Ex 3.4, 1

Transcript

Ex 3.4, 1 Represent the rational numbers 2/3,−5/4 and 1 1/2 on a single number line. To represent all of them in one number line, we make their denominators same Our rational numbers are 𝟐/𝟑, (−𝟓)/𝟒 and 1 1/2=1+1/2=(1 × 2 + 1)/2=(2 + 1)/2=𝟑/𝟐 For these three denominators 3, 4 and 2 Common denominator = LCM of 2, 3 and 4 = LCM of 2, 3 and 4 = 2 × 2 × 3 = 4 × 3 = 12 So, our numbers with same denominator are 𝟐/𝟑=2/3 ×4/4=𝟖/𝟏𝟐 (−𝟓)/𝟒=(−5)/4 ×3/3=(−𝟏𝟓)/𝟏𝟐 𝟑/𝟐=3/2 ×6/6=𝟏𝟖/𝟏𝟐 Now, let’s figure out between what points we have to draw the number line Here, 𝟖/𝟏𝟐 < 1 (−𝟏𝟓)/𝟏𝟐, since numerator is bigger (−𝟏𝟓)/𝟏𝟐 < –1 𝟏𝟖/𝟏𝟐, since numerator is bigger 𝟏𝟖/𝟏𝟐 > 1 Here, 𝟖/𝟏𝟐 < 1 (−𝟏𝟓)/𝟏𝟐, since numerator is bigger (−𝟏𝟓)/𝟏𝟐 < –1. So, we draw number line till –2 𝟏𝟖/𝟏𝟐, since numerator is bigger 𝟏𝟖/𝟏𝟐 > 1. So, we draw number line till 2 Thus, we draw number line from –2 to 2 Since denominator is 12 ∴ We divide number line between 0 & 1 into 12 equal parts. And, continue for 1 to 2 Similarly, do same for 0 to –2 Now, marking our points