NCERT CLASS 8 MATHS

 CHAPTER 1 

RATIONAL NUMBERS

ONLINE CLASS 

Exercise 1.1

Question 1:

Name the property under multiplication used in each of the following:

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(i)

$$\frac{-4}{5}\times 1=1\times \frac{-4}{5}=\frac{-4}{\mathrm{5}}$$

✅ Property: Multiplicative Identity Property

Explanation:
Any number multiplied by 1 gives the same number.

$$a \times 1 = 1 \times a = a$$

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(ii)

$$\frac{-13}{17} \times \frac{-2}{7} = \frac{-2}{7} \times \frac{-13}{17}$$

✅ Property: Commutative Property of Multiplication

Explanation:
Changing the order of multiplication does not change the product.

$$a \times b = b \times a$$

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(iii)

$$\frac{-19}{29} \times \frac{29}{-19} = 1$$

✅ Property: Multiplicative Inverse Property

Explanation:
The product of a number and its reciprocal (multiplicative inverse) is 1.

$$a \times \frac{1}{a} = 1$$

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Question 2:

Tell what property allows you to compute

$$\frac{1}{3} \times (6 \times \frac{4}{3}) \text{ as } (\frac{1}{3} \times 6) \times \frac{4}{3}$$

✅ Property: Associative Property of Multiplication

Explanation:
Grouping of numbers does not change the product.

$$a \times (b \times c) = (a \times b) \times c$$

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Question 3:

The product of two rational numbers is always a ———.

✅ Answer: Rational number

Explanation:
The set of rational numbers is closed under multiplication.
That means multiplying any two rational numbers gives another rational number.