Problem 13 - Algebra and Trigonometry

Question

\(13-20=\) Evaluate the expression. $$ \left(\begin{array}{l}{6} \\ {4}\end{array}\right) $$

Step-by-Step Solution

Answer

-7

Step 1: Understanding the Expression

We start with the expression \(13 - 20\). This is a subtraction problem where a smaller number (13) is subtracted by a larger number (20). Our goal is to evaluate this expression.

Step 2: Performing Subtraction

In this step, we calculate \(13 - 20\). Since 20 is larger than 13, we will end up with a negative result. Specifically, subtracting larger numbers from smaller numbers results in a negative difference. So, \(13 - 20 = -7\).

Key Concepts

Subtraction

Subtraction is one of the basic operations in arithmetic, and it represents the process of taking away one quantity from another. When you see an expression like \( 13 - 20 \), it's asking you to find out how much 13 is smaller than 20. Unlike addition, where numbers are combined, subtraction focuses on the difference between numbers.

Here's a simple way to understand subtraction:

• Identify the minuend: the number you start with, which is 13 in this case.
• Identify the subtrahend: the number to be taken away, which is 20 here.
• Subtract the subtrahend from the minuend.

If the minuend is smaller than the subtrahend, as in this case, the difference will be a negative number. Remember, the order of numbers is crucial in subtraction.

Negative Numbers

Negative numbers are numbers less than zero, and they have a minus sign (-) in front of them. Think of negative numbers as steps below zero on a number line. When dealing with subtraction, if your result is a negative number, it simply means you've moved below zero.

In our expression \( 13 - 20 \), we are subtracting a larger number from a smaller one, leading to a negative difference of \(-7\). This indicates that if you start at 13 and subtract 20, you go 7 steps beyond zero into the negative zone. Negative numbers are essential in real life for understanding debts, temperatures below freezing, and other situations where quantities drop below a baseline.

• Negative numbers are opposite to positive numbers.
• They represent a deficit or a loss when used in arithmetic expressions.
• Always treat the minus sign as an indicator of direction or loss.

Arithmetic Expressions

Arithmetic expressions are combinations of numbers and operations (like addition, subtraction, multiplication, and division) that produce a value. These expressions follow mathematical rules to be evaluated correctly.

With expressions like \( 13 - 20 \), you're dealing with a simple arithmetic expression focusing on subtraction. To evaluate it, you must understand the operation involved and the order in which to perform it.

• Identify the operation: Subtraction, in this case.
• Follow the order: Left to right for subtraction and addition, respecting any parentheses or special rules like PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction).

Evaluating arithmetic expressions requires careful attention to these operations to arrive at the correct answer. In more complex scenarios, multiple operations will need to be considered with appropriate priority.