Rational Numbers – Introduction, Properties, Methods, Calculation & Examples

Rational Numbers

• Rational numbers are numbers that can be expressed as a ratio of two integers. In other words, rational numbers are numbers that can be written as a fraction, where the numerator and denominator are both integers.
• For example, the rational number 1/2 can be written as the fraction 1/2, and the rational number 3/4 can be written as the fraction 3/4.
• Rational numbers can be positive, negative, or zero. They can also be rational numbers that are irrational numbers.

Standard Form of Rational Numbers

• A rational number is a number that can be expressed as a fraction, where the numerator and denominator are both integers. The most common form of a rational number is a decimal, but rational numbers can also be expressed in fraction form or in percentage form.
• The standard form of a rational number is a decimal. The standard form of a rational number is the form that is most commonly used to express rational numbers. In the standard form of a rational number, the numerator and denominator are both expressed as integers. The decimal point is placed between the two numbers, and the digits to the right of the decimal point are used to express the fractional component of the rational number.

Steps to Express a Rational Number in the Standard Form:

1. Express the number in the form p/q, where p and q are integers and q is not 0.
2. If q is not 0, divide p by q to get a decimal number.
3. Move the decimal point two places to the right to get the standard form of the rational number.

Positive and Negative Rational Numbers

• A rational number is any number that can be expressed as a ratio of two integers. The two integers can be any two whole numbers, positive or negative.
• Positive rational numbers are those that can be expressed as a ratio of two positive integers. Negative rational numbers are those that can be expressed as a ratio of two negative integers.

Properties

Name Type Description

1. parentNode HTMLElement The parent node of this element.
2. previousSibling HTMLElement The previous sibling of this element.
3. nextSibling HTMLElement The next sibling of this element.

Methods, Calculations, and Examples

• The following subsections provide methods, calculations, and examples for deriving the loads and displacements at the supports and at the midspan of a simply supported beam.
• Deriving the Loads at the Supports
• The loads at the supports of a simply supported beam are equal to the weight of the beam itself. The weight of the beam can be calculated using the following equation:

where:

W is the weight of the beam

L is the length of the beam

ρ is the density of the beam material

The weight of a beam can also be calculated using the following equation:

where:

M is the moment of the beam

I is the moment of inertia of the beam

ρ is the density of the beam material

The following example illustrates how to calculate the weight of a beam.

Example

Calculate the weight of a beam that is 8 feet long and has a density of 100 pounds per cubic foot.

The weight of the beam is 800 pounds.

Rational Number – Addition and Subtraction

A rational number is a number that can be expressed as a fraction, or a decimal that either terminates or repeats. In this lesson, we will learn how to add and subtract rational numbers.

Adding Rational Numbers

To add two rational numbers, we will line them up so that their fractions are in the same order, and then add the numerators (top numbers) and the denominators (bottom numbers).

For example, let’s add the rational numbers 3/4 and 5/8.

We will line them up like this:

3/4
+
5/8

We will add the numerators (3 + 5 = 8) and the denominators (4 + 8 = 12), and then divide by the common denominator (12). This will give us the answer 1 1/4.

Subtracting Rational Numbers

To subtract two rational numbers, we will line them up so that their fractions are in the same order, and then subtract the numerators (top numbers) and the denominators (bottom numbers).

For example, let’s subtract the rational numbers 3/4 and 5/8.

We will line them up like this:

3/4
–
5/8

We will subtract the numerators (3 – 5 = -2) and the denominators (4 – 8 = –

Rational Number – Multiplication and Division

To multiply two rational numbers, simply multiply the numerators and multiply the denominators.

To divide two rational numbers, divide the numerators and divide the denominators.

Rational Numbers Examples

1. A rational number is a number that can be expressed as a fraction.
2. Some common rational numbers are 1/2, 1/4, 3/4, and 5/8.
3. Rational numbers can also be negative, such as -1/4.
4. Rational numbers can be expressed in decimal form, such as 0.5 or -0.25.