Problem 106 - Prealgebra

Question

Simplify. $$y+0$$

Step-by-Step Solution

Answer

The expression simplifies to \(y\).

Step 1: Understand the Addition with Zero

When we add zero to a number or a variable, the value of the number or variable remains unchanged. This is because zero is an identity element for addition.

Step 2: Apply the Rule to the Given Expression

Given the expression \(y + 0\), apply the identity property of addition, which states that \(x + 0 = x\). Therefore, \(y + 0\) simplifies to \(y\).

Key Concepts

Addition

Addition is one of the most fundamental concepts in mathematics. It involves combining two or more numbers to find their total or sum. When we talk about addition in a mathematical expression, we are looking at how to combine the values together. This operation is signified by the plus sign "+".

For example, in the equation \(3 + 4 = 7\), three and four are added to get a total of seven. Addition can involve numbers, variables, or a combination of both.

• Numbers: Adding numbers like 5 + 2 = 7.
• Variables: In expressions like \(x + y\), where \(x\) and \(y\) are variables, the operation suggests combining them based on their values.

When adding zero, as we will see in the next section, a special rule applies which simplifies expressions easily.

Zero as Identity Element

Zero holds a unique place in the number system when it comes to addition. Known as the 'identity element' for addition, zero has a special property:

Adding zero to any number or variable doesn't change its value. This property is called the identity property of addition and can be represented as \(x + 0 = x\). For any number or variable \(x\), when you add zero, you simply get \(x\) again.

• \(5 + 0 = 5\)
• \(x + 0 = x\)

Recognizing zero as the identity element helps make computations quicker and is a fundamental property used in algebra to simplify equations and expressions.

Simplification of Expressions

Simplifying expressions is an important skill in algebra. It involves making an expression more straightforward or reducing it to its simplest form. By applying mathematical rules and properties, we can make expressions easier to work with.

One common method of simplification involves using the identity property of addition. For instance, in the expression \(y + 0\), recognizing that zero is the identity element allows us to simplify it to \(y\). This is because adding zero doesn't change the value.

Here are general steps to simplify expressions using this property:

• Identify the presence of zero added to a number or variable.
• Use the identity property to eliminate zero from the expression.
• Write the final simplified form.

By understanding these methods, reducing expressions becomes more intuitive and less time-consuming.