/*! 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 56 Use the rule for order of operat... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 56

Use the rule for order of operations to simplify each of the following. $$30+(-40+20)+50$$

Short Answer

Expert verified
The simplified expression is 60.

Step by step solution

01

Apply Parentheses

Look at the expression inside the parentheses first: \(-40 + 20\). Evaluate this part first before considering the rest of the expression. Calculate: \(-40 + 20 = -20\). Now, rewrite the original expression using this value: \(30 + (-20) + 50\).
02

Simplify Additions

Evaluate the expression from left to right, resolving the addition: First, calculate \(30 + (-20)\). This is equivalent to subtracting 20 from 30: \(30 - 20 = 10\). Now, rewrite the expression: \(10 + 50\).
03

Final Addition

Finally, perform the last addition in the expression: \(10 + 50 = 60\). The simplified result of the original expression is \(60\).

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.

Simplifying Expressions
Simplifying expressions is all about making a complex mathematical phrase as simple as possible, without changing its value. This often involves performing operations in a specific order and combining like terms.
When simplifying, always look for terms that can be combined or operations that can be performed immediately. An important part of this process is identifying operations within expressions that can be resolved to simplify the expression further.
  • You break down the expression step by step.
  • Solve one operation at a time.
  • Ensure you follow the correct order of operations to get the accurate result.
Expressing any problem in a simpler form makes it easier to understand and solve. Simplifying helps in reducing computational complexity and avoids errors in further calculations.
Parentheses
Parentheses in mathematics are used to group parts of an expression that should be evaluated first, according to the order of operations. This grouping helps to clarify which operations should be carried out before others, preventing confusion.
The pivotal role of parentheses is demonstrated in the order of operations, commonly remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). Parentheses top this list, giving them the highest priority.
  • Evaluate operations within parentheses first.
  • Once simplified, eliminate the parentheses and integrate the simplified term into the main expression.
  • If there are nested parentheses, evaluate the innermost pair first and work outwards.
This way, parentheses ensure that the expression is calculated in the intended order, maintaining mathematical accuracy.
Addition Rules
Addition rules in math help us understand how to efficiently add numbers, including both positive and negative numbers. When dealing with addition, you should consider the signs of the numbers involved.
For example, when adding a positive and a negative number, effectively subtract the smaller number from the larger and take the sign of the number with the larger absolute value. In essence, you calculate the difference and not the straightforward sum.
  • When adding two positive numbers, simply combine them.
  • When adding two negative numbers, combine them and retain the negative sign.
  • When combining positive and negative numbers, subtract the smaller absolute value from the larger and take the sign of the number with the larger absolute value.
These rules ensure calculations are accurately executed and prevent errors when evaluating expressions that involve various numbers.

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. $$292-(-841)$$

In June, 2007 the U.S. Census Bureau released population estimates for the twenty-five cities with the largest population loss between July \(1,2005\) and July \(1,2006 .\) New Orleans had the largest population loss. The city's population fell by \(228,782\) people. Detroit, Michigan experienced a population loss of \(12,344\) people during the same time period. Represent the loss of population for New Orleans and for Detroit as a negative number.

Add or subtract. $$15-10$$

Add or subtract. $$12+15$$

Perform the indicated operations. $$8^{2}$$
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Mechanics Maths

Read Explanation

Applied Mathematics

Read Explanation

Pure Maths

Read Explanation

Calculus

Read Explanation

Discrete 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.