What will you have to do to show - 3 5 , 2 5 , 8 5 , 12 5 etc. on number line.

We know that, positive rational numbers are always represented on the right side of the zero on the number line. While the negative rational numbers are always represented on the left side of zero on the number line. In order to show - 3 5 , 2 5 , 8 5 , 12 5 etc. on number line. Since the rational number - 3 5 is negative. So, it will always be represented on the left side of zero on the number line. So, first we need to divide the number line between zero and - 1 into five equal parts. Since the rational number 2 5 is positive. So, it will always be represented on the right side of zero on the number line. So, first we need to divide the number line between zero and one into five equal parts. Since the rational number 8 5 is positive. So, it will always be represented on the right side of zero on the number line. So, first we need to divide the number line between one and two into five equal parts. Since the rational number 12 5 is positive. So, it will always be represented on the right side of zero on the number line. So, first we need to divide the number line between two and three into five equal parts.

Find any 5 rational numbers between 2 7 and 4 7 .

A rational number between 2 7 and 4 7 is 1 2 2 7 + 4 7 = 3 7 Then, 2 7 < 3 7 < 4 7 A rational number between 2 7 and 3 7 = 1 2 2 7 + 3 7 = 5 14 A rational number between 3 7 and 4 7 = 1 2 3 7 + 4 7 = 7 14 = 1 2 A rational number between 2 7 and 5 14 = 1 2 2 7 + 5 14 = 9 28 A rational number between 3 7 and 1 2 = 1 2 3 7 + 1 2 = 13 28 Therefore, 2 7 < 9 28 < 5 14 < 3 7 < 13 28 < 1 2 < 4 7 Hence, 9 28 , 5 14 , 3 7 , 13 28 and 1 2 are the five rational numbers lying between 2 7 and 4 7 .

Find 3 rational numbers between 1 5 and 1 7 .

We need to find the three rational numbers between 1 5 and 1 7 . Take the LCM of the denominators LCM 5 , 7 = 35 Now multiply and divide both the numerator and denominator of the first rational number by 7 and the second rational number by 5 , we get 1 5 × 7 7 = 7 35 and 1 7 × 5 5 = 5 35 But now there is only a single rational number between them. So we should multiply them by any number which creates three or more rational numbers between them. Multiply both numerator and denominator by 2 . 7 35 × 2 2 = 14 70 and 5 35 × 2 2 = 10 70 Therefore, 14 70 > 13 70 > 12 70 > 11 70 > 10 70 Hence, 11 70 , 12 70 and 13 70 are the three rational numbers lying between 1 5 and 1 7 .

Find 11 rational numbers between - 1 3 and 1 2 .

We need to find 11 rational numbers between - 1 3 and 1 2 . Take the LCM of the denominators LCM 3 , 2 = 6 Now multiply and divide both the numerator and denominator of the first rational number by 2 and the second rational number by 3 , we get - 1 3 × 2 2 = - 2 6 and 1 2 × 3 3 = 3 6 But now there are four rational numbers between them. So we should multiply them by any number which creates three or more rational numbers between them. Multiply both numerator and denominator by 3 . - 2 6 × 3 3 = - 6 18 and 3 6 × 3 3 = 9 18 Therefore, - 6 18 < - 5 18 < - 4 18 < - 3 18 < - 2 18 < - 1 18 < 0 < 1 18 < 2 18 < 3 18 < 4 18 < 5 18 < 9 18 Hence, - 5 18 , - 4 18 , - 3 18 , - 2 18 , - 1 18 , 0 , 1 18 , 2 18 , 3 18 , 4 18 and 5 18 are the eleven rational numbers lying between - 1 3 and 1 2 .