The DAV Class 7 Maths Book Solutions Pdf and **DAV Class 7 Maths Chapter 1 Worksheet 3** Solutions of Rational Numbers offer comprehensive answers to textbook questions.

## DAV Class 7 Maths Ch 1 WS 3 Solutions

Question 1.

Write the following rational numbers

(i) \(\frac{33}{77}\)

Answer:

\(\frac{33}{77}\)

(ii) \(\frac{64}{-20}\)

Answer:

\(\frac{64}{-20}=\frac{64 \div 4}{-20 \div 4}=\frac{16}{-5}\)

(iii) \(\frac{-27}{-15}\)

Answer:

\(\frac{-27}{-15}=\frac{-27 \div 3}{-15 \div 3}=\frac{-9}{-5}\)

(iv) \(\frac{-105}{98}\)

Answer:

\(\frac{-105}{98}=\frac{-105 \div 7}{98 \div 7}=\frac{-15}{14}\)

Question 2.

Find x such that the rational numbers in each of the following pairs, become equivalent.

(i) \(\frac{9}{-5}, \frac{x}{10}\)

Answer:

\(\frac{9}{-5}=\frac{x}{10}\)

⇒ -5x = 90

x = \(\frac{90}{-5}\)

x = -18

∴ Equivalent rational numbers are \(\frac{9}{-5}, \frac{-18}{10}\)

(ii) \(\frac{8}{7}, \frac{x}{-35}\)

Answer:

\(\frac{8}{7}=\frac{x}{-35}\)

⇒ 7 × x = 8 × -35

x = \(\frac{8 \times-35}{7}\)

∴ x = -40

∴ Equivalent rational numbers are \(\frac{8 \times-35}{7}\)

(iii) \(\frac{36}{x}\), 2

Answer:

\(\frac{36}{x}=\frac{2}{1}\)

⇒ 2x = 36

x = 18

∴ Equivalent rational numbers are \(\frac{36}{18}\), 2

(iv) \(\frac{x}{6}\), -13

Answer:

\(\frac{x}{6}\) = -13

⇒ x = -13 × 6

x = -78

∴ Equivalent rational numbers = \(\frac{-78}{6}=\frac{-13}{1}\)

Question 3.

Check whether the following rational numbers are in standard form. If not, write them in standard form.

(i) \(\frac{-3}{19}\)

Answer:

\(\frac{-3}{19}\) is in standard form.

(ii) \(\frac{4}{-7}\)

Answer:

\(\frac{4}{-7}\) is in standard form.

(iii) \(\frac{14}{35}\)

Answer:

\(\frac{14}{35}\) is not in standard form. Its standard form is \(\frac{14 \div 7}{35 \div 7}=\frac{2}{5}\)

(iv) \(\frac{8}{-72}\)

Answer:

\(\frac{8}{-72}\) is not in standard form. Its standard form is \(\frac{8 \div 8}{-72 \div 8}=\frac{1}{-9}\)

Question 4.

Fill in the blanks.

Answer:

Let \(\frac{2}{7}=\frac{8}{x}=\frac{y}{-63}\)

⇒ 2 × x = 7 × 8 and 7 × y = 2 × -63

∴ x = 28

∴ y = -18

Hence x = 28 and y = -18

Answer:

Let \(\frac{36}{x}=\frac{-4}{9}=\frac{-84}{y}\)

⇒ -4x = 36 × 9

x = -81

and \(\frac{-4}{9}=\frac{-84}{y}\)

⇒ -4y = 9 × -84

∴ y = 189

Hence x = 81 and y = 189

Answer:

Let \(\frac{105}{x}=\frac{y}{-99}=\frac{-5}{-11}\)

\(\frac{105}{x}=\frac{-5}{-11}\)

⇒ -5x = 105 × (-11)

⇒ x = \(\frac{105 \times(-11)}{-5}\) = 231

x = 231

\(\frac{y}{-99}=\frac{-5}{-11}\)

⇒ -11y = (-5) × (-99)

⇒ y = \(\frac{(-5) \times(-99)}{(-11)}\) = -45

∴ y = -45

Hence x = 231 and y = -45