/*! 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 68 Evaluate the given expression. R... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 68

Evaluate the given expression. Remember to follow the order of operations. $$18+2 \cdot 9+5$$

Short Answer

Expert verified
41

Step by step solution

01

Identify the expression

The expression to evaluate is: \[ 18 + 2 \cdot 9 + 5 \]
02

Follow the order of operations

The order of operations (PEMDAS/BODMAS) tells us to address multiplication before addition. So, evaluate the multiplication first: \[ 2 \cdot 9 = 18 \]
03

Substitute back into the expression

After calculating the multiplication, substitute back into the expression: \[ 18 + 18 + 5 \]
04

Perform the addition

Now, perform the addition from left to right: \[ 18 + 18 = 36 \]Then, add 5: \[ 36 + 5 = 41 \]

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
When evaluating mathematical expressions, it is crucial to follow the order of operations, often remembered by the acronym 'PEMDAS'. This stands for:
  • P: Parentheses
  • E: Exponents
  • M/D: Multiplication and Division (from left to right)
  • A/S: Addition and Subtraction (from left to right)
Applying PEMDAS ensures that we perform calculations in the correct sequence. In the given exercise: \[ 18 + 2 \cdot 9 + 5 \] we first handle the multiplication before moving on to addition. By correctly applying PEMDAS, we get: 2 \cdot 9 = 18, simplifying the expression to 18 + 18 + 5. This approach guarantees consistent and correct results when evaluating any algebraic expression.
Evaluating Expressions
Evaluating an expression means to find its value by performing all the required operations. Using PEMDAS, we systematically address each part of the expression. For example, in evaluating the expression: \[ 18 + 2 \cdot 9 + 5 \] we first identify the operations: addition and multiplication.
  • Step 1: Perform the multiplication (2 \cdot 9 = 18)
  • Step 2: Substitute the result back into the expression (18 + 18 + 5)
  • Step 3: Carry out the additions in order: (18 + 18 = 36, then 36 + 5 = 41)
By breaking down the expression step-by-step, we make it easier to see the logical flow and understand each part's role in the final result.
Elementary Algebra
Elementary algebra involves using variables and arithmetic operations to create and solve equations. It's a fundamental part of mathematics that builds the foundation for more advanced topics. In this exercise, while there are no variables, we still apply algebraic principles to evaluate the given expression: \[ 18 + 2 \cdot 9 + 5 \] Even simple arithmetic operations follow the rules of algebra.
  • Identifying the components of the expression (numbers and operations)
  • Applying the correct order of operations (PEMDAS)
  • Simplifying step-by-step to find the final value
Understanding and practicing these basics in elementary algebra makes tackling more complex equations manageable. Additionally, this reinforces the importance of following rules to achieve accurate results consistently.

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

Try to find an approximate value for a square root of \(3 .\) That is, try to find a number that when multiplied by itself gives a product of \(3 .\) Give answers correct to the nearest whole number, nearest tenth, nearest hundredth, and nearest thousandth. Use a calculator to help with the multiplication, but not to compute the square root itself.

Sketch the given set on a number line. $$\\{x | x>4\\}$$

We know that multiplication means repeated addition. That is, 4 times 3 means add 3 four times. In view of this and the rule for adding negative integers, what should 4 times \(-3\) be equal to?

In Exercises \(73-84\), evaluate the given expression. $$|-8+6-5|-8+6-5$$

Evaluate the given expression. Remember to follow the order of operations. $$48 \div(12 \div 4)$$
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Probability and Statistics

Read Explanation

Decision Maths

Read Explanation

Geometry

Read Explanation

Mechanics Maths

Read Explanation

Calculus

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.