Finding Rational Numbers between two Rational numbers

Transcript

Finding Rational Numbers between two Rational numbers Suppose we want to find 5 rational numbers between 1 and 2 So, 5 Rational numbers can be 3/2, 5/4, 7/4, 4/3, 5/3 But, there is a better method Find 5 rational numbers between 1 and 2As we have to find 5 rational numbers, we multiply the numbers by 𝟔/𝟔 1 = 1 × 6/6 & 2 = 2 × 6/6 Thus, 5 Rational numbers between 1 & 2 are 𝟕/𝟔 , 𝟖/𝟔 , 𝟗/𝟔 , 𝟏𝟎/𝟔 , 𝟏𝟏/𝟔 Find 6 rational numbers between −2 and −3As we have to find 6 rational numbers, we multiply the numbers by 𝟕/𝟕 −2 = −2 × 7/7 & −3 = −3 × 7/7 Thus, 6 Rational numbers between −2 & −3 are (−𝟏𝟓)/𝟕 , (−𝟏𝟔)/𝟕, (−𝟏𝟕)/𝟕, (−𝟏𝟖)/𝟕, (−𝟏𝟗)/𝟕, (−𝟐𝟎)/𝟕 Find 3 rational numbers between 𝟏/𝟒 and 𝟏/𝟓Since numbers don’t have the same denominator We make denominator same Now, Common denominator = LCM of 4 & 5 = 20 We take denominator as LCM of 𝟏/𝟒 and 𝟏/𝟓 i.e. 20 So, our numbers with same denominator are 1/4 = 1/4 × 5/5 & 1/5 = 1/5 × 4/4 So, now we need to find 3 rational numbers between 4/20 and 5/20 Since have to find 3 rational numbers, we multiply the numbers by 𝟒/𝟒 4/20 = 4/20 × 4/4 & 5/20 = 5/20 × 4/4 Thus, 3 Rational numbers between 1/4 & 1/5 are 𝟏𝟕/𝟖𝟎 , 𝟏𝟖/𝟖𝟎 , 𝟏𝟗/𝟖𝟎