Problem 53 Select the lesser of the two giv... [FREE SOLUTION]

91影视

Beginning Algebra

Margaret L. Lial, John Hornsby

$Math Studyset 91影视 Explanations$ Math

11 Edition

Chapter 1: Problem 53

Select the lesser of the two given numbers. $$ -11,-3 $$

Short Answer

Expert verified

-11

Step by step solution

Identify the Given Numbers

The numbers provided are $-11$ and $-3$.

Understand the Concept of Negative Numbers

In mathematics, the more negative a number is, the smaller its value. For example, $-11$ is smaller than $-3$ because $-11$ is further to the left on the number line compared to $-3$.

Compare the Numbers

Compare $-11$ and $-3$. Since $-11$ is more negative than $-3$, $-11$ is the lesser of the two numbers.

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.

comparing numbers

When comparing numbers, we are trying to determine which number is bigger, smaller, or if they are equal. Comparisons are important for understanding the relationships between numbers. Let鈥檚 look at the two numbers in the example: $-11$ and $-3$.\
\
\

If both numbers have the same sign, like both are positive or both are negative, we compare them directly.\
For positive numbers, the number with the bigger digit is greater.\
For negative numbers, the number with the bigger digit is actually smaller.\

This makes $-11$ less than $-3$. Starting with this basic understanding is key to moving forward.

number line

A number line is a visual representation of numbers placed in order along a straight line.\
\
When dealing with negative numbers, the number line helps us quickly see which numbers are smaller or larger.\
Let鈥檚 break it down:\
\
\

On a number line, numbers increase as you move to the right and decrease as you move to the left.\
0 is the center - numbers to the right are positive and numbers to the left are negative.\
The further to the left a number is, the smaller it is.\

So, $-11$ is further to the left than $-3$ on a number line, making $-11$ smaller. Using a number line can simplify value comparison visually.

value comparison

Value comparison means determining which number has a higher or lower value. This is especially interesting with negative numbers since they can be a bit tricky.\
\
Let鈥檚 clarify:\
\
\

With positive numbers, simple digit comparison works. 5 is greater than 3.\
With negative numbers, we flip our thinking. More negative means less value. $-15$ is less than $-5$.\
Be mindful that the negative sign inverts the value. So while $-11$ might look higher than $-3$ at first, it鈥檚 actually lower in value.\

Therefore, by understanding how we compare values, especially negative ones, we can correctly identify that $-11$ is less than $-3$. This skill is essential for solving many math problems efficiently.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Select the lesser of the two given numbers. $$ -11,-3 $$

Short Answer

Step by step solution

Identify the Given Numbers

Understand the Concept of Negative Numbers

Compare the Numbers

Key Concepts

comparing numbers

number line

value comparison

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Pure Maths

Calculus

Statistics

Theoretical and Mathematical Physics

Decision Maths

Study anywhere. Anytime. Across all devices.