Insert a rational number between 2 3 and 5 7

We have to find the one rational between 2 3 and 5 7 . Rational number between any two rational numbers a b and c d given by a + c b + d Adding the numerators and denominators of 2 3 and 5 7 So, 2 + 5 3 + 7 = 7 10 Thus, a rational number between 2 3 and 5 7 is 7 10

Insert a rational number between 4 7 and 9 11

We have to find the one rational between 4 7 and 9 11 . Rational number between any two rational numbers a b and c d given by a + c b + d Adding the numerators and denominators of 4 7 and 9 11 So, 4 + 9 7 + 11 = 13 18 Thus, a rational number between 4 7 and 9 11 is 13 18

Insert a rational number between 5 7 and 6 11

We have to find the one rational between 5 7 and 6 11 . Rational number between any two rational numbers a b and c d given by a + c b + d Adding the numerators and denominators of 5 7 and 6 11 So, 5 + 6 7 + 11 = 11 18 Thus, a rational number between 5 7 and 6 11 is 11 18

Insert three rational numbers between 5 9 and 8 11

We have given 5 9 and 8 11 For finding four rational numbers between any numbers first, we make denominator of both same. So, LCM of 9 and 11 is 99 . Now, the given rational number on the denominator of 99 are 5 9 × 11 11 = 55 99 and 8 11 × 9 9 = 72 99 Therefore, three rational numbers between 5 9 and 8 11 = 56 99 , 64 99 and 71 99 .

Insert three rational numbers between 3 8 and 10 13

We have given 3 8 and 10 13 For finding four rational numbers between any numbers first, we make denominator of both same. So, LCM of 8 and 13 is 104 . Now, the given rational number on the denominator of 104 are 3 8 × 13 13 = 39 104 and 10 13 × 8 8 = 80 104 Therefore, three rational numbers between 3 8 and 10 13 = 67 104 , 75 104 and 55 104 .

Insert three rational numbers between 2 7 and 11 17

We have given 2 7 and 11 17 For finding four rational numbers between any numbers first, we make denominator of both same. So, LCM of 7 and 17 is 119 . Now, the given rational number on the denominator of 119 are 2 7 × 17 17 = 34 119 and 11 17 × 7 7 = 77 119 Therefore, three rational numbers between 2 7 and 11 17 = 45 119 , 67 119 and 37 119 .

Without actual division, state 17 125 is a terminating decimal or not.

We have to find whether 17 125 is a terminating decimal or not. If the factors of denominator are 2 or 5 or both 2 and 5 then the given number is terminating decimal. Prime factor of 125 125 = 5 × 5 × 5 = 5 3 Prime factorization of 125 contains only 5 as a factor, Hence, 17 125 is a terminating decimal.