## Maharashtra State Board Class 7 Maths Solutions Chapter 5 Operations on Rational Numbers Practice Set 23

Question 1.

Write three rational numbers that lie between the two given numbers.

i. \(\frac{2}{7}, \frac{6}{7}\)

ii. \(\frac{4}{5}, \frac{2}{3}\)

iii. \(-\frac{2}{3}, \frac{4}{5}\)

iv. \(\frac{7}{9},-\frac{5}{9}\)

v. \(\frac{-3}{4}, \frac{+5}{4}\)

vi. \(\frac{7}{8}, \frac{-5}{3}\)

vii. \(\frac{5}{7}, \frac{11}{7}\)

viii. \(0, \frac{-3}{4}\)

Solution:

i. \(\frac{2}{7}, \frac{6}{7}\)

The three numbers lying between \(\frac { 2 }{ 7 }\) and \(\frac { 6 }{ 7 }\) are \(\frac{3}{7}, \frac{4}{7}, \frac{5}{7}\)

ii. \(\frac{4}{5}, \frac{2}{3}\)

\(\frac{4}{5}=\frac{24}{30}, \frac{2}{3}=\frac{20}{30}\)

The three numbers between \(\frac { 4 }{ 5 }\) and \(\frac { 2 }{ 3 }\) are \(\frac{21}{30}, \frac{22}{30}, \frac{23}{30}\)

iii. \(-\frac{2}{3}, \frac{4}{5}\)

\(\frac{-2}{3}=\frac{-10}{15}, \frac{4}{5}=\frac{12}{15}\)

The three numbers between \(\frac { -2 }{ 3 }\) and \(\frac { 4 }{ 5 }\) are \(\frac{-9}{15}, \frac{-7}{15}, \frac{4}{15}\)

iv. \(\frac{7}{9},-\frac{5}{9}\)

The three numbers between \(\frac { 7 }{ 9 }\) and \(\frac { -5 }{ 9 }\) are \(\frac{6}{9}, 0, \frac{-4}{9}\)

v. \(\frac{-3}{4}, \frac{+5}{4}\)

The three numbers between \(\frac { -3 }{ 4 }\) and \(\frac { +5 }{ 4 }\) are \(\frac{-2}{4}, \frac{-1}{4}, \frac{3}{4}\)

vi. \(\frac{7}{8}, \frac{-5}{3}\)

\(\frac{7}{8}=\frac{21}{24}, \frac{-5}{3}=\frac{-40}{24}\)

The three numbers between \(\frac { 7 }{ 8 }\) and \(\frac { -5 }{ 3 }\) are \(\frac{17}{24}, \frac{11}{24}, \frac{-13}{24}\)

vii. \(\frac{5}{7}, \frac{11}{7}\)

The three numbers between \(\frac { 5 }{ 7 }\) and \(\frac { 11 }{ 7 }\) are \(\frac{6}{7}, \frac{8}{7}, \frac{9}{7}\)

viii. \(0, \frac{-3}{4}\)

The three numbers between 0 and \(\frac { -3 }{ 4 }\) are \(\frac{-1}{8}, \frac{-2}{8}, \frac{-5}{8}\)

**Maharashtra Board Class 7 Maths Chapter 5 Operations on Rational Numbers Practice Set 23 Intext Questions and Activities**

Question 1.

Answer the following questions: (Textbook pg. no. 36)

- Write all the natural numbers between 2 and 9.
- Write all the integers between -4, and 5.
- Which rational numbers are there between \(\frac { 1 }{ 2 }\) and \(\frac { 3 }{ 4 }\) ?

Solution:

- 3, 4, 5, 6, 7, 8
- -3, -2, -1, 0, 1, 2, 3, 4
- \(\frac{1}{2}=\frac{1 \times 2}{2 \times 2}=\frac{2}{4}=\frac{2 \times 10}{4 \times 10}=\frac{20}{40}\)

\(\frac{3}{4}=\frac{3 \times 10}{4 \times 10}=\frac{30}{40}\)

∴ The rational numbers between \(\frac { 1 }{ 2 }\) and \(\frac { 3 }{ 4 }\) are \(\frac{21}{40}, \frac{22}{40}, \frac{25}{40}, \frac{27}{40}\) etc.