Q . What are the multiplicative and additive identities of rational numbers?
Answers
ANSWERS:
▪ 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
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Q . What are the multiplicative and additive identities of rational numbers?
Ans : 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.
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Q . what are rational numbers ?
=> A rational number is a number that can be express as the ratio of two integers. ... However, one third can be express as 1 divided by 3, and since 1 and 3 are both integers, one third is a rational number. Likewise, any integer can be expressed as the ratio of two integers, thus all integers are rational.
Q . What are positive and negative rational number give three example of each?
=> In other words, a rational number is negative, if its numerator and denominator are of the opposite signs. Each of the rational numbers -1/6, 2/-7, -30/11, 13/-19, -15/23 are negative rationals, but -11/-18, 2/5, -3/-5, 1/3 are not negative rationals. ... Note: The rational number 0 is neither positive nor negative.