Represent Rational Numbers on the Number Line

Key Concepts

• Understand rational numbers.
• Compare and order rational numbers.
• Interpret rational numbers in real-world contexts.

Introduction: 

Rational numbers: 

Rational numbers include integers, fractions and decimals. Fractions and decimals can be positive or negative. 

A rational number can be expressed as a fraction in the form

p/q or –p/q, where p and q are integers and b≠0. 

Examples of rational numbers are, 

• 1/2 
• –3/4 

• 0.7 or 7/10 
• –0.3 or -3/10 
• 0.141414… or 14/99 

2.2.1 Understand rational numbers 

Example 1: 

How can you find and position – 5/4 and –1.75 on the number lines? 

Solution: 

Using a horizontal number line: 

Write – 5/4 as mixed number. 

– 5/4 = – 1¼

Using a vertical number line: 

Write –1.75 as mixed number. 

– 1.75 = – 1¾

2.2.2 Compare and order rational numbers 

Example 2: 

Ms. Jackson wants to compare and order three rational numbers. Show how she can use <, >, or = to compare –1.75, 3/5 and 1.25. Then order these numbers from the least to greatest. Can you help Jackson in doing this? 

Solution: 

So, -1.75 < 3/5 < 1.25, and their order from the least to greatest is -1.75,3/5, 1.25 

Example 3: 

The table below shows the possible locations of different animals relative to the ocean’s surface. Compare the rational numbers using <, >, or = and then order these numbers from the least to the greatest. 

Solution: 

Decimal form of – 2/3 is – 0.6666… 

Decimal form of – 2 ¼ is – 2.25 

Decimal form of – 3/10 is – 0.3 

2.2.3 Interpret rational numbers in real-world contexts 

Example 4: 

The locations of four animals relative to the sea level are shown below.  

Use <, >, or = to compare their depths and explain their relationship. 

Solution: 

Exercise:

1. How do you find the least rational number plotted on a number line?
2. Use the number line, and position the numbers from the least to the greatest.

1.25, – 3/2, – 1.25, 11/2

3. Use the number line, and position the numbers from the least to the greatest.

– 0.5, 1/2, – 0.75, 3/4

4. Compare each integer to the given fraction or decimal using < or >.

−2 _______ – 9/4

5. Use <, >, or = to compare.

6. Order the numbers from the least to the greatest.
−4.3, 3, -2 ½, 1

7. Order the numbers from the least to the greatest.
– ¾, -1, -1 2/3, −1.4

8. Order the rational numbers from the least to the greatest.

9. Order the rational numbers from the least to the greatest.

1. Two scientists compared measurements they took during different experiments. The first scientist had 0.375, –1.5, and 1.4 written down. The second scientist wrote down 3/4, –1 5/8, and 1 3/5. Order their measures from the least to the greatest.

Concept Map: 

What have we learned:

• Understand rational numbers and plot them on a number line.
• Compare rational numbers using <, >, or = and order them.
• Interpret rational numbers in real-world contexts.