DAV Class 7 Maths Chapter 1 Worksheet 3 Solutions

by

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 = \(\frac{-78}{6}=\frac{-13}{1}\)

DAV Class 7 Maths Chapter 1 Worksheet 3 Solutions

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.
DAV Class 7 Maths Chapter 1 Worksheet 3 Solutions 1
Answer:
Let \(\frac{2}{7}=\frac{8}{x}=\frac{y}{-63}\)
⇒ 2 × x = 7 × 8 and 7 × y = 2 × -63
DAV Class 7 Maths Chapter 1 Worksheet 3 Solutions 2
∴ x = 28
∴ y = -18
Hence x = 28 and y = -18

DAV Class 7 Maths Chapter 1 Worksheet 3 Solutions 3
Answer:
Let \(\frac{36}{x}=\frac{-4}{9}=\frac{-84}{y}\)
⇒ -4x = 36 × 9
DAV Class 7 Maths Chapter 1 Worksheet 3 Solutions 4
x = -81
and \(\frac{-4}{9}=\frac{-84}{y}\)
⇒ -4y = 9 × -84
DAV Class 7 Maths Chapter 1 Worksheet 3 Solutions 7
∴ y = 189
Hence x = 81 and y = 189

DAV Class 7 Maths Chapter 1 Worksheet 3 Solutions

DAV Class 7 Maths Chapter 1 Worksheet 3 Solutions 5
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