Operations with Rational Numbers

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What is a rational number?

A rational number is any number that can be expressed as the quotient or fraction of two integers, with a non-zero denominator.

How do you add two rational numbers?

To add two rational numbers, make sure they have a common denominator, then add their numerators.

What is the additive inverse of a rational number?

The additive inverse of a rational number is another rational number that, when added to the original, equals zero.

How do you subtract rational numbers?

To subtract rational numbers, change the sign of the number being subtracted and then add them using common denominators.

How do you multiply two rational numbers?

To multiply two rational numbers, multiply their numerators together and their denominators together.

What is the reciprocal of a rational number?

The reciprocal of a rational number is obtained by swapping its numerator and denominator.

How do you divide one rational number by another?

To divide by a rational number, multiply by its reciprocal.

What is the result when a rational number is multiplied by zero?

When a rational number is multiplied by zero, the result is zero.

How do you find a common denominator for two rational numbers?

Find the least common multiple (LCM) of the denominators to use as a common denominator.

What is the associative property in the context of rational numbers?

The associative property states that the way numbers are grouped does not affect their sum or product.

What is the commutative property when working with rational numbers?

The commutative property allows the order of addition or multiplication to be changed without affecting the result.

What does simplifying a rational number mean?

Simplifying a rational number means reducing it to its lowest terms by dividing the numerator and denominator by their greatest common divisor (GCD).

How do you express a mixed number as a rational number?

To express a mixed number as a rational number, convert the whole number to a fraction and add it to the fractional part.

Can two rational numbers be equal? Give an example.

Yes, for example, 1/2 is equal to 2/4.

What happens when you add a rational number to its opposite?

Adding a rational number to its opposite results in zero.