/*! 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 55 Simplify each of the numerical e... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 55

Simplify each of the numerical expressions. $$ 7+8 \cdot 2 $$

Short Answer

Expert verified
The simplified expression is 23.

Step by step solution

01

Identify the Operations

In the expression \(7+8 \cdot 2\), we have two operations: addition and multiplication. Based on the order of operations (PEMDAS/BODMAS), multiplication and division should be done before addition and subtraction.
02

Perform the Multiplication

Execute the multiplication operation first. Multiply 8 by 2: \[8 \cdot 2 = 16\]
03

Perform the Addition

After completing the multiplication, substitute 16 in its place and add 7 to get the final result:\[7 + 16 = 23\]

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
The acronym PEMDAS is a helpful tool that reminds us of the order in which we should solve operations in mathematics. It stands for:
  • P: Parentheses - Solve anything inside parentheses first.
  • E: Exponents - Next, any exponents or powers should be calculated.
  • M: Multiplication and D: Division - Perform from left to right as they appear in the equation.
  • A: Addition and S: Subtraction - Finally, perform addition and subtraction from left to right.
In the original exercise, applying PEMDAS helps us determine that multiplication is done before addition. This ensures that our calculations maintain accuracy and follow mathematical conventions.
BODMAS
BODMAS is another acronym that guides us through solving mathematical expressions, particularly used outside of the United States. It stands for:
  • B: Brackets - Work on anything inside brackets first.
  • O: Orders - Deal with orders, such as exponents or roots.
  • D: Division and M: Multiplication - Like PEMDAS, process from left to right.
  • A: Addition and S: Subtraction - Lastly, address these as they appear, left to right.
In the expression from the exercise, BODMAS tells us that multiplication is prioritized over addition. This clarifies which steps to perform first and leads to the correct answer.
Mathematical Expressions
A mathematical expression is a combination of numbers, operators, and sometimes variables, structured to show a calculation. Expressions do not have an "equals" sign, which differentiates them from equations.
Understanding the correct order of these operations is crucial. Incorrect application can lead to incorrect answers.
In the example given, the expression \(7 + 8 \cdot 2\) includes two operations. We first handle multiplication to find the product of 8 and 2. Only once that is calculated, do we proceed to addition. This ensures we discover the correct solution, 23, aligning with proper mathematical practices.

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

When asked to write an algebraic expression for " 8 more than a number," you wrote \(x+8\) and another student wrote \(8+x\). Are both expressions correct? Explain your answer.

Simplify the algebraic expressions by removing parentheses and combining similar terms. $$ 5(3 x-1)+6(2 x+3) $$

Answer the question with an algebraic expression. How would you help someone who is having difficulty expressing \(n\) nickels and \(d\) dimes in terms of cents?

Use your calculator and evaluate each of the algebraic expressions for the indicated values. Express the final answers to the nearest tenth. $$ \pi r^{2} h, \quad \pi=3.14, r=1.6, \text { and } h=11.2 $$

Translate each English phrase into an algebraic expression and use \(n\) to represent the unknown number. A number decreased by 7
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Statistics

Read Explanation

Decision Maths

Read Explanation

Mechanics Maths

Read Explanation

Probability and Statistics

Read Explanation

Logic and Functions

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.