  Ncert solutions

# Question 1

Q1) List five rational numbers between:

(i) –1 and 0 (ii) –2 and –1 (iii)-\frac{4}{5}\ and\ -\frac{2}{3}

(iv) -\frac{1}{2}\ and\ \frac{2}{3}

Solution 1:

(i) Let's, write, rational no with denominator 6

-\frac{6}{6}<\ -\frac{5}{6}<-\frac{4}{6}<-\frac{3}{6}<-\frac{2}{6}<-\frac{1}{6}<0\

-\frac{5}{6},-\frac{4}{6},-\frac{3}{6},-\frac{2}{6},-\frac{1}{6}

(ii) Lets write, rational no with denominator 6

-2=-\frac{12}{6} , -1=-\frac{6}{6\ }

-\frac{12}{6}<-\frac{11}{6}<-\frac{10}{6}<-\frac{9}{6}<-\frac{8}{6}<-\frac{7}{6}<-\frac{6}{6}

=-\frac{11}{6},-\frac{5}{6},-\frac{3}{2},-\frac{4}{2},-\frac{7}{6}

(iii)Let us write rational number with same denominator

-\frac{4}{5},\ -\frac{2}{3}

LCM of the two rational no 3 and 5 = 45

-\frac{36}{45},\ -\frac{30}{45}

-\frac{36}{45}<\ -\frac{35}{45}<-\frac{34}{45}<-\frac{33}{45}<-\frac{32}{45}<-\frac{31}{45}<-\frac{30}{45}

therefore, five rational no

-\frac{7}{9},\ -\frac{34}{45},\ -\frac{11}{15},-\frac{32}{45},\ -\frac{31}{45},\ -\frac{2}{3}

(iv) Let the denominator of rational no be same

-\frac{1}{2}\times3\ =\ -\frac{3}{2}\ \ ,\ \ \ \frac{2}{3}\times2\ =\ \frac{4}{6}

therefore, -\frac{3}{6}<-\frac{2}{6}<-\frac{1}{6}<0<\frac{1}{6}<\frac{2}{6}<\frac{3}{6}<\frac{2}{3}<\frac{4}{6}

therefore, five rational no between -\frac{1}{2}\ and\ \frac{2}{3} will be

-\frac{1}{3},\ -\frac{1}{6},\ 0,\ \frac{1}{6},\ \frac{1}{3}

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