Understanding Rational Numbers: Definition, Examples, and Operations

rational number

A rational number is a number that can be expressed as a fraction, where both the numerator and the denominator are integers

A rational number is a number that can be expressed as a fraction, where both the numerator and the denominator are integers. In other words, a rational number 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 1/2, -3/4, 2, and -5. These numbers can be written as fractions or as whole numbers, but they all fit the criteria of being able to be expressed as a ratio of two integers.

It is important to note that not all numbers are rational. For example, numbers like √2 (the square root of 2) or π (pi) are not rational numbers because they cannot be expressed as fractions. These numbers are called irrational numbers.

Rational numbers can be added, subtracted, multiplied, and divided just like whole numbers. When adding or subtracting rational numbers, make sure to have a common denominator. When multiplying or dividing rational numbers, you can simply multiply or divide the numerators and denominators.

For example, to add 1/2 + 3/4, you need to find a common denominator, which in this case is 4. The equivalent fractions are 2/4 and 3/4, so the sum is 5/4.

To multiply 2/3 and 3/5, you can simply multiply the numerators to get 6, and multiply the denominators to get 15. Therefore, the product is 6/15, which can be simplified to 2/5.

To divide 5/6 by 2/3, you can multiply the first fraction by the reciprocal of the second fraction. The reciprocal of 2/3 is 3/2, so the division becomes (5/6) * (3/2). Multiplying the numerators gives 15, and multiplying the denominators gives 12. Therefore, the quotient is 15/12, which simplifies to 5/4.

In summary, rational numbers are numbers that can be expressed as fractions. They can be manipulated using the basic operations of addition, subtraction, multiplication, and division.

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