Problem 56 - Prealgebra

Question

Perform the indicated operations. $$2+0.75$$

Step-by-Step Solution

Answer

2 + 0.75 equals 2.75.

Step 1: Understand the problem

The problem asks us to perform the simple arithmetic operation of addition between two numbers: the whole number 2 and the decimal number 0.75.

Step 2: Align the numbers

To add 2 and 0.75 together, align them by their decimal points. In this case: 2.00 (this is 2 written with decimal places for alignment) +0.75

Step 3: Perform the addition

Add the numbers starting from the rightmost digit. First, add the thousandths place: 0.00 + 0.75 = 0.75. Thus, the result is 2.75.

Key Concepts

Arithmetic Operations

Arithmetic operations form the core of basic mathematical calculations. These operations include addition, subtraction, multiplication, and division. In the problem given, we are dealing with the addition operation, which is one of the simplest.
Addition involves combining numbers to get a total. Numbers can be whole numbers, decimals, or fractions. In this context, we have a whole number and a decimal number to add together.
Understanding the nature of the numbers involved and the operation required is crucial. When you see an addition problem like \(2 + 0.75\), know it requires simply combining the values of these numbers to get the sum.

• Identify the numbers clearly.
• Understand what operation to perform - in this case, addition.
• Know how to combine whole numbers with decimals.

These basics set the foundation for successfully tackling the problem.

Aligning Decimals

One crucial step when adding decimals, is ensuring the numbers are aligned correctly. This means making sure the decimal points are in a vertical line when setting up your problem to solve. Misalignment can easily lead to incorrect answers.
Why is aligning important? Because it ensures that each digit is in the correct place value. Here's how you do it:

• Write the numbers down vertically, ensuring the decimal points are directly above each other.
• Fill in with zeroes as placeholders if necessary.
• Make sure each digit is in its correct position: ones under ones, tenths under tenths, etc.

This helps in keeping your columns neat and ensures the addition is performed correctly. In our problem, by writing \(2\) as \(2.00\), we aligned it with \(0.75\), making it straightforward to proceed with the operation.

Performing Addition

Once the numbers are aligned by their decimal points, the next step is to perform the addition. Start from the smallest decimal place on the right and proceed to the left, just like you do with whole numbers.
When you add, consider each column separately. In this example, you add \(0\) (from 2.00) to \(5\) in the hundredths place, \(0\) to \(7\) in the tenths place, and finally \(2\) to \(0\) in the ones place.
The resulting sum, \(2.75\), combines all digits and carries over any necessary values, just like in whole number addition. Remember:

• Start from the rightmost place value and move to the left.
• Add each column, carrying over values if the sum exceeds 9.
• Keep an eye on the decimal point place – it should stay aligned in your result.

With practice, adding decimals becomes as smooth as adding whole numbers, ensuring accuracy every time.