Problem 62 - Algebra 1: Concepts and Skills

Question

Evaluate the expression for the given value of the variable. \(3 y\) when \(y=0\)

Step-by-Step Solution

Answer

The expression '3y' when y=0 is equal to 0.

Step 1: Substituting the given value

Replace 'y' with 0 in the expression '3y', which gives us '3 * 0'.

Step 2: Simplification

Multiply 3 and 0 together. The multiplication of any number by zero results in zero.

Key Concepts

Substitution

Substitution is a fundamental concept in algebra. It involves replacing a variable with a given number to simplify and solve expressions or equations. In the provided exercise, the expression is \(3y\) where \(y\) is the variable. We know from the exercise that \(y=0\).
When substituting, simply replace every occurrence of \(y\) with the number 0. Once the substitution is done, the expression \(3y\) becomes \(3 \times 0\). This allows us to move forward to further simplify and evaluate the expression.
Substitution helps by removing the variable from the equation, transforming it into a more straightforward arithmetic operation involving plain numbers. This process is very useful not only for simple expressions like this one but also for more complex equations that you may encounter in algebra and beyond.

Multiplication by Zero

Multiplying by zero is a straightforward but crucial part of arithmetic and algebra. The rule is simple: any number multiplied by 0 equals 0. This property can help solve not only algebraic expressions but also complex equations.
In our given expression, once we've substituted \(y=0\) into \(3y\), we end up with \(3 \times 0\). According to the multiplication property of zero, the product is 0.
This property remains true regardless of how large or complex the initial number is. Whether it's 3, 1000, or even larger numbers, multiplying these by zero will always result in zero. This simplification technique is especially useful when dealing with polynomials, where terms containing zero can simplify entire sections of an expression or equation.

Evaluation of Expressions

Evaluating an expression means finding out what it is worth by performing the necessary calculations. In algebra, it's often about substituting variable values and performing arithmetic operations to reach a simplified number value.
In this exercise, evaluating the expression \(3y\) when \(y=0\) involves two straightforward steps: substituting the value of \(y\) and multiplying by zero. So first, we swapped \(y\) for 0, leading to \(3 \times 0\), and then performed the multiplication which gave us 0.
Evaluating expressions is a skill that builds your understanding of how mathematical rules and properties operate together. It helps to practice frequently, as you can apply these skills to solve more complex problems across various branches of mathematics.