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Chapter 1: Problem 54

Apply the associative property of addition to find the sum. $$ 87.6+(2.4+1.7) $$

Short Answer

Expert verified
The sum using the associative property is 91.7.

Step by step solution

01

Identify the Expression

The given expression is \(87.6 + (2.4 + 1.7)\). Our goal is to apply the associative property of addition to simplify this expression.
02

Apply the Associative Property

The associative property of addition states that the way in which numbers are grouped does not change their sum. Therefore, we can rewrite the expression as \((87.6 + 2.4) + 1.7\).
03

Evaluate the Inner Parentheses

Add the numbers within the new parentheses: \(87.6 + 2.4 = 90\).
04

Complete the Addition

Add the result from the previous step to the last number, completing the expression: \(90 + 1.7 = 91.7\).

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Key Concepts

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

Addition
Addition is one of the basic operations in arithmetic and mathematics. It involves combining numbers or quantities to find a total, often referred to as a sum. The process is straightforward whether you're working with whole numbers, fractions, or decimals. For example, in the problem \[ 87.6 + (2.4 + 1.7) \], addition is used multiple times to find a solution.
A key element in mastering addition is understanding the properties that govern it, such as the associative property.
It's important to remember:
  • Adding zero to any number returns the original number.
  • When numbers are added together, each is termed a summand, and the result is the sum.
Addition is foundational for more complex mathematical concepts.
Algebra
Algebra introduces more complexity to arithmetic by allowing the use of variables. These variables represent numbers, making it possible to form equations and expressions that solve more dynamic problems.
In the exercise \[ 87.6 + (2.4 + 1.7) \], we treat the numbers as constants, similar to variables in algebra. Algebraic properties, like the associative property, help simplify expressions.
Understanding algebra includes grasping the following:
  • Variables, often denoted by letters such as \(x\) or \(y\), can represent unknown values or changeable data.
  • Equations express the equality between two expressions, which are often simplified using algebraic properties.
Algebra bridges basic arithmetic to higher mathematics.
Mathematical Expression
A mathematical expression is a combination of numbers, variables, operations, and sometimes brackets or parentheses. Expressions can be simple or complex, but they do not include an equals sign (which would make them equations).
Consider the expression \(87.6 + (2.4 + 1.7)\). Here, numbers are grouped using parentheses to indicate the order of operations.
When working with expressions, it's useful to remember:
  • Parentheses dictate which operations to perform first, changing the result if moved or removed.
  • Applying properties like the associative property simplifies expressions and makes them easier to evaluate.
Expressions are the building blocks of mathematical communication and problem-solving.

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