Class 8 RD Sharma - Chapter 1 Rational Numbers - Exercise 1.7 | Set 2

Exercise 1.7 | Set 2 in Chapter 1 of RD Sharma's Class 8 mathematics textbook represents an advanced exploration of rational numbers, building upon the concepts introduced in previous exercises and Set 1. This set is designed to challenge students with complex problems that require a deep understanding of rational number properties, operations, and applications. The problems in this set are carefully curated to push students beyond mere computational skills, encouraging them to develop critical thinking, analytical reasoning, and creative problem-solving abilities. Set 2 introduces more sophisticated mathematical concepts and techniques, often bridging the gap between arithmetic and elementary algebra. Students are expected to apply their knowledge of rational numbers in multifaceted scenarios, including complex word problems that mirror real-world situations, advanced algebraic manipulations involving rational expressions, and proofs of mathematical statements about rational numbers.

Problem 11. The cost of 2 1/3 meters of cloth is Rs 75 ¼. Find the cost of cloth per meter.

Solution:

2 1 / 3 = 7 / 3 meters of cloth = Rs 301 / 4

Let us consider a number = x

 x (7 / 3) = 301 / 4

x = (301 / 4) / (7 / 3)

  = (301 / 4) × (3 / 7)

  = (301 × 3) / (4 × 7)

7 is the common factor

= (43 × 3) / (4 × 1)

= 129 / 4

= 32.25

Cost of cloth per meter is Rs 32.25

Problem 12. By what number should -33/16 be divided to get -11/4?

Solution:

Let us consider a number = x

(-33 / 16) / x = -11 / 4

-33 / 16 = x (-11 / 4)

x = (-33 / 16) / (-11 / 4)

   = (-33 / 16) × (4 / -11)

4 and 11 are the common factors

= (-33 × 4) / (16 × -11)

= (-3 × 1) / (4 × -1)

= 3 / 4

The number should be divided by 3 / 4

Problem 13. Divide the sum of -13/5 and 12/7 by the product of -31/7 and -1/2.

Solution:

Sum of -13 / 5 and 12 / 7

= -13 / 5 + 12 / 7

LCM is 35

= ((-13 × 7) + (12 × 5)) / 35

= (-91 + 60) / 35

= -31 / 35

Product of -31 / 7 and -1 / 2

= -31 / 7 × -1 / 2

= (-31 × -1) / (7 × 2)

= 31 / 14

Dividing the sum and the product,

= (-31 / 35) / (31 / 14)

= (-31 / 35) × (14 / 31)

= (-31 × 14) / (35 × 31)

31 and 7 is the common factor

= -2 / 5

Problem 14. Divide the sum of 65/12 and 12/7 by their difference.

Solution:

Sum = 65 / 12 + 12 / 7

LCM is 84

= (65 × 7 + 12 × 12) / 84

= (455 + 144) / 84

= 599 / 84

Difference i = 65 / 12 – 12 / 7

 = (65 × 7 – 12 × 12) / 84

= (455 – 144) / 84

= 311 / 84

After dividing, (599 / 84) / (311 / 84)

= (599 / 84) × (84 / 311)

84 is the common factor

= 599 / 311

Problem 15. If 24 trousers of equal size can be prepared in 54 meters of cloth, what length of cloth is required for each pair oftrousers?

Solution:

Total number trousers = 24

The total length of the cloth = 54 m

Length of the cloth required for each trouser = total length of the cloth / number of trousers = 54 / 24

6 is the common factor

Hence it can be written as 9 / 4

9 / 4 meters is required for each trouser.

Summary

Exercise 1.7 | Set 2 in Chapter 1 of RD Sharma's Class 8 mathematics textbook offers an advanced and comprehensive collection of problems focusing on rational numbers. This set builds upon the foundational concepts covered earlier, presenting students with complex, multi-step problems that require a deep understanding of rational number operations, properties, and applications. The questions span a wide range of topics, including algebraic manipulations, geometric applications, word problems reflecting real-life scenarios, and mathematical proofs. By engaging with these challenging problems, students are encouraged to develop critical thinking skills, apply mathematical concepts creatively, and build a strong foundation for more advanced mathematical studies. This exercise set serves as an excellent tool for reinforcing students' understanding of rational numbers and preparing them for higher-level mathematics courses.