# Exercise 1.3 class 8 solution

### Exercise 1.3 class 8 solution-

Rational numbers are a subset of real numbers and can be defined as numbers that can be expressed as the quotient or fraction of two integers, where the denominator is not zero. In other words, a rational number is any number that can be written in the form a/b, where “a” and “b” are integers, and “b” is not equal to zero.

Here are some key characteristics of rational numbers:

1. Fractional Form: Rational numbers are most commonly represented as fractions. For example, 1/2, -3/4, and 5 are all rational numbers.
2. Terminating or Repeating Decimals: Rational numbers can also be represented as decimal numbers. If the decimal representation of a rational number either terminates (ends) or repeats periodically, it is still considered rational. For example, 0.75 (which is the same as 3/4) and 0.333… (repeating threes, which is the same as 1/3) are rational numbers.
3. All Integers Are Rational: Every integer is a rational number because it can be expressed as a fraction with a denominator of 1. For example, 5 can be expressed as 5/1.
4. Closure under Addition and Subtraction: When you add, subtract, or multiply two rational numbers, the result is always a rational number, as long as the denominator is not zero. This means that rational numbers are closed under the these operations.
5. Not Closed under Division:
6. Rational numbers are not closed under division if the denominator of the result is zero, which is undefined.
7. Examples of rational numbers include:
8. 1/2
9. -3/4
10. 5
11. 0.25 (same as 1/4)
12. -2.333… (repeating -2s, which is the same as -7/3)
13. Rational numbers are a fundamental concept in mathematics and are used in various mathematical operations, equations, and real-world applications.

### Exercise 1.3 class 8 solution -solution pdf

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#### Exercise 1.3 class 8 solution-Commutative property of rational number under multiplication

The commutative property of multiplication holds for rational numbers, just as it does for real numbers. This property states that the order in which you multiply rational numbers does not affect the result. In other words, for any rational numbers a and b:

a * b = b * a

This property is true for all rational numbers, and it simplifies calculations because you can freely rearrange the numbers being multiplied without changing the final product. For example, if you have the rational numbers 3/4 and 2/5:

(3/4) * (2/5) = (2/5) * (3/4)

Regardless of the order in which you multiply them, the result will be the same. This property applies to all rational numbers and is a fundamental concept in arithmetic and algebra.

#### Exercise 1.3 class 8 solution-Associative property of rational numbers under multiplication

The associative property of multiplication holds for rational numbers, just as it does for real numbers. This property states that when you multiply three or more rational numbers, the way you group them does not affect the result. In other words, for any rational numbers a, b, and c:

(a * b) * c = a * (b * c)

This property is true for all rational numbers and is fundamental in arithmetic and algebra. It allows you to regroup and multiply rational numbers in any order, and the result remains the same. For example, if you have the rational numbers 2/3, 3/4, and 4/5:

(2/3 * 3/4) * 4/5 = 2/3 * (3/4 * 4/5)