Problem 47 - Elementary Algebra

Question

Find the sums. \(0+(-4)\)

Step-by-Step Solution

Answer

Answer: The sum of 0 and -4 is -4.

Step 1: Identify the numbers to be added

The numbers to be added in this exercise are \(0\) and \(-4\).

Step 2: Add the numbers

Add the numbers together: \(0 + (-4) = -4\).

Step 3: Write the final result

The sum of \(0\) and \(-4\) is \(-4\).

Key Concepts

Understanding Negative Numbers

Negative numbers are numbers less than zero. They are often represented with a minus sign (-). If you think about a number line, negative numbers are placed to the left of zero. They are commonly seen in everyday situations, such as temperatures below freezing or financial debt.
Negative numbers can also be tricky when performing arithmetic operations like addition and subtraction. For example, when you add a negative number, it is the same as moving left on the number line. So, if you add -4 to zero, you end up at -4 on the number line. This process is useful to understand when tackling operations involving negative values.

Basic Arithmetic: Addition Involving Negative Numbers

Basic arithmetic is made up of simple mathematical operations like addition, subtraction, multiplication, and division. In this section, we'll focus on addition, especially involving negative numbers.
When adding a positive and a negative number, you essentially subtract the smaller absolute value from the larger one and take the sign of the larger number. For instance, adding 0 and -4:

• Start by comparing 0 and -4.
• Since -4 is negative and there is no positive part to subtract, the result is simply -4.

This may seem counterintuitive at first, but practice makes perfect. Always refer back to the number line if you're unsure. Remember, the direction on the number line shows you whether to move left (negatives) or right (positives).

The Zero Property

The zero property of addition states that any number plus zero is the number itself. Zero is known as the additive identity because it does not change the value of the number it is added to.
For example, if you add zero to any whole number, such as 5 or -4, the result remains the same:

• 5 + 0 = 5
• 0 + (-4) = -4

Understanding this property helps simplify calculations and reinforces the concept of zero's neutral role in arithmetic. It is a powerful tool for verifying steps in more complex math problems.