Numbers are everywhere in the world around us, from counting objects to measuring distances. Similarly, knowledge of rational numbers is essential for solving problems involving fractions and decimals. This math lesson on rational numbers will help you learn how to identify numbers and understand how they work in math.
Rational numbers are simply numbers that can be written as fractions where both the top (numerator) and the bottom (denominator) are whole numbers.
Note: The denominator (the bottom number) cannot be zero because dividing by zero is not possible.
Take the Quiz :
There are some simple rules and examples to identify rational numbers -
Numbers That Are Not Rational:
Type of Rational Number | Description | Examples |
Whole Numbers | Numbers that start from 0 and include all positive numbers, with no fractions. | 0, 1, 2, 3, 4, 10 |
Integers | Whole numbers and their negative counterparts (no fractions or decimals). | -3, -2, -1, 0, 1, 2, 3 |
Fractions | Numbers written as a part of a whole, where the top number (numerator) is divided by the bottom number (denominator). | 1/2, 3/4, 7/10 |
Decimals (Terminating) | Numbers with a finite number of digits after the decimal point. | 0.5, 2.75, 4.6 |
Decimals (Repeating) | Numbers with one or more digits that repeat endlessly after the decimal point. | 0.333… (1/3), 0.666… |
Rational numbers have some cool properties or rules they follow.
1. Closure Property: Staying Within the Lines
2. Commutative Property: Order Doesn't Matter
3. Associative Property:
4. Additive Identity:
5. Multiplicative Identity: The One and Only
This table gives a simple example of rational and irrational numbers using easy examples.
Category | Rational Numbers | Irrational Numbers |
What Are They? | Numbers that can be written as fractions (like a/b). | Numbers that cannot be written as simple fractions. |
Examples | 1/2, 3/4, 7, -5, 0.75, 5.5, 0.3, 0, 4 (These can be written as fractions!) | √2, π (Pi), √3, 1.414... (They go on forever without repeating!) |
Decimals | Decimals that either end (like 0.5) or repeat in a pattern (like 0.333…). | Decimals that go on forever without repeating or ending (like 3.14159…). |
Can You Count Them? | Yes! You can count and list rational numbers. | No! You cannot list all irrational numbers because they go on forever without a pattern. |
Can You Write Them as Fractions? | Yes! All rational numbers can be written as fractions. | No! Irrational numbers cannot be written as fractions. |
Take the Quiz :
Example 1: Add the rational numbers
3/4 and 1/2.
Solution:
Final Answer:
5/4 is an improper fraction. You can also write it as 1 1/4 (one and one-fourth).
Example 2: Subtracting Rational Numbers
Problem:
Subtract 3/5 from 4/5.
Solution:
Final Answer:
The answer is 1/5.
Example 3: Multiplying Rational Numbers
Problem:
Multiply 2/3 by 3/4.
Solution:
Answer:
1/2.
Example 4: Dividing Rational Numbers
Problem:
Divide 5/6 by 2/3.
Solution:
Answer:
5/4.
Rational Numbers Assessment
a) 5
b) √2
c) 1/3
d) π
a) -4
b) 0.5
c) √3
d) 2/5
a) 3/4
b) 2/3
Answer:
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