/*! 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 18 Apply the associative property t... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 18

Apply the associative property to expression, and then simplify the result. \(2+(8+y)\)

Short Answer

Expert verified
The expression simplifies to \(10 + y\) using the associative property.

Step by step solution

01

Understand the Associative Property

Remember that the associative property allows us to regroup numbers in an addition or multiplication problem without changing the result. Specifically, for addition, it states that \( (a + b) + c = a + (b + c) \).
02

Apply the Associative Property

In the expression \( 2 + (8 + y) \), we can use the associative property to regroup the terms. According to the property, we can change this to \( (2 + 8) + y \).
03

Simplify the Expression

Now, simplify the expression \( (2 + 8) + y \). Calculate the sum inside the parentheses: \( 2 + 8 = 10 \). Substitute the result back into the expression to simplify it further: \( 10 + y \).

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
An algebraic expression is a mathematical phrase that can include numbers, variables, and operation symbols like plus or minus. The fundamental part of understanding algebraic expressions lies in recognizing how these different elements interact. For example, in the expression \(2 + (8 + y)\), there are both numbers, such as \(2\) and \(8\), and a variable, \(y\).
Variables represent unknown values and are often used to generalize mathematical statements. Here, \(y\) can be replaced by different numeric values.
  • **Constants**: Fixed numbers, like \(2\) and \(8\) in this example.
  • **Variables**: Symbols representing unspecified numbers, such as \(y\).
  • **Operators**: Indicate calculations, such as plus signs \(+\).
Understanding these components will help you manipulate and simplify expressions effectively.
Simplifying Expressions
Simplifying an expression involves reducing it to its simplest form without changing its value. This process can make expressions easier to work with or solve.
Look at \((2 + 8) + y\). Here, we simplify part of the expression by performing the arithmetic operation inside the parentheses first. Calculate the sum: \(2 + 8 = 10\). This makes the expression simpler: \(10 + y\).
  • **Combine Like Terms**: Simplify expressions by adding or subtracting numbers and variables when possible.
  • **Arithmetic Simplification**: Always perform any operations inside parentheses first.
After simplifying, you're left with an expression that is easier to understand and work with: \(10 + y\). This expression is now in its simplest form.
Properties of Addition
One major property of addition used in algebra is the associative property. This property tells us that no matter how we group the numbers when adding, the result will remain the same.
For example, in \(2 + (8 + y)\), using the associative property allows us to "regroup" the numbers as \((2 + 8) + y\). This rearranging doesn鈥檛 change the outcome, which simplifies the work needed to find a solution.
  • **Associative Property**: Rearranging the parentheses in an addition operation does not change the sum.
  • **Usage**: Especially useful in simplifying complex expressions like \(a + (b + c)\) into \((a + b) + c\).
It's critical to understand that the associative property is about how numbers are grouped, not the sequence of the numbers themselves. This basic principle simplifies problem-solving in algebra by allowing more flexibility in computation.

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

Simplify each of the following. $$(6+2)(6-2)$$

Subtract. $$156-(-243)$$

Simplify as much as possible by first changing all subtractions to addition of the opposite and then adding left to right. $$-29-53-37$$

Yamina is flying from Phoenix to San Francisco on a Boeing 737 jet. When the plane reaches an altitude of \(33,000\) feet, the temperature outside the plane is 61 degrees below zero Fahrenheit. Represent this temperature with a negative number. If the temperature outside the plane gets warmer by 10 degrees, what will the new temperature be?

Work Problems \(55-60\) mentally, without pencil and paper or a calculator. Is \(-161-(-62)\) closer to \(-200\) or \(-100 ?\)
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Decision Maths

Read Explanation

Geometry

Read Explanation

Calculus

Read Explanation

Probability and Statistics

Read Explanation

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.