Problem 33 - Beginning and Intermediate Algebra

Question

Find each sum. $$ -2.34+(-3.67) $$

Step-by-Step Solution

Answer

-6.01

Step 1: Identify the terms

Locate the numbers to be added: -2.34 and -3.67.

Step 2: Recognize the sign

Notice that both numbers are negative. When adding two negative numbers, the sum will also be negative.

Step 3: Add the magnitudes

Ignore the negative signs for now and just add the absolute values (magnitudes) of the numbers: 2.34 + 3.67

Step 4: Perform the addition

Calculate the sum: 2.34 + 3.67 = 6.01

Step 5: Apply the negative sign

Since both original numbers were negative, their sum will also be negative. Therefore, the final answer is: -6.01

Key Concepts

Absolute Value

Absolute value refers to the distance a number is from zero on the number line, regardless of direction.
For example, the absolute value of both 3 and -3 is 3.
It's always a non-negative value.
When solving problems involving negative numbers, you often deal with absolute values to simplify your calculations.

How To Find Absolute Value

• Look at the number in question.
• Ignore the sign (whether positive or negative).
• The resulting number is the absolute value.

For instance, the absolute value of both -2.34 and 2.34 is 2.34.
This concept is particularly useful when dealing with addition or subtraction of negative numbers as it allows you to focus on the magnitude of the numbers involved.

Negative Numbers

Negative numbers are numbers less than zero.
They are usually represented with a minus sign (-).
For example, -1, -2, and -2.34 are all negative numbers.

Why Are Negative Numbers Important?

• They help us represent losses, deficits, and temperatures below zero.
• They follow specific rules when performing arithmetic operations.

When adding two negative numbers, like -2.34 and -3.67, you add their absolute values first:
2.34 + 3.67 = 6.01.
After finding the sum of the absolute values, you reapply the negative sign to the result.
So, -2.34 + (-3.67) equals -6.01.

Understanding how to handle negative numbers is crucial for solving real-world problems and more complex math problems.

Addition of Decimals

Adding decimals involves aligning the decimal points and then performing the addition as you would with whole numbers.

Steps for Adding Decimals:

• Write down the numbers, aligning their decimal points.
• Fill in any empty spaces with zeros to ensure every column has a digit.
• Add each column starting from the rightmost digit, moving to the left.
• If necessary, carry over extra digits.

For example, to add 2.34 and 3.67, you align the decimal points:
2.34
+3.67
-----
6.01
Perform the addition column by column (right to left) and the sum is 6.01.

In the context of adding negative decimals, like -2.34 and -3.67, you follow the same steps for addition but remember to reapply the negative sign to your final answer.