Problem 15 - Algebra and Trigonometry

Question

\(13-20=\) Evaluate the expression. $$ \left(\begin{array}{c}{100} \\ {98}\end{array}\right) $$

Step-by-Step Solution

Answer

The value of the expression is \(-7\).

Step 1: Understanding the Problem

First, we need to evaluate the expression \(13 - 20\). This involves a simple subtraction operation between two integers, where 13 is subtracted from 20.

Step 2: Perform the Subtraction

Now, perform the subtraction \(13 - 20\). When subtracting a larger number (20) from a smaller number (13), the result is a negative number. Thus, \(13 - 20 = -7\).

Key Concepts

Subtraction

Subtraction is one of the fundamental operations in arithmetic. It involves taking away a number from another number. In its simplest form, subtraction is about determining the difference between two numbers.
When we subtract, the number we start with is called the minuend, and the number we take away is the subtrahend. The result of the subtraction is called the difference.
For instance, in the problem \(13 - 20\), 13 is the minuend and 20 is the subtrahend. When we subtract 20 from 13, we're determining how much less 13 is than 20. This brings us to the result of -7, the difference.

• Subtraction can be thought of as the opposite of addition.
• It is an arithmetic operation that can be used across various scenarios, from simple calculations to solving complex equations.

Understanding subtraction helps us find out the difference in many contexts, including time, length, and other measurements.

Negative Numbers

Negative numbers are numbers less than zero. These are used to express values below zero, such as temperatures, debts, or levels below sea level. In the expression \(13 - 20\), we subtract a larger number from a smaller one, resulting in a negative number, -7.
When dealing with negative numbers, it's essential to understand that they have a direction. A positive number is like moving forward, while a negative number is like moving backward. In this way, -7 represents 7 steps backward from zero.

• Negative numbers are usually represented with a minus sign in front of them, for example, -1, -2, -3, etc.
• On a number line, negative numbers appear to the left of zero.
• They are fundamental in various fields, including mathematics, science, and engineering.

Getting comfortable with negative numbers is crucial, as they are present in many real-world situations and help us understand a range of concepts.

Integers

Integers are a set of numbers that include all whole numbers, both positive and negative, along with zero. They do not include fractions or decimals.
In the expression \(13 - 20 = -7\), all the numbers involved (13, 20, and -7) are integers. This illustrates how integers can be both positive and negative.

• Positive integers include numbers like 1, 2, 3, and so on.
• Negative integers include numbers like -1, -2, -3, and so forth.
• Zero is also considered an integer.

Integers are essential in mathematics because they provide a complete picture of numbers without any fractions or decimals, making calculations straightforward. Their properties are used not only in everyday arithmetic but also in more complex areas such as algebra and number theory.