Problem 26 - Introductory and Intermediate Algebra for College Students 4th

Question

Perform the indicated subtraction. $$0-(-15)$$

Step-by-Step Solution

Answer

The result of 0-(-15) is 15.

Step 1: Identify the operation

The expression 0-(-15) is identified as a subtraction. But due to the (-15) being subtracted, it becomes a negative subtraction, which is equivalent to a positive addition.

Step 2: Apply the rules of arithmetic operations

Applying the rules of arithmetic operations, the expression 0 - (-15) becomes 0 + 15.

Step 3: Perform the addition

Finally, perform the addition operation of 0 and 15, which is equal to 15.

Key Concepts

Subtraction

Subtraction is one of the basic arithmetic operations and involves taking away or removing something from a quantity. It is usually represented by the minus sign (-). In subtraction, the number from which another number is subtracted is called the minuend, and the number that is subtracted is known as the subtrahend. For example, in the expression 10 - 3, 10 is the minuend and 3 is the subtrahend.

• Subtraction results in a difference, which is the outcome of the operation.
• Subtraction can often be rewritten as addition of the opposite. For example, subtracting a negative number (like in our original exercise) turns the operation into an addition.

Remember, when you come across a subtraction, think about it in the context of removing something, or alternatively, as adding the opposite—especially when negative numbers are involved.

Negative Numbers

Negative numbers are numbers less than zero and usually have a minus sign (-) in front of them. They are commonly used to represent values that are below a defined zero point, such as temperatures below zero degrees, or owing money (debt).

• On the number line, negative numbers lie to the left of zero.
• When you subtract a negative number, it is the same as adding its positive counterpart. For instance, subtracting \(-15\) is equivalent to adding 15.

Understanding negative numbers is crucial because they often change the nature of arithmetic operations. In many cases, they highlight situations where subtraction and addition converge, which can simplify problem-solving.

Addition

Addition is another essential arithmetic operation that involves combining or bringing together quantities. It is symbolized by the plus sign (+). In addition, you're calculating the total or sum of numbers.

• When adding numbers, you line them up and compute their sum.
• Addition is commutative, meaning the order in which you add does not change the result. For example, 3 + 5 is the same as 5 + 3.

A special case occurs when you encounter expressions cleverly transformed from subtraction to addition, as seen in 0 - (-15), which becomes 0 + 15. It illustrates the rule where subtracting a negative amount effectively increases your initial value, as if you were adding.