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Chapter 1: Problem 5

Evaluate the expression for the given value of the variable. $$5 \cdot 6 y \text { when } y=5$$

Short Answer

Expert verified
The simplified expression is 150.

Step by step solution

01

Identify the Variable

In the given expression \(5 \cdot 6y\), the variable is \(y\). In this case, \(y\) has been given a value of 5.
02

Substitute the Variable

Substitute the value of \(y\) into the expression. So, the expression becomes \(5 \cdot 6 \cdot 5\).
03

Simplify the Expression

Carry out the multiplication operation to obtain the simplified expression. So, \(5 \cdot 6 \cdot 5 = 150\).

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Key Concepts

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

Substitution in Algebraic Expressions
One of the fundamental skills in algebra is learning how to make use of the substitution method. When you are given an algebraic expression that includes variables, substitution means replacing those variables with given numerical values. Let's say you have the expression 5 × 6y, and you're told that y = 5. You then substitute 5 for every instance of y in the expression.

For a clearer illustration, let's break it down:
  • Begin by looking at the expression and identifying the variables. In our original problem, the variable is 'y'.
  • Next, replace the variable 'y' with its assigned numerical value, which in this case is 5. This turns the expression into 5 × 6 × 5.
  • Now you've successfully transformed the algebraic expression into an arithmetic problem!
It is essential to follow the prescribed order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction), after substituting to obtain the correct result.
Simplifying Algebraic Expressions
Simplifying an algebraic expression is all about making it as straightforward as possible. This involves performing operations like addition, subtraction, multiplication, and division to combine like terms and eliminate any unnecessary complexity.

To simplify 5 × 6 × 5, which is our example after substitution, you only need to follow one type of operation since it's all multiplication:
  • Multiply the numbers in succession or all at once, here, 5 × 6 × 5.
  • The result is a single numerical value, 150, which is simpler than the original algebraic expression.
Simplification is a hugely advantageous skill, especially when dealing with more complex expressions that can be reduced significantly, making them easier to work with in subsequent calculations.
Performing Arithmetic Operations
Performing arithmetic operations such as addition, subtraction, multiplication, and division is the cornerstone of evaluating expressions. Once the expression has been set up through substitution and is ready to be simplified, it's time to do the math.

As demonstrated in our example, after replacing 'y' with 5, we multiply the numbers: \(5 \times 6 \times 5\). This process is a fundamental arithmetic operation. Here are some tips to keep in mind:
  • Adhere to the order of operations (PEMDAS) for expressions involving multiple types of arithmetic operations.
  • Operations must be carried out from left to right 鈥� multiplication and division as they appear in the expression, followed by addition and subtraction.
  • Double-check your arithmetic calculations to avoid simple mistakes that can lead to incorrect solutions.
Through consistent practice, performing these basic operations becomes instinctive, which is invaluable for more complex problem-solving in algebra.

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Most popular questions from this chapter

You are budgeting money to buy a violin and bow that cost \(\$ 250\) including tax. If you save \(\$ 5\) per week, will you have enough money in a year? You write the inequality \(5 n \geq 250\) to model the situation. What do \(5, n,\) and 250 represent? Solve the inequality.

Match the problem with the formula needed to solve the problem. Then use the Guess, Check, and Revise strategy or another problem-solving strategy to solve the problem. Area of a rectangle \(\quad A=l w \quad\) Distance \(\quad d=r t\) Simple interest \(\quad I=P r t \quad\) Volume of a cube Temperature \(\quad C=\frac{5}{9}(F-32)\) Surface area of a cube \(S=6 s^{2}\) A cubic storage box is made with 96 square feet of wood. What is the length of each edge?

Evaluate the expression for the given value of the variable. (Review 1.1) $$\frac{5}{16}-p \text { when } p=\frac{3}{8}$$

Evaluate the expression. $$5+8 \cdot 2-4$$

You are playing a new computer game. For every eight screens you complete, you receive a bonus. You want to know how many bonuses you will receive after completing 96 screens. You write the equation \(8 x=96\) to model the situation. What do \(8, x,\) and 96 represent? Solve the equation. Check your solution.
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