Question

Product is same
hy 1 Product of two rational numbers remains the same even if we chang
their order, ie, if x and y are rational numbers, then
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This is commutative law of multiplication,
erily that the product of rational numbers
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remains the same even aft
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hanging the groupinga.​

Answer 1

Answer:

The product of two rational numbers is rational."

So, multiplying two rationals is the same as multiplying two such fractions, which will result in another fraction of this same form since integers are closed under multiplication. Thus, multiplying two rational numbers produces another rational number.

Answer 2

Step-by-step explanation:

Rational Number- Any Number that can be expressed in the form p/q , where p and q are integers and q ≠ 0, is known as rational number. The collection or group of rational numbers is denoted by Q.

Properties of a Rational Number

▪ Closure- Rational numbers are closed under addition, subtraction and multiplication. For eg.- If p and q are any two rational numbers, then and the sum, difference and product of these rational numbers is also a rational number. This is known as the closure law

▪ Commutativity- Rational numbers are commutative under addition and multiplication. If p and q are two rational numbers, then:

Commutative law under addition says- p + q = q + p.

Commutative law under multiplication says p x q = q x p.

Note- Rational numbers, integers and whole numbers are commutative under addition and multiplication. Rational numbers, integers and whole numbers are non commutative under subtraction and division.

▪ Associativity- Rational numbers are associative under addition and multiplication. If a, b, c are rational numbers, then:

Associative property under addition: p + (q + r) = (p + q) + r

Associative property under multiplication: p(qr) = (pq)r

▪ Role of zero and one- 0 is the additive identity for rational numbers. 1 is the multiplicative identity for rational numbers.

▪ Multiplicative inverse- If the product of two rational numbers is 1, then they are called multiplicative inverse of each other.

Eg. 4/9 * 9/4 = 1