Try and represent and on a number line.
To represent and on the number line, we first convert them into mixed fractions to determine the integers between which they lie. We have , which lies between 1 and 2. Also, , which lies between -2 and -1. To represent , we divide the unit intervals on the number line into 5 equal parts each. We then move 8 parts to the right of 0 (or 3 parts to the right of 1) to mark the point.
To represent , we divide the unit intervals into 4 equal parts each. We then move 7 parts to the left of 0 (or 3 parts to the left of -1) to mark the point.
Explanation
The textbook explains that to represent a rational number p/q on the number line, one must divide the unit interval (distance between consecutive integers) into q equal parts. For positive numbers, we move p parts to the right of 0, and for negative numbers, we move p parts to the left. Converting improper fractions to mixed fractions (like 9/4 = 2 1/4 in the text) helps identify the specific integer interval where the point lies, making it easier to draw and label the number line accurately.
Solution Steps
Step 1: Convert the rational numbers to mixed fractions: (lies between 1 and 2) and (lies between -2 and -1).
Step 2: For , divide the intervals between 0, 1, and 2 into 5 equal parts. Move 8 parts to the right of 0 (or 3 parts right of 1).
Step 3: For , divide the intervals between -2, -1, and 0 into 4 equal parts. Move 7 parts to the left of 0 (or 3 parts left of -1).