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Chapter 1: Problem 21

Determine which property of addition is depicted by the given identity. $$ 79+0=79 $$

Short Answer

Expert verified
The property is the Additive Identity Property.

Step by step solution

01

Understanding the Identity

The expression given is \( 79 + 0 = 79 \). We need to identify which property of addition this equation represents.
02

Identifying the Property

In the equation \( 79 + 0 = 79 \), we observe that adding 0 to any number does not change the value of that number. This is one of the fundamental properties of addition.
03

Addition Property

The property depicted in the expression \( 79 + 0 = 79 \) is called the Additive Identity Property. This property states that adding zero to any number results in the original number itself, demonstrating the unique role of zero in addition as the identity element.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Additive Identity
When you hear about the Additive Identity, zero is the star of the show. The concept of additive identity is all about how zero interacts with other numbers when it comes to addition. So, what does that mean? Simply put,
  • Additive Identity refers to zero being the number that, when added to any other number, leaves the original number unchanged.
  • If you have, let's say, the number 79, and you add 0, you're still going to have 79鈥攋ust like magic, but with math!
  • Mathematically: if you add 0 to any number \( a \), expressed as \( a + 0 \), the result is \( a \).
Zero is special in this way because it doesn't alter the identity of the number it's added to. That's why it's called the "additive identity." Anytime you see an equation like \( x + 0 = x \), it's showcasing this property.
Fundamental Properties
Understanding fundamental properties in mathematics helps us handle numbers better, making math straightforward and predictable. Among these foundation bricks are properties of addition, crucial for calculations and solving mathematical problems systematically.
  • Commutative Property: It states that changing the order of numbers when adding does not affect the sum, such as \( a + b = b + a \).
  • Associative Property: This tells us that how numbers are grouped in addition doesn't change the total, meaning \( (a + b) + c = a + (b + c) \).
  • The star of our show today, the Additive Identity Property: Shows us that adding zero to any number keeps the number unchanged (as in \( a + 0 = a \)).
These fundamental properties are tools that help in simplifying algebraic equations and calculations, ensuring we work accurately and efficiently.
Identity Element
The term identity element might sound complicated, but it's quite simple when you break it down. In mathematics, an identity element for an operation is a number that doesn't change other numbers in that operation. For addition, this miracle number is zero.
  • When we say zero is an identity element for addition, we mean adding zero to any number doesn't change its identity.
  • This is why we use the term "identity" to describe zero鈥檚 role in this scenario. It's like a mirror, reflecting the original number unchanged.
Take the expression \( 79 + 0 = 79 \). Here, zero confirms its role as the identity element in addition. Remembering that every main math operation has an identity can make things easier as you learn more complex math concepts. For multiplication, this identity element would be one since any number multiplied by one remains the same.

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