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Chapter 3: Problem 55

What does it mean for one number to be less than another?

Short Answer

Expert verified
A number is less than another if it is to the left of the other number on the number line.

Step by step solution

01

- Understanding the Number Line

Visualize the number line, where numbers increase as you move to the right and decrease as you move to the left. Any number to the left of another number is less than the one on the right.
02

- Defining 'Less Than'

For two numbers, say 'a' and 'b', 'a' is considered less than 'b' if 'a' is positioned to the left of 'b' on the number line. This is denoted as 'a < b'.
03

- Practical Example

Consider the numbers 3 and 5. On the number line, 3 is to the left of 5. Therefore, 3 < 5, meaning 3 is less than 5.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

number line
Understanding the number line is essential in mathematics as it helps visually represent numbers and their relationships. Imagine a horizontal line with evenly spaced marks representing numbers. As you move to the right on this line, numbers get larger. Conversely, as you move to the left, numbers get smaller.
For instance, consider the numbers 3 and 5. On a number line, 3 is located to the left of 5, indicating that 3 is less than 5. This visual cue makes it easier to understand numerical comparisons and inequalities.
inequality
Inequality in mathematics helps compare sizes or values of different numbers. When we say one number is less than another, we write it using the 'less than' symbol, which looks like this: '<'.
For two numbers, a and b, if a is less than b, we write it as 'a < b'. This means that on a number line, 'a' would be located to the left of 'b'.
For example, with 3 and 5, since 3 is less than 5, we write it as 3 < 5. Understanding inequalities is critical because it helps us solve equations and understand many mathematical concepts.
numerical comparison
Numerical comparison involves analyzing two numbers to determine their relationship. It can tell us whether one number is less than, greater than, or equal to another number. This comparison is crucial in arithmetic and algebra.
For example, if you have two numbers such as 4 and 7, numerical comparison helps you determine that 4 is less than 7. You'd write this relationship as 4 < 7.
Knowing how to compare numbers is a fundamental skill in mathematics, aiding in activities as simple as counting and as complex as solving mathematical equations. Numerical comparison is foundational to understanding and using inequalities, both of which are visualized clearly on a number line.

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Most popular questions from this chapter

Set up an inequality and solve it. Be sure to clearly label what the variable represents. The length of a rectangle is 18 in. If the perimeter is to be at least 50 in. but not greater than 70 in., what is the range of values for the width?

Translate the given phrase or sentence algebraically. 7 is greater than \(x\)

Solve the inequality and sketch the solution set on a number line. $$-1 \leq 2-3 x<11$$

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Solve each of the problems algebraically. That is, set up an equation and solve it. Be sure to clearly label what the variable represents. Round your answer to the nearest tenth where necessary. Anthropologists often extrapolate the appearance of a human being from the parts of a skeleton they uncover. The following mathematical model relates the height \(h\) (in centimeters) of the individual to the length \(f\) (in centimeters) of the femur (thigh bone): $$h=3.68 f+21.44$$ (a) Use this model to find the height of an individual whose femur measures \(35 \mathrm{cm}\) (b) Use this model to find the length of a femur corresponding to an individual who is \(180 \mathrm{cm}\) tall.
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