/*! 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 106 Rewrite the following using the ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 106

Rewrite the following using the associative property of multiplication. $$4(6 \cdot y)$$

Short Answer

Expert verified
\((4 \cdot 6) \cdot y\).

Step by step solution

01

Identify the Problem Structure

The given expression is \(4(6 \cdot y)\). We'll use the associative property of multiplication to rewrite it.
02

Understand the Associative Property

The associative property of multiplication states that the way in which numbers are grouped does not change their product. Mathematically, \((a \cdot b) \cdot c = a \cdot (b \cdot c)\).
03

Apply the Property

By applying the associative property, we rearrange the expression as \((4 \cdot 6) \cdot y\).
04

Rewrite the Expression

The expression \(4(6 \cdot y)\) becomes \((4 \cdot 6) \cdot y\). This shows the associative property at work.

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.

Understanding Algebraic Expressions
Algebraic expressions are combinations of numbers, variables, and operations. For example, in the expression \(4(6 \cdot y)\), the number 4 and 6 are constants, \(y\) is a variable, and the dot (\(\cdot\)) represents multiplication.
These expressions help us represent mathematical situations and are foundational in algebra.
  • Constants are fixed numbers.
  • Variables symbolize unknown or variable quantities.
  • Operations like addition, subtraction, multiplication, and division connect numbers and variables.
Understanding how to manipulate algebraic expressions like \(4(6 \cdot y)\) is essential for solving equations and simplifying designs.
Exploring the Properties of Operations
In mathematics, the properties of operations help us understand how numbers relate to each other. One of these properties, crucial in this exercise, is the associative property, specifically in the context of multiplication. This property tells us that the grouping of numbers doesn't affect their product. For multiplication, we express it as:\[ (a \cdot b) \cdot c = a \cdot (b \cdot c) \]This means whether we multiply \(a\) and \(b\) first or \(b\) and \(c\) first, the result will stay the same.
Applying this to our problem, \(4(6 \cdot y)\) can be reorganized to \((4 \cdot 6) \cdot y\).
  • The order of grouping in multiplication doesn鈥檛 change the result.
  • This property makes calculations more flexible and manageable.
Mastering Mathematical Rewriting
Mathematical rewriting involves using mathematical properties to transform expressions into equivalent forms. Through these transformations, we often find it easier to solve or simplify an expression.When we talk about rewriting using the associative property, we're applying a mathematical principle to a real problem.
In the expression \(4(6 \cdot y)\), rewriting it as \((4 \cdot 6) \cdot y\) doesn't change the value. Rewriting expressions is vital in:
  • Simplifying calculations.
  • Solving complex algebraic problems.
  • Introducing efficiencies in computational processes.
This skill is powerful, enabling students to handle algebraic expressions systematically and with confidence.

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

Subtract. $$-50-60$$

Work Problems \(55-60\) mentally, without pencil and paper or a calculator. The answer to the problem \(-52-49\) is closest to which of the following numbers? a. 100 b. 0 c\(-100\)

Simplify as much as possible by first changing all subtractions to addition of the opposite and then adding left to right. $$-8+3-4$$

Work Problems \(55-60\) mentally, without pencil and paper or a calculator. The answer to the problem \(52-(-49)\) is closest to which of the following numbers? a. 100 b.\( 0 \) c\(-100\)

Translate each of the following and simplify the result. What number do you subtract from \(-3\) to get \(-9 ?\)
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Discrete Mathematics

Read Explanation

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation

Geometry

Read Explanation

Applied Mathematics

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.