/*! 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 81 Use the order of operations to f... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 81

Use the order of operations to find the value of each expression. \(7+6 \cdot 3\)

Short Answer

Expert verified
The value of the expression \(7+6 \cdot 3\) is 25.

Step by step solution

01

Identify Operations

In the given expression, \(7+6 \cdot 3\) there are two operations: addition and multiplication.
02

Apply Order of Operations

According to the order of operations rule (PEMDAS/BODMAS), multiplication should be performed before addition. Multiply \(6 \cdot 3\) to get 18.
03

Perform Addition

Now perform the last operation, the addition of 7 and 18, which equals 25.

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.

PEMDAS: Understanding the Order
When solving mathematical expressions like \(7 + 6 \cdot 3\), it's important to know the correct sequence of operations. This sequence is best remembered by the acronym **PEMDAS**: which stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction. By following this order, we ensure that every expression is calculated correctly. Here鈥檚 a quick breakdown:
  • Parentheses (P): Always resolve operations inside parentheses first.
  • Exponents (E): Next, handle any exponents in the expression.
  • Multiplication & Division (MD): These operations come next and are evaluated from left to right.
  • Addition & Subtraction (AS): Finally, perform addition and subtraction, also from left to right.
Realizing the importance of PEMDAS is crucial for expressions involving multiple operations, as a misplaced operation can lead to incorrect answers. By sticking to this order, you will avoid mistakes and ensure accurate results.
Expression Evaluation: Step-by-Step Process
Expression evaluation is the process of finding the value of a mathematical expression by following specific rules and steps. For instance, in evaluating \(7+6 \cdot 3\), you need to identify the correct sequence of steps to process every operation efficiently.
A reliable approach would be:
  • Identify the Operations: Begin by noting the operations in the expression. Here, we see addition and multiplication.
  • Apply the Rule: Remember PEMDAS comes into play now. Perform the multiplication before addition here.
  • Calculate: Start with multiplication: \(6 \cdot 3 = 18\).
  • Resolve Remaining Operations: With the multiplication done, only addition remains: \(7 + 18 = 25\).
By taking each operation in turn and according to its hierarchical importance, you arrive at the correct solution efficiently.
Mathematical Operations: Key Concepts
Mathematical operations form the foundation of arithmetic and algebra. Understanding the basic operations helps solve complex expressions with ease. Below are the main types of operations you'll typically encounter:
  • Addition (+): Combining values to get a sum. Example: \(2 + 3 = 5\).
  • Subtraction (鈭�): Removing a value from another. Example: \(5 - 2 = 3\).
  • Multiplication (脳): Repeatedly adding a number of times. Example: \(4 \times 3 = 12\).
  • Division (梅): Splitting a number into equal parts. Example: \(10 \div 2 = 5\).
Recognizing and applying these operations correctly is vital when working through expressions. They serve as the building blocks for more advanced math concepts and ensure mathematical fluency in problem-solving tasks. Understanding and practicing these simple operations through exercises and examples is key to mastering math.

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

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The sequence \(1,4,8,13,19,26, \ldots\) is an arithmetic sequence.

Write the first six terms of the geometric sequence with the first term, \(a_{1}\), and common ratio, \(r\). \(a_{1}=2, r=3\)

Determine whether each sequence is arithmetic or geometric. Then find the next two terms. \(\sqrt{3}, 3,3 \sqrt{3}, 9, \ldots\)

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I've noticed that the big difference between arithmetic and geometric sequences is that arithmetic sequences are based on addition and geometric sequences are based on multiplication.

Determine whether each statement makes sense or does not make sense, and explain your reasoning. There's no end to the number of geometric sequences that I can generate whose first term is 5 if I pick nonzero numbers \(r\) and multiply 5 by each value of \(r\) repeatedly.
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Mechanics Maths

Read Explanation

Probability and Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Applied Mathematics

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.