/*! 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 70 Simplify. $$\frac{1}{3}(9 x)$$... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 70

Simplify. $$\frac{1}{3}(9 x)$$

Short Answer

Expert verified
The simplified form of the given expression is \(3x\).

Step by step solution

01

- Distribute

Distribute the fraction \(\frac{1}{3}\) across the expression \(9x\). This entails multiplying \(\frac{1}{3}\) by \(9x\).
02

- Carry Out Multiplication

The multiplication of the fraction \(\frac{1}{3}\) by \(9x\) can be calculated as \(\frac{1}{3} * 9x = 3x\).

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.

Distributive Property
The distributive property is a fundamental concept in algebra that helps in simplifying expressions and making calculations easier. It allows you to distribute or "multiply out" an expression across terms inside parentheses. The general form is:
  • For multiplication over addition: \( a(b + c) = ab + ac \)
  • For multiplication over subtraction: \( a(b - c) = ab - ac \)
When you apply the distributive property, you are essentially multiplying each term inside the parentheses by the term outside. In this exercise, we used the distributive property to multiply \( \frac{1}{3} \) across \( 9x \). This meant we took the fraction \( \frac{1}{3} \) and multiplied it by the entire term \( 9x \), which is simplified by performing the multiplication step-by-step.
Multiplying Fractions
Multiplying fractions is simpler than it might initially seem. When you multiply fractions, you multiply the numerators to get the new numerator and the denominators to get the new denominator. But what about multiplying a fraction with a whole number or a term like \( 9x \)? Here is how it works:
  • Convert the whole number to a fraction by putting it over 1.
  • Multiply the numerators and the denominators.
In our exercise, \( \frac{1}{3} \) was multiplied by \( 9x \). We can think of \( 9x \) as \( \frac{9x}{1} \), so the multiplication becomes:
  • Numerator: \( 1 \times 9x = 9x \)
  • Denominator: \( 3 \times 1 = 3 \)
Hence, \( \frac{9x}{3} \) simplifies directly to \( 3x \), as you can divide both the numerator and the denominator by 3.
Basic Algebra Concepts
Basic algebra is the branch of mathematics that uses symbols and letters to represent numbers in equations and expressions. It is about managing expressions and equations to solve for unknown values. Here are a few core ideas:
  • **Expressions**: Combinations of numbers, variables, and operations, like \( 9x \) or \( a + b \).
  • **Simplification**: Reducing expressions to a simpler form, which is what we did by calculating \( \frac{1}{3} \times 9x = 3x \).
  • **Variables**: Symbols that stand for unknown values, such as \( x \) in our solution.
Understanding and mastering these basic concepts is crucial, as they are the building blocks for all higher-level algebraic operations. Remember, simplifying expressions often involves using several basic concepts like the distributive property and multiplication of fractions.

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

Simplify. $$5\left(x^{2}+y^{2}\right)$$

Simplify. $$-5\left(-2 x^{2}-3 x+7\right)$$

Football In football, the number of points awarded for a touchdown is three times the number of points awarded for a safety. Express the number of points awarded for a touchdown in terms of the number of points awarded for a safety.

Simplify. $$5\left(2 x^{2}-4 x y-y^{2}\right)$$

A recent survey conducted by Turbotax. com asked, "If you receive a tax refund, what will you do?" About two-fifths of respondents said they would pay down their debt. (Source: USA Today, March 27, 2008) Express the number of people who would pay down their debt in terms of the number of people surveyed.
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Calculus

Read Explanation

Probability and Statistics

Read Explanation

Decision Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Statistics

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.