/*! 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 2 Choose the correct response Th... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 2

Choose the correct response The identity element for multiplication is \(\mathbf{A} .-a\) \(\begin{array}{lll}{\text { B. } 0} & {\text { C. } 1} & {\text { D. } \frac{1}{a}}\end{array}\)

Short Answer

Expert verified
Option C (1) is the identity element for multiplication.

Step by step solution

01

- Understand the Identity Element for Multiplication

The identity element for an operation is a value that, when used in the operation with another number, leaves that number unchanged. For multiplication, this means we need a number that, when multiplied by any other number, does not change the value of that other number.
02

- Test Each Option

Test each option to see if it satisfies the condition of being an identity element for multiplication: - Option A: Multiply a number by '-a' and observe if it remains unchanged.- Option B: Multiply a number by '0' and observe the result.- Option C: Multiply a number by '1' and observe if it remains unchanged.- Option D: Multiply a number by '\(\frac{1}{a}\)' and observe the result.
03

- Analyze the Outcomes

- Multiplying any number by '-a' changes the number.- Multiplying any number by '0' results in '0', changing the number.- Multiplying any number by '1' leaves it unchanged, satisfying the identity property.- Multiplying any number by '\(\frac{1}{a}\)' changes the number.
04

- Choose the Correct Answer

Based on the analysis, Option C (1) leaves the number unchanged when used in multiplication, making it the correct identity element for multiplication.

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.

identity property
The identity property is a fundamental concept in mathematics. It refers to a number that, when used in an operation with another number, leaves the other number unchanged.
There are different identity elements for various operations:
  • In addition, the identity element is 0. This means any number plus 0 remains unchanged.
  • For multiplication, the identity element is 1. This means any number multiplied by 1 stays the same.
Understanding the identity property helps to simplify and solve equations efficiently. Always remember that the identity element does not alter the other number in an operation.
multiplication
Multiplication is one of the basic arithmetic operations. It involves combining several equal groups into one total amount.
Here are key points about multiplication:
  • The result of multiplying numbers is called the product.
  • The numbers being multiplied are called factors.
  • Multiplication is commutative, which means the order of factors does not change the product (e.g., 3 脳 4 is the same as 4 脳 3).
When working with multiplication, especially in algebra, it's crucial to understand how the identity element works to make equations easier to handle and solve.
algebraic operations
Algebraic operations are the set of mathematical operations used on algebraic expressions. These operations include addition, subtraction, multiplication, division, and exponentiation.
Important points about algebraic operations:
  • They follow specific rules and properties, such as commutative, associative, and distributive properties.
  • They allow us to manipulate and simplify expressions and solve equations.
  • Using identity elements like 1 in multiplication can help streamline solving complex problems.
A solid grasp of algebraic operations is essential for progressing into more advanced areas of math and science.
mathematical properties
Mathematical properties are the rules that numbers and operations follow. Some key properties include:
  • Identity Property: Using 0 in addition or 1 in multiplication leaves the number unchanged.
  • Commutative Property: The order of numbers doesn鈥檛 affect the result (e.g., a + b = b + a or a 脳 b = b 脳 a).
  • Associative Property: The grouping of numbers doesn鈥檛 affect the result (e.g., (a + b) + c = a + (b + c) or (a 脳 b) 脳 c = a 脳 (b 脳 c)).
  • Distributive Property: This property distributes multiplication over addition (e.g., a(b + c) = ab + ac).
Understanding these properties aids in solving equations faster and with greater accuracy.

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

Solve each problem. Kayla Koolbcck has $$ 37.60\( in her checking account. She uses her debit card to make purchases of \) 25.99\( and \) 19.34,\( which overdraws her account. Her bank charges her account an overdraft fee of \) 25.00 .\( She then deposits her paycheck for \) 58.66$ from her part-time job at Subway. What is the balance in her account?

Provide more practice on operations with fractions and decimals. Perform the indicated operations. $$-32.84 \div 8$$

Exercises \(91-116\) provide more practice on operations with fractions and decimals. Perform the indicated operations. $$\frac{12}{5} \div\left(-\frac{18}{25}\right)$$

Frank Capek鈥檚 grandson was asked to evaluate the following expression. $$ 9+15 \div 3 $$ Frank gave the answer as \(8,\) but his grandson gave the answer as \(14 .\) The grandson explained that the answer is 14 because of the "Order of Process rule" which says that in a problem like this, you proceed from right to left rather than left to right. (Note: This is a true story.) (a) Whose answer was correct for this expression, Frank's or his grandson's? (b) Was the reasoning for the correct answer valid? Explain.

Explain why the reciprocal of a nonzero number must have the same sign as the number.
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Calculus

Read Explanation

Mechanics Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Statistics

Read Explanation

Geometry

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.