Problem 12 - Elementary and Intermediate Algebra

Question

Write each of the following in words. $$ 4-(-1) $$

Step-by-Step Solution

Answer

Four plus one.

Step 1: Identify the operation

The given expression is 4 minus negative 1. Notice that the operation between 4 and negative 1 is subtraction.

Step 2: Simplify the expression

Understand that subtracting a negative number is equivalent to adding the absolute value of that number. Thus, 4 - (-1) simplifies to 4 + 1.

Step 3: Convert to words

The simplified expression 4 + 1 can be written out in words as 'four plus one'.

Key Concepts

Subtraction

Subtraction is one of the basic arithmetic operations. It involves taking away a quantity from another quantity. For instance, in the expression 4 - (-1), the operation is subtraction, denoted by the minus sign (-). To understand subtraction better, remember these key points:

• The number before the minus sign is known as the minuend (in this case, 4).
• The number after the minus sign is called the subtrahend (in this case, -1).

In simple terms, subtraction determines how much one number is less than another number.

Negative Numbers

Negative numbers are numbers less than zero. They are denoted by a minus sign (–). For example, -1 is a negative number. Negative numbers can often be tricky, especially when used in operations like subtraction. Here are a few important tips to understand them better:

• A negative number is always less than zero. So, -5 is less than 0.
• When subtracting negative numbers, things can get a little complicated. Remember that two negatives make a positive.

In the given expression, 4 - (-1), you are essentially dealing with two negative signs. Learning how to handle these signs is crucial for simplifying the expression.

Simplification

Simplification is the process of reducing an expression to its simplest form. For example, simplifying 4 - (-1) involves changing the subtraction of a negative number into an addition. Here's how you can think about it:
Subtracting a negative number is the same as adding its absolute value. So, 4 - (-1) can be simplified to 4 + 1. This step makes the expression easier to understand and work with. Simplification helps in solving mathematical problems more efficiently, allowing you to focus on the core arithmetic.

Absolute Value

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is always a non-negative number. The absolute value of -1, denoted as \(| -1 |\), is 1. Think of absolute value as a way to ignore the sign of a number.
This concept is particularly useful when dealing with negative numbers. For example, when simplifying 4 - (-1), you consider the absolute value of -1, which is 1, and then add it to 4. So, the expression becomes 4 + 1.
Understanding absolute values can make many mathematical operations more intuitive, especially those involving negative numbers.