/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 38 Simplify each expression. $$(4... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 38

Simplify each expression. $$(4 \cdot p) \cdot 6$$

Short Answer

Expert verified
The simplified expression is \(24p\).

Step by step solution

01

Understand the expression

The expression given is \((4 \cdot p) \cdot 6\). It involves multiplying three terms together: the constant 4, the variable \(p\), and the constant 6.
02

Apply the Associative Property of Multiplication

The Associative Property states that when three or more numbers are multiplied, the way they are grouped does not affect the product. Therefore, we can rewrite \((4 \cdot p) \cdot 6\) as \(4 \cdot (p \cdot 6)\).
03

Multiply the Constants

We can reorder and multiply the constants together first: \(4 \cdot 6 = 24\). Now the expression simplifies to \(24 \cdot p\).
04

Write the Final Simplified Expression

The simplified expression is \(24p\). Write this as the product of the simplified constant and the variable.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Simplifying Expressions
Simplifying expressions is a crucial skill in algebra. It involves reducing expressions to their simplest form, making them easier to handle and understand. When simplifying, the goal is to create a new representation of an algebraic expression that retains the original value.
  • Focus on reducing terms by combining like terms or simplifying operations within the expression.
  • Use properties of arithmetic, such as the distributive, associative, and commutative properties, to rearrange and combine elements effectively.
Simplifying the expression \((4 \cdot p) \cdot 6\) involves using the associative property that allows us to group and multiply parts of the expression in a different order. This approach reduces the expression to a simpler and more manageable form.
Multiplication of Constants
When you encounter constants in an expression, multiplication is straightforward. Numbers with no variables involved are constants, and when multiplying them, it results in a single constant product.
In our example \((4 \cdot p) \cdot 6\), constants are 4 and 6. Here, we can multiply these constants together first, aligning with the associative property, to make the calculation easier.
  • By multiplying \(4 \cdot 6\), we get 24.
After handling constants, we then focus on the remaining variable part of the expression. This approach provides a neat and tidy expression \(24p\) by the end of the process.
Algebraic Expressions
Algebraic expressions are combinations of variables, constants, and arithmetic operations. Variables represent unknown values, and along with constants, they form the fundamental parts of algebraic expressions.
  • In our expression, \(p\) is a variable, and it interacts with constants 4 and 6 through multiplication.
  • Algebraic expressions can be simplified by following specific arithmetic rules and properties.
Understanding how variables and constants coexist within an expression helps in identifying the appropriate operations necessary to simplify it. Mastering this makes dealing with more complex equations more intuitive and effective.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Solve each equation. $$28=j-13$$

Find each product. $$48 \times 5$$

Define a variable. Then write an equation and solve. The sum of 7 and a number is \(23 .\)

The space shuttle can carry a payload of about \(65,000\) pounds. If a compact car weighs about 2450 pounds, about how many compact cars can the space shuttle carry?

A telephone tree is set up so that every person calls three other people. Jeffrey needs to tell his co-workers about a time change for a meeting. Suppose it takes 2 minutes to call 3 people. In 10 minutes, how many people will know about the change of time?
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Discrete Mathematics

Read Explanation

Calculus

Read Explanation

Decision Maths

Read Explanation

Logic and Functions

Read Explanation

Probability and Statistics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.