Give one example each to show that the rational numbers are closed under addition, subtraction and multiplication. Are rational numbers closed under division? Give two examples in support of your answer.

Solution:

(A) For addition of rational numbers

Ex: 1/3 + 2/3 = 3/3 = 1 = 2/3 + 1/3

Rational numbers closed under addition

(B) For subtraction of rational numbers

Ex: 2/3 - 1/3 = 1/3 but 1/3 - 2/3 = -1/3

Rational numbers not closed under subtraction

(C) For multiplication of rational numbers

Ex: 1/2 × 1/3 = 1/6 = 1/3 × 1/2

Rational numbers closed under multiplication

(D) For division of rational numbers

Ex: 1/3 ÷ 3/4 = 4/9 but 3/4 ÷ 1/3 = 9/4

Rational numbers are not closed under division

✦ Try This: Give one example to show that the rational numbers exhibit distributive property.

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 1

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NCERT Exemplar Class 8 Maths Chapter 1 Problem 104

Give one example each to show that the rational numbers are closed under addition, subtraction and multiplication. Are rational numbers closed under division? Give two examples in support of your answer

Summary:

Rational numbers are closed under addition and multiplication but not under subtraction and division

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☛ Related Questions:

• Verify the property x + y = y + x of rational numbers by taking (a) x = 1/2, y = 1/2, (b) x = -2/3, . . . .
• Simplify each of the following by using suitable property. Also name the property. (a) [1/2 × 1/4] + . . . .
• Tell which property allows you to compute 1/5 × [5/6 × 7/9] as [1/5 × 5/6] × 7/9