QUESTION BANK CLASS 8 RATIONAL NUMBERS

  QUESTION BANK  CLASS 8 RATIONAL NUMBERS

EXERCISE 1.1

 1. Name the property under multiplication used in each of the following

2. Tell what property allows you to compute

3. The product of two rational numbers is always a ___.

POINTS TO REMEMBER

• A number which can be written in the form p q , where p and q are integers and q ≠ 0 is called a rational number
• rational numbers are closed under addition. That is, for any two rational numbers a and b, a + b is also a rational number.
• rational numbers are closed under subtraction. That is, for any two rational numbers a and b, a – b is also a rational number.
• rational numbers are closed under multiplication. That is, for any two rational numbers a and b, a × b is also a rational number.
• for any rational number a, a ÷ 0 is not defined. So rational numbers are not closed under division.
• two rational numbers can be added in any order. We say that addition is commutative for rational numbers. That is, for any two rational numbers a and b, a + b = b + a.
• subtraction is not commutative for integers and integers are also rational numbers. So, subtraction will not be commutative for rational numbers too.
• multiplication is commutative for rational numbers. In general, a × b = b × a for any two rational numbers a and b.
• division is not commutative for rational numbers.
• addition is associative for rational numbers. That is, for any three rational numbers a, b and c, a + (b + c) = (a + b) + c.
• Subtraction is not associative for rational numbers.
• multiplication is associative for rational numbers. That is for any three rational numbers a, b and c, a × (b × c) = (a × b) × c.
• division is not associative for rational numbers.
• Zero is called the identity for the addition of rational numbers. It is the additive identity for integers and whole numbers as well.
• a × 1 = 1 × a = a for any rational number a 
• 1 is the multiplicative identity for rational numbers.
• Distributivity of Multiplication over Addition and Subtraction. For all rational numbers a, b and c, a (b + c) = ab + ac a (b – c) = ab – ac

1. Rational numbers are closed under the operations of addition, subtraction and multiplication. 

2. The operations addition and multiplication are (i) commutative for rational numbers. (ii) associative for rational numbers. 

3. The rational number 0 is the additive identity for rational numbers. 

4. The rational number 1 is the multiplicative identity for rational numbers. 

5. Distributivity of rational numbers: 

For all rational numbers a, b and c, a(b + c) = ab + ac and a(b – c) = ab – ac 

6. Between any two given rational numbers there are countless rational numbers. 

The idea of mean helps us to find rational numbers between two rational numbers.