Problem 44 Graph each set of numbers on the... [FREE SOLUTION]

Chapter 1: Problem 44

Graph each set of numbers on the number line. $$ 4.5,-\frac{9}{4}, 1.75,-\frac{7}{2} $$

Short Answer

Expert verified

Convert to decimals, order them, and plot on the number line: -3.5, -2.25, 1.75, 4.5.

Step by step solution

Convert All Numbers to Decimals

First, we need to convert all fractions into decimal form for easier plotting. The number $-\frac{9}{4}$ can be converted to decimal by dividing 9 by 4, which gives $-2.25$. Similarly, $-\frac{7}{2}$ is $-3.5$. So, now we have the decimals: 4.5, -2.25, 1.75, and -3.5.

Determine the Order on the Number Line

Arrange the numbers in order from least to greatest so we can correctly position them on the number line. The sorted order is: $-3.5, -2.25, 1.75, 4.5$.

Sketch the Number Line

Draw a horizontal line to represent the number line. Mark evenly spaced intervals and label them with integers that cover the range of the numbers: -4 to 5, for instance, since our numbers range from $-3.5$ to 4.5.

Plot Each Number on the Number Line

Plot each number on the number line by marking a point along the line. Place $-3.5$ to the left of $-3$, $-2.25$ slightly before $-2$, 1.75 between 1 and 2, and 4.5 between 4 and 5.

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.

Decimal Conversion

When dealing with numbers, especially on a number line, converting fractions to decimals can make the process easier. This conversion helps in visual comparisons and simplifies plotting. To convert a fraction like $-\frac{9}{4}$ into a decimal, divide the numerator (9) by the denominator (4). In this case, it results in $-2.25$. Similarly, we convert $-\frac{7}{2}$ by dividing 7 by 2, which gives us $-3.5$. By having all numbers in decimal form, it becomes much simpler to compare and plot them accurately on the number line.

Ordering Numbers

Once you have your decimals, ordering these numbers from smallest to largest is crucial for plotting. This lets you arrange numbers correctly on the number line. For example, with the decimals $-3.5, -2.25, 1.75,$ and $4.5$, the logical sequence from least to greatest is: $-3.5, -2.25, 1.75,$ and $4.5$. This step ensures clarity and precision, dictating where each point should be plotted along the line. Remember that negative numbers are smaller than positive numbers, and larger negative numbers are placed further left on the number line.

Plotting Points

With your ordered list, you can now focus on plotting these points on the number line. Draw a horizontal line, ensuring it has the necessary range, here from at least $-4$ to $5$. Each number is plotted at a specific position:

$-3.5$ slightly left of $-3$.
$-2.25$ before $-2$.
$1.75$ between $1$ and $2$.
$4.5$ between $4$ and $5$.

By spacing these intervals evenly, you ensure that your line accurately represents numerical relationships and distances.

Fractions to Decimals

To successfully navigate number lines, converting fractions to decimals is often a first step. It simplifies visualization and comparison. Consider fractions like $-\frac{9}{4}$ and $-\frac{7}{2}$. Converting $-\frac{9}{4}$ to decimal form yields $-2.25$, and $-\frac{7}{2}$ converts to $-3.5$. Use division for this process: divide the top number by the bottom. Decimal conversions make aligning these numbers on a number line much more intuitive. Remember, a decimal provides a straightforward way to express exactly where to place a fraction numerically, especially in exercises involving multiple number positions.

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

Graph each set of numbers on the number line. $$ 4.5,-\frac{9}{4}, 1.75,-\frac{7}{2} $$

Short Answer

Step by step solution

Convert All Numbers to Decimals

Determine the Order on the Number Line

Sketch the Number Line

Plot Each Number on the Number Line

Key Concepts

Decimal Conversion

Ordering Numbers

Plotting Points

Fractions to Decimals

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Geometry

Theoretical and Mathematical Physics

Pure Maths

Probability and Statistics

Logic and Functions

Study anywhere. Anytime. Across all devices.