/*! 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 43 Find the value of each expressio... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 43

Find the value of each expression. $$ 3(4+2)+8 \cdot 3 $$

Short Answer

Expert verified
42

Step by step solution

01

- Simplify Inside the Parentheses

First, handle the expression inside the parentheses. Calculate the sum inside the parentheses first: \(4 + 2 = 6\)
02

- Multiply Outside the Parentheses

Next, multiply the result from inside the parentheses by 3: \(3 \times 6 = 18\)
03

- Apply the Order of Operations (PEMDAS)

Proceed to handle the multiplication part outside the parentheses before addition: 8 multiplied by 3: \(8 \times 3 = 24\)
04

- Add the Results

Finally, add the results from the previous steps together: \(18 + 24\) which equals \(42\)

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 Parentheses
One of the first and essential steps in the order of operations is dealing with parentheses. Consider what鈥檚 inside the parentheses as a priority in the equation. For example, in the expression \(3(4+2)+8 \cdot 3\), we first focus on the value inside the parentheses: \(4 + 2\). After calculating that sum, we get \(6\). Parentheses help in grouping numbers and operations, ensuring calculations are carried out in the correct sequence.
Key points about parentheses:
  • Always handle expressions inside parentheses first.
  • They can include numbers and other operations.
  • Calculating inside parentheses first avoids errors and ensures correct results.

Multiplication in the Order of Operations
After handling the parentheses, the next critical step is multiplication. This operation needs to be done before addition according to the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right)).
In our example:
  • After simplifying the parentheses, we get \(6\).
  • The expression updates to \(3 \cdot 6 + 8 \cdot 3\).
  • Next, multiply \(3 \cdot 6\) which results in \(18\).
  • Also, handle \(8 \cdot 3\) resulting in \(24\).
Multiplication is straightforward but sometimes can be missed if rushed. Always ensure to perform these steps before moving to addition.
Simplifying by Addition
Once multiplication is complete, the final step involves addition. This is the part where we sum up the previous results to get the final answer.
In our exercise, after executing all inside parentheses and multiplication, we were left with: \(18 + 24\).
  • Add these two numbers to get the final result.
  • The final answer is \(42\).
Addition is simpler compared to other operations but crucial in achieving the correct solution. Always ensure each number added is from your previous steps鈥� results.

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

Find each difference. $$ 5.7-(-11.6) $$

Solve each problem. Linda Des Jardines owes \(\$ 870.00\) on her MasterCard account. She returns two items costing \(\$ 35.90\) and \(\$ 150.00\) and receives credit for these on the account. Next, she makes a purchase of \(\$ 82.50\) and then two more purchases of \(\$ 10.00\) each. She makes a payment of \(\$ 500.00 .\) She then incurs a finance charge of \(\$ 37.23 .\) How much does she still owe?

Write a numerical expression for each phrase and simplify. \(-2\) added to the sum of \(-18\) and 11

The operation of division is used in divisibility tests. A divisibility test allows us to determine whether a given number is divisible (without remainder) by another number. An integer is divisible by 9 if the sum of its digits is divisible by \(9,\) and not otherwise. Show that (a) \(4,114,107\) is divisible by \(9 \quad\) and \(\quad\) (b) \(2,287,321\) is not divisible by \(9 .\)

Decide whether each statement is true or false. \(-6 \leq-(-3)\)
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Logic and Functions

Read Explanation

Applied Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Statistics

Read Explanation

Decision 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.