Test: Rational Numbers- 1 - Class 8 MCQ

The additive inverse of a number is the number that, when added to the original number, results in zero. The additive inverse of -2/3 is 2/3 because:

-2/3 + 2/3 = 0

Hence the additive inverse of - 2/3 is 2/3.

In order to  find the multiplicative inverse of  the given number, find the reciprocal of that number.
Here the given number is -13
So the reciprocal of -13 will be -1/13
Therefore, option C is the correct answer. 

• Rational Numbers: a rational number is defined as one that can be expressed in the form a/b, where a is an integer and b is a natural number. This means that every fraction is a rational number.
• But every rational number is not a fraction. For example, -4/9 is a rational number but not a fraction, as fractions include only whole numbers as numerators and natural numbers only as denominators.
• In addition, every integer can be expressed as a fraction (for example, as the integer divided by 1). Therefore, all three statements are true.

It is the associative property and we know that the rational numbers are associative under addition.
 For eg: 5/3 + (3/2 + 1/3) = 7/2;
  (5/3 + 3/2) + 1/3 = 7/2
Here, Option 'a' is the correct answer.

Therefore, a+(b+c) = (a+b)+c

Option C: -2/3, because -2/3 is a rational number that lies between 0 and -1. The number 0 is greater than -2/3, and -3 is less than -1, while 4/3 is greater than 1, making it outside the range. ​

The property used here is the Associative Property of Multiplication. This property states that the grouping of numbers in multiplication does not affect the product. In other words, for any numbers a, b, and c, we have:

a × (b × c) = (a × b) × c

In this case:

1/3 × (6 × 4/3) = (1/3 × 6) × 4/3

-7 / 8 x 4 / 21 = - 1 / 6 - To find the product of two fractions, multiply the numerators together and the denominators together.
- (-7/8) * (4/21) = (-7 * 4) / (8 * 21) = -28 / 168
- Simplifying the fraction by dividing both the numerator and denominator by 4, we get -7 / 42
- Further simplifying by dividing both the numerator and denominator by 7, we get -1 / 6
- Therefore, the correct answer is A: -1/6.

So option A is the correct answer. 

Answer: B) A number that can be written as p/q, where p and q are integers and q ≠ 0.
A rational number is defined as any number that can be expressed as the ratio of two integers, where the denominator q is not equal to zero.

Corrected Option c:
-1.9, -1, 0, 1, 2

• Numbers in this set greater than -2: -1.9, -1, 0, 1, 2.
• This set now contains exactly 5 rational numbers greater than -2.

The sum of two rational numbers is always a rational number because the sum of two fractions (where the denominator is not zero) always results in another fraction, which remains rational.