The document RD Sharma Solutions - Ex-5.4 & Ex-5.5, Operations On Rational Numbers, Class 7, Math Class 7 Notes | EduRev is a part of the Class 7 Course RD Sharma Solutions for Class 7 Mathematics.

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**Ex-5.4**

**Q1. Divide:**

**Solution.**

**Q2. Find the value and express as a rational number in standard form:**

**Solution.**

**Q3. The product of two rational numbers is 15. If one of the numbers is -10, find the other.**

**Solution.**

Let the number to be found be x

Hence the number is

**Q4. The product of two rational numbers is âˆ’8/9. If one of the numbers is âˆ’4/15, find the other.**

**Solution.**

Let the number to be found be x

Hence the number is x = 10/3

**Q5. By what number should we multiply âˆ’1/6 so that the product may be âˆ’23/9?**

**Solution.**

Let the number to be found be x

Hence the number is x = 46/3

**Q6. By what number should we multiply âˆ’15/28 so that the product may be âˆ’5/7?**

**Solution.**

Let the number to be found be x

Hence the number is x = 4/3

**Q7. By what number should we multiply âˆ’8/13 so that the product may be 24?**

**Solution.**

Let the number to be found be x

Hence the number is x=âˆ’39

**Q8. By what number should âˆ’3/4 be multiplied in order to produce âˆ’2/3?**

**Solution.**

Let the number to be found be x

Hence the number is x = âˆ’39

**Q9. Find (x + y)Ã·(x â€”y), if**

**Solution.**

**Q10. The cost of metres of rope is Rs. Find its cost per metre.**

**Solution.**

metres of rope cost= Rs

Cost per metre

**Q11. The cost of metres of cloth is Rs Find the cost of cloth per metre. **

**Solution.**

metres of rope cost =

Cost per metre

**Q12. By what number should âˆ’33/16 be divided to get âˆ’11/4?**

**Solution.**

The number is x = 3/4

**Q13. Divide the sum of âˆ’13/5 and 12/7 by the product of âˆ’31/7 and âˆ’1/2**

**Solution.**

**Q14. Divide the sum of 65/12 and 8/3 by their difference.**

**Solution.**

**Q15. If 24 trousers of equal size can be prepared in 54 metres of cloth, what length of cloth is required for each trouser?**

**Solution.**

Length of cloth required for each trouser

= 54/24

= 94metres

9/4mmetres of cloth is required to make each trouser

**Ex-5.5**

**Q1. Find six rational numbers between âˆ’4/8 and 3/8**

We know that

-4,-3,-2,-1,0,1,2,3

Therefore

Hence 6 rational numbers between

**Q2. Find 10 rational numbers between 7/13 and âˆ’4/13**

We know that

76543210-1-2-3-4

Therefore

Hence the 10 rational numbers between 7/13 and âˆ’4/13 are

*Q3. State true or false:*

*(i) Between any two distinct integers there is always an integer.*

FALSE

*(ii) Between any two distinct rational numbers there is always a rational number.*

TRUE

*(iii) Between any two distinct rational numbers there are infinitely many rational numbers.*

TRUE

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