The DAV Class 7 Maths Book Solutions Pdf and DAV Class 7 Maths Chapter 1 Worksheet 6 Solutions of Rational Numbers offer comprehensive answers to textbook questions.
DAV Class 7 Maths Ch 1 WS 6 Solutions
Question 1.
Determine which rational number is greater in each cases:
(i) \(\frac{5}{8}, \frac{-3}{7}\)
Answer:
\(\frac{5}{8}, \frac{-3}{7}=\frac{5 \times 7}{8 \times 7}, \frac{-3 \times 8}{8 \times 7}\)
= \(\frac{35}{56}, \frac{-24}{56}\)
Here 35 is greater than -24
∴ \(\frac{5}{8}\) is greater than \(\frac{-3}{7}\)
(ii) \(\frac{2}{3}, \frac{8}{9}\)
Answer:
\(\frac{2}{3}, \frac{8}{9}=\frac{2 \times 9}{3 \times 9}, \frac{8 \times 3}{9 \times 3}\)
= \(\frac{18}{27}, \frac{24}{27}\)
Here 24 > 18
∴ \(\frac{8}{9}>\frac{2}{3}\)
(iii) \(\frac{-4}{3}, \frac{-6}{7}\)
Answer:
\(\frac{-4}{3}, \frac{-6}{7}=\frac{-4 \times 7}{3 \times 7}, \frac{-6 \times 3}{7 \times 3}\)
= \(\frac{-28}{21}, \frac{-18}{21}\)
Here -18 > -28
∴ \(\frac{-6}{7}\) is greater than \(\frac{-4}{3}\)
(iv) \(\frac{-8}{3}, \frac{19}{-6}\)
Answer:
\(\frac{-8}{3}, \frac{19}{-6}=\frac{-8 \times 6}{3 \times 6}, \frac{19 \times 3}{-6 \times 3}\)
⇒ \(\frac{-48}{18}, \frac{-57}{18}\)
Here -48 > -57
∴ \(\frac{-8}{3}>\frac{19}{-6}\)
(v) \(\frac{-3}{-13}, \frac{-5}{-21}\)
Answer:
\(\frac{-3}{-13}, \frac{-5}{-21}=\frac{3}{13}, \frac{5}{21}\)
= \(\frac{3 \times 21}{13 \times 21}, \frac{5 \times 13}{21 \times 13}\)
= \(\frac{63}{273}, \frac{65}{273}\)
Here 65 > 63
∴ \(\frac{-5}{-21}>\frac{-3}{-13}\)
(vi) \(\frac{-7}{11}, \frac{5}{-8}\)
Answer:
\(\frac{-7}{11}, \frac{5}{-8}=\frac{-7 \times-8}{11 \times-8}, \frac{5 \times 11}{-8 \times 11}\)
= \(\frac{56}{-88}, \frac{55}{-88}\)
Here 56 > 55
∴ \(\frac{-7}{11}>\frac{5}{-8}\)
Question 2.
Find the value of x, if:
(i) \(\frac{3}{-5}=\frac{x}{15}\)
Answer:
\(\frac{3}{-5}=\frac{x}{15}\)
⇒ 5x = 3 × 15
⇒ x = \(\frac{3 \times 15}{-5}\)
⇒ x = -9
(ii) \(\frac{9}{15}=\frac{x}{-50}\)
Answer:
\(\frac{9}{15}=\frac{x}{-50}\)
⇒ 15x = 9 × -50
⇒ x = \(\frac{9 \times-50}{15}\)
⇒ x = -30
(iii) \(\frac{36}{x}\) = -4
Answer:
\(\frac{36}{x}\) = -4
⇒ -4x = 36
⇒ x = \(\frac{36}{-4}\)
⇒ x = -9
(iv) \(\frac{7}{-x}\) = 7
Answer:
\(\frac{7}{-x}\) = 7
⇒ – 7x = 7
⇒ x = -1
Question 3.
(i) \(\frac{-2}{9}, \frac{8}{-36}\)
Answer:
\(\frac{-2}{9}, \frac{8}{-36}\) = -2 × -36 and 9 × 8 = 72 = 72
∴ The given rational numbers are same.
(ii) \(\frac{5}{9}, \frac{4}{6}\)
Answer:
\(\frac{5}{9}, \frac{4}{6}\) = 5 × 6 and 4 × 9 = 30 < 36
∴ \(\frac{5}{9}<\frac{4}{6}\)
(iii) \(\frac{-7}{-8}, \frac{14}{17}\)
Answer:
\(\frac{-7}{-8}, \frac{14}{17}\)
⇒ 7 × 17 and 8 × 14
⇒ 119 and 112
⇒ 119 > 112
∴ \(\frac{-7}{-8}>\frac{14}{17}\)
(iv) \(\frac{-4}{7}, \frac{5}{-9}\)
Answer:
\(\frac{-4}{7}, \frac{5}{-9}\)
= -4 × -9 and 5 × 7 = 36 < 35
∴ \(\frac{-4}{7}>\frac{5}{-9}\)
(v) \(\frac{-5}{8}, \frac{-3}{4}\)
Answer:
\(\frac{-5}{8}, \frac{-3}{4}\)
= -5 × 4 and -3 × 8 = -20 > -24
∴ \(\frac{-5}{8}>\frac{-3}{4}\)
(vi) \(\frac{6}{7}, \frac{-54}{-63}\)
Answer:
\(\frac{6}{7}, \frac{-54}{-63}\)
= 6 × -63 and 7 × -54 = -378
= -378
∴ \(\frac{6}{7}=\frac{-54}{-63}\)
Question 4.
Arrange the following in ascending order:
(i) \(\frac{4}{7}, \frac{5}{9}, \frac{2}{5}\)
Answer:
\(\frac{4}{7}, \frac{5}{9}, \frac{2}{5}\)
L.C.M of 7, 9, 5 = 315
= \(\frac{4 \times 45}{7 \times 45}, \frac{5 \times 35}{9 \times 35}, \frac{2 \times 63}{5 \times 63}\)
= \(\frac{180}{315}, \frac{175}{315}, \frac{126}{315}\)
Here 126 < 175 < 180
∴ \(\frac{2}{5}<\frac{5}{9}<\frac{4}{7}\)
(ii) \(\frac{-3}{4}, \frac{-5}{-12}, \frac{-7}{16}\)
Answer:
\(\frac{-3}{4}, \frac{-5}{-12}, \frac{-7}{16}\)
L.C.M. of 4, 12, 16 = 48
= \(\frac{-3 \times 12}{4 \times 12}, \frac{5 \times 4}{12 \times 4}, \frac{-7 \times 3}{16 \times 3}\)
= \(\frac{-36}{48}, \frac{20}{48}, \frac{-21}{48}\)
as -36 < -21 < 20
∴ \(\frac{-3}{4}<\frac{-7}{16}<\frac{-5}{-12}\)
Question 5.
Arrange the following in descending order:
(i) \(\frac{2}{5}, \frac{-1}{2}, \frac{8}{-15}, \frac{-3}{-10}\)
Answer:
\(\frac{2}{5}, \frac{-1}{2}, \frac{8}{-15}, \frac{-3}{-10}\)
= \(\frac{2}{5}, \frac{-1}{2}, \frac{-8}{15}, \frac{3}{10}\)
L.C.M. of 5, 2, 15 and 10 = 30
\(\frac{2 \times 6}{5 \times 6}, \frac{-1 \times 15}{2 \times 15}, \frac{-8 \times 2}{15 \times 2}, \frac{3 \times 3}{10 \times 3}\)
= \(\frac{12}{30}, \frac{-15}{30}, \frac{-16}{30}, \frac{9}{30}\)
Here 12 > 9 > -15 > – 16
∴ \(\frac{2}{5}>\frac{-3}{-10}>\frac{-1}{2}>\frac{8}{-15}\)
(ii) \(\frac{-7}{10}, \frac{8}{-15}, \frac{19}{30}, \frac{-2}{-5}\)
Answer:
\(\frac{-7}{10}, \frac{8}{-15}, \frac{19}{30}, \frac{-2}{-5}\)
= \(\frac{-7}{10}, \frac{-8}{15}, \frac{19}{30}, \frac{2}{5}\)
L.C.M. of 10, 15, 30, 5 = 30
\(\frac{-7 \times 3}{10 \times 3}, \frac{-8 \times 2}{15 \times 2}, \frac{19 \times 1}{30 \times 1}, \frac{2 \times 6}{5 \times 6}\)
= \(\frac{-21}{30}, \frac{-16}{30}, \frac{19}{30}, \frac{12}{30}\)
Here 19 > 12 > -16 > – 21
∴ \(\frac{19}{30}>\frac{-2}{-5}>\frac{8}{-15}>\frac{-7}{10}\)
DAV Class 7 Maths Chapter 1 Value Based Questions
Question 1.
Sukhdev, a farmer, had a son and a daughter. He decided to divide his property amount in his children. He gave \(\frac{2}{5}\) of the property to his son and \(\frac{4}{10}\) to his daughter, and rest in a charitable trust.
(i) Whose share was more, son’s or daughter’s
Answer:
Son’s share in property = \(\frac{2}{5}=\frac{2 \times 2}{5 \times 2}=\frac{4}{10}\)
And, daughter’s share in property = \(\frac{4}{10}\)
So, both son and daughter have equal share in property.
(ii) What do you feel about Sukhdev’s decision? Which values are exhibited here?
Answer:
Sukhdev made a good decision. He divided his property equally among his children without any gender bias.
It shows that both children are important for him. He is also dedicated for the development of poor people in the society.
Question 2.
Kavita along with her family zvs planning a vacation at a hill station. But, they were confused where to go. Kavita’s mother asked her to find out the maximum temperature of few hill stations for deciding on the place to visit. She checked the weather report at the internet and found that—
Shimla’s temperature = \(\left(\frac{-7}{2}\right)^0\) C
Dalhousie’s temperature = -5° C
Manali’s temperature = \(\left(\frac{-8}{5}\right)^0\)C
(i) Arrange the temperatures of these hill stations in ascending order.
(ii) Which place will they decide to visit?
(iii) What value is exhibited in the above situation?
Answer:
(i) Shimla’s temperature = \(\left(\frac{-7}{2}\right)^0\)C
= -3.5° C
Dalhousie’s temperature = -5° C
Manali’s temperature = \(\left(\frac{-8}{5}\right)^0\) C
= -1.60 C
As we can see Dalhousie’s temperature is the minimum temperature and Manali’s temperature is the maximum temperature.
So, the temperature of these hill stations is ascending order are as follows:
-5° C < -3.5° C < -1.6° C
i.e., -1.6° C > -3.5° C > -5° C
(ii) As Manali has the maximum temperature, so they will decide to visit Manali.
(iii) Kavita is an intelligent and nature loving girl. She has good knowledge of computers and internet. She knows very well that internet is a better place for searching any information. It is a good source for collecting any information and data.