/*! 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 39 Rewrite each expression using th... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 39

Rewrite each expression using the indicated property. \(k+4 ;\) commutative

Short Answer

Expert verified
The rewritten expression using the commutative property is: \(4+k\).

Step by step solution

01

Identify the terms

In the given expression, \(k+4\), \(k\) and \(4\) are the terms we will rearrange using the commutative property.
02

Apply the commutative property

Using the commutative property, we can rewrite the expression as \(4+k\). This is because, according to the commutative property, \(k+4=4+k\).
03

Write the final expression

The rewritten expression using the commutative property is: \(4+k\).

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.

Algebraic Expressions
Algebraic expressions are combinations of numbers, variables, and operations. They can be as simple as a single number or variable, or as complex as a combination involving multiple operations and terms.
For example, in the expression \(k+4\), \(k\) and \(4\) are the terms, and the plus sign indicates the operation of addition. In algebraic expressions:
  • Terms are the distinct parts separated by addition or subtraction signs.
  • Coefficients are numbers multiplying the variables.
  • Constants are numbers on their own.
When working with algebraic expressions, rearrangement of the terms may be desired for simplification or solving purposes, which is where mathematical properties like the commutative property come in handy.
Commutative Property of Addition
The commutative property of addition is a fundamental mathematical rule that states that the order in which two numbers are added does not affect the sum. Symbolically, this property can be represented as \(a + b = b + a\).
In the context of the exercise, the expression \(k+4\) can be rewritten as \(4+k\) by utilizing this property. It's important to note:
  • This property only applies to addition and multiplication, not to subtraction or division.
  • It allows flexibility in algebraic manipulation, making calculations easier and more convenient.
By applying the commutative property of addition, you can reorient terms to suit your needs without altering the expression's value.
Mathematical Properties
Mathematical properties are rules that apply to numbers and equations, aiding in the simplification and solving of problems. Key properties that are often used in algebra include:
  • **Commutative Property:** Discussed above for addition and applies to multiplication too.
  • **Associative Property:** States that the grouping of numbers does not affect their add or multiply outcome \((a + b) + c = a + (b + c)\).
  • **Distributive Property:** Allows multiplication across an addition or subtraction operation \(a(b + c) = ab + ac\).
Understanding and applying these properties can greatly empower your algebraic problem-solving skills by offering diverse approaches to expression manipulation.
Beginning Algebra
Beginning algebra lays the foundation for understanding more advanced mathematical concepts. It involves learning the basics of working with variables and mathematical properties like the commutative property. Starting points often include:
  • Understanding variables as symbols representing numbers.
  • Learning how to form and solve algebraic expressions and equations.
  • Applying mathematical properties to simplify calculations.
Grasping these fundamentals equips you with the skills to tackle progressively complex mathematical challenges, and confidently apply various properties and rules such as the commutative property in different scenarios.

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

Write a mathematical expression for each and simplify. Two-thirds of \(-27\)

Rewrite each expression using the distributive property. Simplify if possible. $$12(2 a-3 b+c)$$

Rewrite each expression using the distributive property. Simplify if possible. $$-(x-4 y+10 z)$$

Divide. $$\frac{360}{-280}$$

Write a mathematical expression for each and simplify. The quotient of 63 and \(-9\) increased by 7
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Statistics

Read Explanation

Geometry

Read Explanation

Discrete Mathematics

Read Explanation

Pure Maths

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.