Represent 3 7 on a number line.

Given the rational number is 3 7 The given rational number is a positive and proper fraction. So, it lies between 0 and 1 on the number line. We need to divide the unit distance between 0 and 1 in 7 parts as 7 is the denominator of 3 7 Now, moving to the right side of 0 by 3 places we get: Hence, the representation of 3 7 on the number line is shown above.

Represent 29 6 on a number line.

Given the rational number is 29 6 The given rational number is a positive and improper fraction. Now, converting the improper fraction into mixed fraction we get: 29 6 = 4 5 6 So, it lies between 4 and 5 on the number line. We need to divide the unit distance between 4 and 5 in 6 parts as 6 is the denominator. Now, moving to the right side of 4 by 5 places we get: Hence, the representation of 29 6 on the number line is shown above.

Check whether the standard form of - 22 - 55 is - 2 5 or not.

We know a rational number can be expressed in p q form when q ≠ 0 To express a rational number in its standard form, ensure that a ) The denominator is not expressed as a negative number. If it is, multiply both the numerator and denominator by - 1 b ) The HCF of numerator and denominator is 1 . If it is not, divide both the numerator and denominator by the HCF to reduce to the lowest terms. Given rational number is - 22 - 55 The numerator is - 22 and the denominator is - 55 After multiplying the numerator and denominator by - 1 we get 22 55 The rational number is not in simplest form. To reduce it to the lowest term, we need to find the HCF of numerator and denominator. Now, HCF ( 22 , 55 ) = 11 So, dividing the numerator and the denominator by 11 , we get 22 ÷ 11 55 ÷ 11 = 2 5 Hence, 2 5 is the standard form of - 22 - 55 Therefore, - 2 5 is not the standard form of - 22 - 55

Check whether the standard form of 3 15 is 1 5 or not.

We know a rational number can be expressed in p q form when q ≠ 0 To express a rational number in its standard form, ensure that a ) The denominator is not expressed as a negative number. If it is, multiply both the numerator and denominator by - 1 b ) The HCF of numerator and denominator is 1 . If it is not, divide both the numerator and denominator by the HCF to reduce to the lowest terms. Given rational number is 3 15 The rational number is not in the simplest form. To reduce it to the lowest term we need to find the HCF of numerator and denominator. Now, HCF ( 3 , 15 ) = 3 So, dividing the numerator and the denominator by 3 , we get 3 ÷ 3 15 ÷ 3 = 1 5 Hence, 1 5 is the standard form of 3 15 Therefore, 1 5 is the standard form of 3 15

The standard form of 12 - 42 is - 2 7

We know a rational number can be expressed in p q form when q ≠ 0 To express a rational number in its standard form, ensure that a ) The denominator is not expressed as a negative number. If it is, multiply both the numerator and denominator by - 1 b ) The HCF of numerator and denominator is 1 . If it is not, divide both the numerator and denominator by the HCF to reduce to the lowest terms. Given rational number is 12 - 42 The numerator is 12 and the denominator is - 42 After multiplying the numerator and denominator by - 1 , we get - 12 42 The rational number is not in the simplest form. To reduce it to the lowest term we need to find the HCF of numerator and denominator. Now, HCF ( 12 , 42 ) = 6 So, dividing the numerator and the denominator by 6 , we get - 12 ÷ 6 42 ÷ 6 = - 2 7 Therefore, - 2 7 is the standard form of 12 - 42