Today we’re going to explore the world of rational numbers. A rational number is any number that can be expressed as the fraction of two integers. An integer is a whole number (not a fractional number) that can be positive, negative, or zero. So, when we say a rational number is a fraction, it means it’s in the form of a/b where ‘a’ (the numerator) and ‘b’ (the denominator) are both integers, and ‘b’ is not zero.
Examples of Rational Numbers
- Positive Rational Number: 1/2 is a rational number because it represents half of a whole, and both 1 and 2 are integers.
- Negative Rational Number: -3/4 is also a rational number. It’s negative because the numerator is negative, and 3 and 4 are integers.
- Whole Numbers as Rational: Even a whole number like 5 can be considered a rational number because it can be written as 5/1 where 5 is an integer and 1 is also an integer.
It’s important to note that every whole number is a rational number, but not every rational number is a whole number. This is because rational numbers can represent parts of a whole as well.
Characteristics of Rational Numbers
- They can be written in a fraction form (a/b).
- The denominator in a rational number cannot be zero because division by zero is undefined.
- Rational numbers can be either positive or negative.
- When a rational number has a positive numerator and a positive denominator, or a negative numerator and a negative denominator, the number itself is positive.
- If one of the numerator or denominator is negative, the rational number is negative.
Visual Representation
We can also place rational numbers on a number line. This helps us see that they have an order and can be compared to one another. For example, 1/2 is to the right of 1/4 on the number line because it is larger.
Questions Learners May Have
Can a rational number be a decimal?
Yes, rational numbers can be represented as decimals. However, these decimals are either terminating or repeating. For example, 1/4 equals 0.25 (which is a terminating decimal), and 1/3 equals 0.333… (which is a repeating decimal).
Is zero a rational number?
Yes, zero is a rational number because it can be represented as 0/1 or 0/-1, etc. The numerator is zero, which makes the whole fraction zero.
How do you know if a number is rational?
To determine if a number is rational, see if you can write it as a fraction with integers in the numerator and the denominator (and the denominator is not zero). If you can, then it’s a rational number.
Are all fractions rational numbers?
Most fractions where both numerator and the denominator are integers will be rational. However, fractions that have irrational numbers in the numerator or the denominator are not considered rational. For example, the fraction 1/√2 is not a rational number because √2 is not an integer.
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