/*! 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 110 For the following problems, eval... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 110

For the following problems, evaluate each numerical expression. $$ 28 \cdot 14^{-1} $$

Short Answer

Expert verified
Answer: The evaluated value of the given numerical expression is 2.

Step by step solution

01

Find the reciprocal of 14

To find the reciprocal of a number, we just take the fraction of that number with 1 as the numerator. So the reciprocal of 14 will be: $$ 14^{-1} = \frac{1}{14} $$
02

Multiply 28 by the reciprocal of 14

Now that we have the reciprocal of 14, we will multiply it by 28: $$ 28 \cdot 14^{-1} = 28 \cdot \frac{1}{14} $$
03

Simplify the expression

Now, we need to simplify the expression by performing the multiplication: $$ 28 \cdot \frac{1}{14} = \frac{28}{14} $$ Since 28 and 14 have a common factor of 14, we can simplify the fraction by dividing both the numerator and the denominator by 14: $$ \frac{28}{14} = \frac{28\div14}{14\div14} = \frac{2}{1} $$ Therefore, the evaluated value of the given numerical expression is: $$ 28 \cdot 14^{-1} = 2 $$

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.

Multiplying Fractions
Multiplying fractions may seem tricky at first, but with a little practice, it becomes straightforward. When you multiply fractions, you need to follow these simple steps:
  • Multiply the numerators (the top numbers of the fractions) together to get the new numerator.
  • Multiply the denominators (the bottom numbers of the fractions) together to get the new denominator.
In our example, you started with the expression \[ 28 \cdot \frac{1}{14} \]Here's why it worked:
  • 28 can be written as \( \frac{28}{1} \) as a fraction. This means the multiplication becomes \( \frac{28}{1} \cdot \frac{1}{14} \).
  • Multiplying the numerators: \( 28 \cdot 1 = 28 \).
  • Multiplying the denominators: \( 1 \cdot 14 = 14 \).
  • Thus, \( \frac{28}{1} \cdot \frac{1}{14} \) equals \( \frac{28}{14} \).
Multiplying fractions can often lead to larger numbers, which is why it helps to simplify them. This takes us to our next point.
Simplifying Fractions
Simplifying fractions means making them as simple as possible. This makes it easier to work with them. A fraction is simplified when both the numerator and the denominator have no common factors other than 1. Here's how you do it:
  • Identify the greatest common divisor (GCD) of both numbers.
  • Divide both the numerator and the denominator by the GCD.
Let's look at our earlier result:\[ \frac{28}{14} \]Both 28 and 14 have a common factor of 14:
  • Divide the numerator (28) by 14, which gives 2.
  • Divide the denominator (14) by 14, which gives 1.
Therefore, \( \frac{28}{14} \) simplifies to \( \frac{2}{1} \), or simply 2. Always check if your fraction can be simplified further. In this case, it couldn't go any simpler than 2. Simplifying not only makes expressions easier to handle but often provides insight into the relationships between numbers.
Numerical Expressions
A numerical expression is a mathematical phrase involving numbers and operation symbols but no equal sign. Evaluating numerical expressions involves carrying out operations to arrive at a single number. Take our expression \( 28 \cdot 14^{-1} \) as an example:
  • First, understand what each part of the expression means. Here, \( 14^{-1} \) indicates multiplying by the reciprocal of 14.
  • Convert \( 14^{-1} \) to \( \frac{1}{14} \).
  • Then, perform the multiplication \( 28 \cdot \frac{1}{14} \) as shown in the previous sections.
By performing these steps, we simplified and evaluated the expression to find that it equals 2. Numerical expressions require careful processing of their components to arrive at a result. Once you get the hang of it, they become much easier to manage, allowing for smooth calculations and problem-solving.

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

Find the value of each of the following expressions. \(z=\frac{x-u}{s} . \quad\) Find \(z\) if \(x=410, u=430,\) and \(s=2.5 .\)

For the following problems, convert the numbers from scientific notation to standard decimal form. The sun is about \(1 \times 10^{8}\) meters from earth.

Convert the numbers used in the following problems to scientific notation. The mass of the Eiffel tower in Paris, France, is 8,000,000 grams.

Convert the numbers used in the following problems to scientific notation. Near the surface of the earth, the speed of sound is 1195 feet per second.

Find the product for the following problems. Write the result in scientific notation. $$ \left(9.3806 \times 10^{52}\right)\left(1.009 \times 10^{-31}\right) $$
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Decision Maths

Read Explanation

Geometry

Read Explanation

Pure Maths

Read Explanation

Discrete Mathematics

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.