/*! 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 107 Apply the distributive property ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 107

Apply the distributive property to each expression and then simplify the result. $$2(3+4)$$

Short Answer

Expert verified
The expression simplifies to 14.

Step by step solution

01

Apply the Distributive Property

The distributive property states that for any numbers \(a\), \(b\), and \(c\), \(a(b+c) = ab + ac\). In this problem, we apply it by distributing the \(2\) to both \(3\) and \(4\), which gives us \(2 \times 3 + 2 \times 4\).
02

Perform the Multiplications

Now, we carry out the multiplications: \(2 \times 3 = 6\) and \(2 \times 4 = 8\). The expression now becomes \(6 + 8\).
03

Simplify the Expression

Finally, add the numbers obtained from the multiplication: \(6 + 8 = 14\). So the expression simplifies to \(14\).

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.

Prealgebra
Prealgebra forms the core foundation for all higher-level math concepts. It involves basic arithmetic, number sense, and introduces algebraic thinking in a simple way to help students transition smoothly to more advanced topics. In prealgebra, students focus on:
  • Understanding numbers and how they relate to one another.
  • Learning operations such as addition, subtraction, multiplication, and division.
  • Beginning to think about mathematical problems more abstractly.
Prealgebra serves as a bridge, ensuring students are comfortable with these fundamental operations. This solid understanding enables them to tackle more complex problems involving variables and unknowns when they move on to algebra.
Mathematical Expressions
Mathematical expressions are combinations of numbers, variables, and operators that represent a particular value or set of values. They do not have an "equals" sign because they are not equations. Expressions can look like simple numbers or more complex strings using operations such as addition, subtraction, multiplication, and division.
  • An example of a mathematical expression is \(2(3+4)\).
  • Expressions can be simplified using properties such as the distributive property, which helps break down expressions into easier parts.
When you simplify or work with expressions, your goal is often to reduce them to their simplest form, which makes it easier to spot patterns or understand their meanings. Learning how to manipulate and simplify mathematical expressions is a key skill in all areas of math and science.
Simplification
Simplification makes expressions easier to understand and work with by reducing them to a simpler form. In mathematics, especially in algebra, you simplify expressions by:
  • Applying properties like the distributive property, which allows you to multiply a number by a group of numbers added together, e.g., \(a(b+c) = ab + ac\).
  • Performing operations, such as combining like terms or carrying out arithmetic calculations.
  • Breaking down complex expressions into simpler ones.
In our example, \(2(3+4)\), applying simplification involved:1. Using the distributive property to transform the expression into \(2 \times 3 + 2 \times 4\).2. Carrying out the multiplication to get \(6+8\).3. Finally, adding the results to achieve a simplified expression, which is \(14\).Simplification helps make mathematical solutions more concise and reveals the core concepts easily, which is especially beneficial when dealing with extensive and intricate algebraic expressions.

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 metric system, the scale we use to measure temperature is the Celsius scale. On this scale water boils at 100 degrees and freezes at 0 degrees. When we write 100 degrees measured on the Celsius scale, we use the notation \(100^{\circ} \mathrm{C},\) which is read "100 degrees Celsius." If we know the temperature in degrees Fahrenheit, we can convert to degrees Celsius by using the formula $$c=\frac{5(F-32)}{9}$$ where \(F\) is the temperature in degrees Fahrenheit. Use this formula to find the temperature in degrees Celsius for each of the following Fahrenheit temperatures. \(41^{\circ} \mathrm{F}\)

Subtract. $$-4-(-7)$$

Simplify each of the following expressions. $$\frac{6-(3-4)-3}{1-2-3}$$

Add the following numbers left to right. $$-571+437+(-502)$$

Use the rule for order of operations along with the rules for addition, subtraction, and multiplication to simplify each of the following expressions. Find the product of \(-3,-2,\) and \(-1\)
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Geometry

Read Explanation

Statistics

Read Explanation

Applied Mathematics

Read Explanation

Theoretical and Mathematical Physics

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.