/*! 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 73 In the following exercises, simp... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 73

In the following exercises, simplify. $$ 9(8 w) $$

Short Answer

Expert verified
72w

Step by step solution

01

Rewrite the expression

The given expression is \(9(8w)\). This can be interpreted as the product of 9 and \(8w\).
02

Apply the associative property

Use the associative property of multiplication, which states \((a \times b) \times c = a \times (b \times c)\) to rewrite \(9(8w)\) as \((9 \times 8) \times w\).
03

Multiply the constants

Calculate the product of the constants 9 and 8: \(9 \times 8 = 72\). This simplifies our expression to \(72w\).

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.

Associative Property
The associative property is a fundamental idea in mathematics. It helps you rearrange numbers and variables without changing the value of an expression. When you multiply numbers, the associative property states that how you group them does not matter.

In mathematical terms, it means \( (a \times b) \times c = a \times (b \times c) \).
For example:
  • \( (2 \times 3) \times 4 = 2 \times (3 \times 4) \)
  • \( 6 \times 4 = 2 \times 12 \)
  • Both sides equal 24.
Applying the associative property can make calculations easier. In the exercise, we used it to rearrange the terms in \( 9(8w) \) to \( (9 \times 8) \times w \). This helps with multiplying constants first, simplifying our math.
Multiplication
Multiplication is one of the basic arithmetic operations. It combines groups of equal sizes to find a total amount. When you multiply numbers, you're essentially adding groups together.
For example:
\ 3 \times 4 \ means three groups of four.
In our exercise, we had to multiply constants. We multiplied 9 by 8:
\( 9 \times 8 = 72 \)
Once constants are multiplied, the result can be multiplied with a variable to simplify the expression.
Here, \ 9(8w) \ became \( 72w \)
Simplifying Expressions
Simplifying expressions means making them easier to work with by combining like terms and performing basic operations. It helps in solving equations faster.
When simplifying, follow these steps:
  • Identify parts of the expression.
  • Use properties, like the associative property, to rearrange terms.
  • Perform arithmetic operations.
In our exercise, the problem was \( 9(8w) \). After rewriting using the associative property, it became \( (9 \times 8) \times w \). We then multiplied the constants:
\( 9 \times 8 = 72 \).
The simplified expression is \( 72w \).
Understanding each step ensures you simplify expressions correctly and more confidently.

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

In the following exercises, simplity using the distributive property. $$ -3(6 m-1) $$

In the following exercises, convert between U.S. units. Round to the nearest tenth. The play lasted 1\(\frac{3}{4}\) hours. Convert the time to minutes.

In the following exercises, simplity using the distributive property. $$ 7(x+9) $$

In the following exercises, convert between U.S. and metric units. Round to the nearest tenth. Caroline walked 2.5 kilometers. Convert this length to miles.

In the following exercises, simplify. $$ 0 \div \frac{2}{3} $$
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Applied Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Calculus

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.