Problem 14 - Algebra 1: Concepts and Skills

Question

Use the properties of addition to find the sum. $$ -3+0+7 $$

Step-by-Step Solution

Answer

The sum of -3, 0, and 7 is 4.

Step 1: Identity Property of Addition

The identity property of addition states that the sum of any number and zero is that number itself. So, -3 + 0 remains -3.

Step 2: Apply Commutative Property

The commutative property means that the order in which numbers are added does not affect the sum. Therefore, we can write -3 + 0 + 7 as -3 + 7.

Step 3: Solve

Adding -3 and 7 gives us a result of 4.

Key Concepts

Identity Property of Addition

The identity property of addition is a simple yet fundamental concept in mathematics. It states that any number added to zero remains unchanged. This property helps us understand how zero behaves in arithmetic operations. For example, when we add 0 to -3, our result remains -3.

• Example: 5 + 0 = 5
• Example: -4 + 0 = -4

This property is crucial because it tells us that adding zero does not affect the sum, making it easier to calculate and understand other mathematical operations.

Commutative Property of Addition

The commutative property of addition allows us to rearrange the numbers we are adding without changing the result. This means the sum will be the same no matter the order in which you add the numbers.

For example, with -3 + 0 + 7, you can reorder and still get the same result, -3 + 7.

• Example: a + b = b + a
• Example: 1 + 2 = 2 + 1

Changing the order can often simplify problems, making calculations easier to manage.

Arithmetic Operations

Arithmetic operations are basic math functions that include addition, subtraction, multiplication, and division. They are the foundation for more complex math topics.

Addition, such as shown in the exercise, is the process of calculating the total of two or more numbers. Understanding properties of addition, like the identity and commutative properties, makes performing arithmetic operations easier and more intuitive. These properties help solve problems faster and with greater accuracy.

• Performing addition: Combining numbers
• Useful properties: Identity, commutative

Mastering arithmetic operations is essential for tackling more advanced math concepts.