.

Decimal Calculations

Decimal calculations can sometimes feel a bit intimidating, but they're really just an extension of whole number arithmetic. Understanding decimals involves recognizing that they are parts of a whole, much like fractions.

When performing operations such as subtraction with decimals, remember to:

• Line up the decimal points to ensure that you're working with the correct place values.
• Apply the same subtraction rules as you would with whole numbers, but keep an eye on the decimal places.

In our example of subtracting 1.3 from 3.8, after aligning the decimals, you subtract as you normally would, carefully keeping the decimal point in your result in the correct place. Completing the operation shows the result is 2.5, demonstrating the importance of accurate decimal calculations.