Problem 76 - Beginning and Intermediate Algebra

Question

Find each difference. $$ -4.4-8.6 $$

Step-by-Step Solution

Answer

-13.0

Step 1: Understand the Problem

The task is to find the difference between two numbers, -4.4 and 8.6.

Step 2: Set Up the Equation

Write the equation to represent the problem: \[-4.4 - 8.6\]

Step 3: Combine Like Terms

Since both numbers are negative, add their absolute values and keep the negative sign: Absolute value of -4.4 is 4.4.Absolute value of -8.6 is 8.6.Add these two values together: \[4.4 + 8.6 = 13.0\]

Step 4: Apply the Negative Sign

Since both original numbers are negative, the result will also be negative: \[-13.0\]

Step 5: State the Final Answer

The difference between -4.4 and 8.6 is -13.0.

Key Concepts

absolute value

Absolute value is a fundamental concept in mathematics. The absolute value of a number is the distance between that number and zero on a number line. This distance is always a non-negative number. For example, the absolute value of -4.4 is 4.4 because it is 4.4 units away from zero. Similarly, the absolute value of 8.6 is 8.6.

When you see the absolute value symbol \(\textbar \cdot \textbar\), it denotes that only the magnitude or size of the number matters, not its sign. This makes the absolute value crucial in simplifying expressions and solving equations involving negative numbers.

In our exercise, understanding absolute values helped in adding the magnitudes of -4.4 and 8.6 together to find the difference.

negative numbers

Negative numbers can sometimes be tricky to work with. These are numbers that are less than zero and are typically expressed with a minus sign (-).
When you subtract a negative number, you are essentially adding its absolute value. For instance, in the problem \(-4.4 - 8.6\), subtracting 8.6 from -4.4 means you have to add the absolute values of both numbers because they are both negative.

The concept here is to treat the subtraction of a negative as the addition of its absolute value. This makes -4.4 - 8.6 translate into -(4.4 + 8.6), which sums up to -13.0 as per our solution. Remember, adding two negative numbers results in a more negative sum.

combining like terms

Combining like terms is a method used to simplify expressions and equations in algebra. Like terms are terms that have the same variable raised to the same power, but for numbers without variables, it's straightforward.

In our specific exercise, both -4.4 and 8.6 are like terms because they are real numbers. The process involves handling their signs and absolute values to combine them correctly.

The absolute values of -4.4 and 8.6 are 4.4 and 8.6, respectively. Adding them together (because they are negative, you add their absolute values) gets you 4.4 + 8.6 = 13.0. Finally, since the terms were negative, the result retains the negative sign, yielding -13.0.

Mastering the skill of combining like terms is essential for simplifying equations and solving mathematical problems efficiently.