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Chapter 5: Problem 49

For Exercises 49鈥�60, graph the fraction on a number line. $$\frac{1}{3}$$

Short Answer

Expert verified
Answer: The fraction \(\frac{1}{3}\) is located at the end of the first third of the interval between 0 and 1 on a number line.

Step by step solution

01

Draw a number line

Draw a straight, horizontal line. Mark evenly spaced points along the line, and label these points with consecutive whole numbers, such as -2, -1, 0, 1, and 2. Make sure to have 0 in the rough center, as we need to place the fraction between 0 and 1.
02

Identify the fraction's position between two whole numbers

The given fraction, \(\frac{1}{3}\), has a value between 0 and 1. So, locate where 0 and 1 are on the number line and look for the correct position in that interval for the fraction.
03

Divide the interval between these whole numbers

As the denominator of the fraction is 3, we need to divide the interval between 0 and 1 into three equal sections. The first section represents the first third of the interval, the second section represents the second third, and the third section represents the last third.
04

Mark and label the fraction on the number line

The numerator of the fraction is 1, so we are dealing with the first third of the interval between 0 and 1. Mark the point representing \(\frac{1}{3}\), which is located at the end of the first third of the interval between 0 and 1. Label this point with the given fraction: \(\frac{1}{3}\). Now, the fraction is represented on the number line.

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Key Concepts

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

Understanding Number Line Representation
Picture the number line as a long, straight road that stretches infinitely in both directions. It's marked with evenly spaced hash marks, each one representing a distinct value. These marks are like mileposts on our road, giving us a fixed reference to measure distance and represent numbers. Whole numbers, including zero, are typically placed at significant points along this line to create a framework for understanding numerical relationships.
Deciphering Fractions
Imagine you have a delicious pie, and you decide to share it with a group of friends. If you cut this pie into three equal slices and take one slice for yourself, you're left with a simple visual representation of the fraction \(\frac{1}{3}\). The bottom number, called the denominator, tells us into how many slices the pie is cut, while the top number, the numerator, shows how many of these slices you've taken. In the realm of mathematics, fractions like this help us express quantities that are less than a whole.
Dividing Intervals on a Number Line
When we're dealing with fractions, we want to see exactly where they fall on our number line road. To do this, we need to slice the stretch between two whole number 'mileposts' into equal parts. This process is akin to dividing a ruler into smaller increments to measure finer lengths. For any fraction we encounter, we slice the interval on the number line into as many equal parts as the denominator suggests, turning a single step between whole numbers into a series of smaller, equal steps.
Grasping Number Line Intervals
An interval on a number line is a section of the road between two mileposts鈥攁 stretch of the journey. If whole numbers are cities, then intervals are the roads connecting these cities. Understanding these intervals is crucial for accurately placing fractions on our number line because it's within these intervals that fractions live. Just as cities can have many different streets, an interval can be divided into many parts, depending on the denominator. By marking these sub-parts, we identify the exact location of the fraction on our mathematical road map.

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