Problem 46 - Elementary Algebra

Question

Find the sums. \(0+(-12)\)

Step-by-Step Solution

Answer

Answer: The sum is -12.

Step 1: Identify the numbers to be added

In this exercise, the numbers to be added are \(0\) and \((-12)\).

Step 2: Apply the properties of addition

When adding a positive number and a negative number, we can think of it as moving on a number line. In this case, we start at 0 and move to -12 spots to the left on the number line.

Step 3: Find the sum

Since we started at 0 and moved to -12, the sum is \(-12\). So the answer is: \(0+(-12)=(-12)\).

Key Concepts

Number Line

A number line is a straight horizontal line that helps us understand numbers and arithmetic operations visually. It has numbers placed at equal intervals along its length. The center of the number line is usually marked with zero, and numbers extend to the positive on the right and the negative on the left.

• Starting at 0: To solve addition problems, we need to know where to start. For example, starting at zero is like placing your finger on the zero point of a ruler.


• Moving Direction: Movement to the right indicates adding positive numbers, while movement to the left signifies adding negative numbers. In our exercise, moving left (0 to -12) means adding a negative number.

Visualizing math on a number line makes it easier to see the steps and conclusion. So, when you add 0 and -12 on a number line, you start at 0 and move 12 units to the left to arrive at the solution -12.

Negative Numbers

Negative numbers are less than zero and represented with a minus (-) sign. They are found on the left side of the number line. Understanding their role in arithmetic is essential for working with real-world scenarios, such as debts or temperature below zero.

• Identifying Negative Numbers: When you see numbers like -5 or -12, these are negative numbers.


• Interpreting Negative Moves: In the number line, moving left corresponds to reaching a lower value.

In our example, adding -12 to 0, signifies moving into negative territory on the number line, which simply reaches -12. This understanding is crucial when dealing with real-life problems, such as calculating losses or decreases.

Properties of Addition

Addition has several properties that simplify arithmetic tasks. These properties are crucial in understanding how numbers interact when combined. Let's explore a few key properties:

• Commutative Property: This property states that the order in which you add two numbers does not affect the result. For example, 2+3 is the same as 3+2.


• Associative Property: For any numbers a, b, and c, the way numbers are grouped in addition does not change their sum. For instance, (1+2)+3 equals 1+(2+3).


• Identity Property: Adding 0 to any number does not change the value. This property is directly applied in our exercise when we add 0 to -12 to get -12.

These properties provide a basis for more complex calculations and underline the consistency of addition operations. By embracing these principles, mathematics becomes a predictable and more manageable field.