Understanding Rational Numbers: Definition, Examples, and Operations

Rational numbers

Rational numbers are numbers that can be expressed as a fraction, where the numerator and denominator are both integers

Rational numbers are numbers that can be expressed as a fraction, where the numerator and denominator are both integers. In other words, rational numbers can be written in the form a/b, where a and b are integers and b is not equal to zero.

Examples of rational numbers include 3/4, -2/5, 1/2, and 7/1. These numbers can be represented as a ratio or division of two integers.

Rational numbers can be positive, negative, or zero. They can be represented on a number line, where they are located between the integers. For example, 1/2 is located between 0 and 1.

It is important to note that not all real numbers are rational. For example, the square root of 2 (√2) is an irrational number, as it cannot be expressed as a fraction. Irrational numbers cannot be represented as a finite or repeating decimal.

Operations with rational numbers, such as addition, subtraction, multiplication, and division, can be performed in a similar way as with integers. To add or subtract rational numbers, we need to find a common denominator, then perform the operation. To multiply or divide rational numbers, we can simply multiply or divide the numerators and denominators.

For example, to add 3/4 and 1/3, we need to find a common denominator. In this case, the least common multiple of 4 and 3 is 12. So, we rewrite both fractions with a denominator of 12:

3/4 = 9/12
1/3 = 4/12

Now, we can add the fractions:

9/12 + 4/12 = 13/12

To represent 13/12 as a mixed number, divide the numerator by the denominator:

13 ÷ 12 = 1 remainder 1

Therefore, 13/12 can be written as 1 1/12.

Overall, rational numbers are an important concept in mathematics, as they form a fundamental part of the number system. They are used in various calculations, measurements, and applications in fields like science, engineering, finance, and more.

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