Test Of Rational Numbers (Chapter-1)

The given question asks for the greater number between 15/20 and 35/40. To determine the greater number, we can compare the fractions by finding a common denominator. In this case, the common denominator is 40. When we convert both fractions to have a denominator of 40, we get 30/40 and 35/40. Since 35/40 is greater than 30/40, the correct answer is 35/40.

To find the equivalent rational number of 7/9 with a denominator of 45, we need to multiply both the numerator and denominator by the same number to get the desired denominator. In this case, we can multiply both 7 and 9 by 5 to get 35/45. Therefore, the equivalent rational number is 35/45.

The multiplicative identity for rational numbers is 1. This means that when any rational number is multiplied by 1, the result is the original number. For example, if we multiply 1/2 by 1, we get 1/2. Therefore, 1 is the correct answer as it satisfies the definition of a multiplicative identity for rational numbers.

The given options are 0, -3, -2/3, and 2/3. The question asks for a number that lies between 0 and -1. Among the given options, only -2/3 satisfies this condition as it is a negative number that is closer to 0 than -1. Therefore, -2/3 is the correct answer.

To find the product of two fractions, you multiply their numerators together and their denominators together. In this case, the numerator of 7/8 is multiplied by the numerator of -4/21, which gives -28. The denominator of 7/8 is multiplied by the denominator of -4/21, which gives 168. Therefore, the product of 7/8 and -4/21 is -28/168. Simplifying this fraction by dividing both the numerator and denominator by their greatest common divisor, which is 28, we get -1/6.

The reciprocal of a number is obtained by flipping the numerator and denominator of the fraction. In this case, the reciprocal of (2/5) X (-4/9) would be (-9/4) X (5/2), which simplifies to -45/8.

The numbers 1 and -1 are their own reciprocals because when a number is multiplied by its reciprocal, the result is always 1. In this case, 1 multiplied by its reciprocal (1) equals 1, and -1 multiplied by its reciprocal (-1) also equals 1. Therefore, both 1 and -1 can be considered as their own reciprocals.

The given equation (-3/8) + (1/7) = (1/7) + (-3/8) demonstrates the commutative property of addition for rational numbers. This property states that changing the order of the numbers being added does not affect the result. In this case, rearranging the order of the rational numbers (-3/8) and (1/7) does not change the sum, indicating that addition of rational numbers is commutative.

The statement is asking about the number of rational numbers between two given rational numbers. A rational number can be expressed as a fraction, where the numerator and denominator are integers. Between any two rational numbers, there are infinitely many other rational numbers. This is because we can always find a fraction that lies between any two given fractions by taking their average. Therefore, the correct answer is "Infinitely many."