Problem 44 - Introductory and Intermediate Algebra for College Students 4th

Question

Perform the indicated subtraction. $$1.4-(-1.4)$$

Step-by-Step Solution

Answer

The answer is 2.8

Step 1: Identify the double negative

In the expression \(1.4 - (-1.4)\), the term \(-(-1.4)\) is a double negative. In mathematics, a double negative turns into a positive.

Step 2: Turn the double negative into a positive

Replace \(-(-1.4)\) with \(+1.4\). So the original expression \(1.4 - (-1.4)\) becomes \(1.4 + 1.4)\.

Step 3: Perform the addition

Now add these two numbers together. \(1.4 + 1.4\) equals to \(2.8\)

Key Concepts

Understanding Subtraction

Subtraction is a fundamental mathematical operation that involves taking away a number from another. Often represented by the minus sign \(-\), subtraction is used to find the difference between two numbers. In simple terms, if you have a certain amount and you "subtract" something, you are removing part of that amount.
For example:

• In the equation \(5 - 3 = 2\), you start with 5 and remove 3, leaving you with 2.
• Subtraction is the opposite of addition, which means you can think of taking away something from a total.

In problems involving double negatives, as in the exercise above, subtraction can sometimes transform expressions into addition. This is because subtracting a negative is the same as adding a positive. So, understanding subtraction helps you identify when subtraction becomes addition due to double negatives.

Exploring Positive Numbers

Positive numbers are numbers greater than zero, represented without a sign, or with a plus sign \(++\). These numbers indicate a value to the right of zero on the number line.

• Positive numbers are important because they tell us how much of something there is.
• They are straightforward to work with when it comes to operations like addition and multiplication.

In the example \(1.4 - (-1.4)\), the subtraction is applied to a negative number. However, when two negatives (\(-(-)\)) come together, they create a positive number. This results in turning the problem into an easier addition problem, adding two positives \(1.4 + 1.4\).
Recognizing positive numbers and converting double negatives into positives simplifies calculations and helps ensure accurate results.

Mastering Addition

Addition is the process of calculating the total or sum of two or more numbers or quantities. It's often symbolized by a plus sign \(+\), and it's one of the simplest and most commonly used operations in mathematics.
In addition:

• You combine numbers to increase their total value.
• It works well with positive numbers, as they are added to get a bigger number.

In the exercise given, after transforming the double negative into a positive, you perform the addition \(1.4 + 1.4\).
This gives a result of \(2.8\), demonstrating how addition helps bring together amounts. Understanding how to add correctly is crucial in all areas of math, from simple arithmetic to more complex calculations.