Problem 79 - Elementary and Intermediate Algebra

Question

Perform the operations. $$ -0.9-0.2 $$

Step-by-Step Solution

Answer

The result is -1.1.

Step 1: Understand the Operation Type

The exercise asks to perform subtraction: subtracting 0.2 from -0.9.

Step 2: Rewrite the Expression

Rewrite the subtraction operation as an addition, using the rule that subtracting a positive number is the same as adding its negative. Thus, \(-0.9 - 0.2\) becomes \(-0.9 + (-0.2)\).

Step 3: Add the Numbers

Since both numbers are negative, you combine their absolute values and keep the negative sign. The absolute values are 0.9 and 0.2. Performing the addition gives \(0.9 + 0.2 = 1.1\). Thus, \(-0.9 + (-0.2) = -1.1\).

Key Concepts

Subtraction of Decimals

Subtraction of decimals might seem complex, but it is similar to subtracting whole numbers, with an added step of aligning the decimal points. When you're subtracting decimals, remember these simple steps:

• Align the Decimal Points: Make sure numbers are positioned so that the decimal points are in a vertical line.
• Subtract as Usual: Start subtracting from the rightmost digit, just like regular subtraction.
• Borrow if Needed: If the number being subtracted is larger, you may need to "borrow" from the next left digit.

Let's take the example from the exercise, -0.9 - 0.2. In this case, you're making life a bit easier by changing the operation into addition.

Negative Numbers

Negative numbers can be tricky, but they're just another type of number on the number line, representing values less than zero. When dealing with negative numbers, keep in mind:

• Representation: Negative numbers have a minus sign (-) in front of them, showing they're below zero.
• Number Line: Picture a number line extending to the left from zero. Negative numbers are to the left of zero.
• Absolute Value: The only difference between a negative number and its positive counterpart is the sign. So, the absolute value of -3 is 3.

Having a grasp on the basics of negative numbers is essential in understanding operations involving them.

Adding Negative Numbers

Adding negative numbers involves combining values lower than zero. It's just like regular addition but with a focus on direction and absolute value. Here's a breakdown:

• Combine Absolute Values: When you add two negative numbers, add their absolute values as if they're both positive.
• Keep the Negative Sign: The result retains the negative sign because you're adding negatives, not turning them positive.
• Visualize on a Number Line: Picture moving further left from a negative starting point; you're going deeper into negative territory.
  • For example, -0.9 + (-0.2) has you moving 0.2 units left from -0.9.

Understanding this will help you tackle any addition with negative numbers, making math less intimidating.