### 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:

- How do you find the least rational number plotted on a number line?
- 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.

- 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.

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