/*! 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 42 Simplify the given expression. ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 42

Simplify the given expression. $$ 6+3 \cdot[4+4 \cdot(5+8)] $$

Short Answer

Expert verified
The simplified expression is 174.

Step by step solution

01

Solve the innermost parentheses

Identify the innermost parentheses within the expression where the initial calculation will take place: \[(5+8)\]Calculate the sum inside these parentheses.\[5 + 8 = 13\]
02

Solve the expression inside the brackets

Substitute the result from the innermost parentheses into the expression:\[4 + 4 \cdot 13\]Multiply before adding.\[4 \cdot 13 = 52\]Then add the result to 4.\[4 + 52 = 56\]
03

Solve the main expression

Substitute the result from the brackets into the complete expression:\[6 + 3 \cdot 56\]Multiply before adding.\[3 \cdot 56 = 168\]Then add the result to 6.\[6 + 168 = 174\]

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.

Parentheses
Parentheses are the rounded brackets \(( )\) used in mathematical expressions to indicate which operations should be performed first. In the order of operations, calculations within parentheses are always prioritized. This is why they must be handled before any other operations.

Consider the expression from the problem:\[6+3 \cdot[4+4 \cdot(5+8)]\] Here, \((5+8)\) is the innermost parentheses. Thus, it's the first part of the expression we need to solve. When dealing with complex expressions, always search for innermost parentheses and compute those operations first. This method ensures clarity and accuracy.

To solve,\[5+8=13\] before moving to any further calculations.
Brackets
Brackets, typically shown as \([ ]\), are another element in math problems that delineate which operations to perform early on, right after operations within parentheses are completed. They're included in expressions to maintain the structure and grouping of terms our operations act upon.

In our example expression:\[6+3 \cdot[4+4 \cdot(5+8)]\] once the parentheses were solved, they simplified to \([4+4 \cdot 13]\). Within these brackets, the order of operations still applies, processing multiplication before addition.
  • Find and multiply terms, \[4 \cdot 13 = 52\].
  • Then, sum it with 4 to get the total of 56, \[4+52=56\].
Brackets are key in keeping calculations structured, especially with multiple operations.
Multiplication
Multiplication is a fundamental arithmetic operation that represents adding a number to itself a certain number of times.In the context of simplifying expressions, it's typically performed after operations within parentheses and brackets but before addition or subtraction.

Inside our worked example\[6+3 \cdot[4+4 \cdot(5+8)]\]the multiplication happens at two crucial stages after simplifying parentheses and brackets:
  • Multiply 4 by the result from the inner parentheses, \[4 \cdot 13 = 52\].
  • Following this, multiply 3 with the outcome from the brackets: \[3 \cdot 56 = 168\].
Each time, multiplication is completed before any additions, maintaining the mathematical hierarchy. This process ensures results remain accurate and consistent across similar problems.

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 the given expression. $$ 3 \cdot[4+9 \cdot(8+5)] $$

Simplify the given expression. $$ \frac{19-(4 \cdot 3-2)}{6 \cdot 3-9} $$

Simplify the given expression. $$ 5^{3}-(17+15) $$

Simplify the given expression. $$ (4+2)^{2} $$

Simplify the given expression. $$ 19+3\left[12-\left(2^{3}+1\right)\right] $$
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Pure Maths

Read Explanation

Applied Mathematics

Read Explanation

Discrete Mathematics

Read Explanation

Calculus

Read Explanation

Mechanics 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.