Rational Numbers Worksheet

Fill in the blanks Type Questions

1. A swimming pool in a society can accommodate up to 25 children at once. But only 4 children are in the pool in the afternoon due to the bright weather.
   
   The amount of pool occupied by people can be expressed as a/b. Now, if we multiply this number by its reciprocal and add the additive identity to the result, the number obtained at the end is ____________.
   
   Multiple Choice Questions
   
   
2. Arya peels off an orange and there are 8 carpels found. 
   
   She claims that one carpel is equivalent to the number 1/8. Name the type of number used to represent one carpel.
   (a) Integer
   (b) Whole Number
   (c) Natural Number
   (d) Rational Number
   
   
3. Bob was very thin and his mother started with a new diet for him. As a result, he gained  kg in first two months. In the next two months, he again gained kg.
   
   Thus, the total amount of weight acquired throughout the course of a new diet after four months will be a/an
   (a) Integer
   (b) Rational number
   (c) Natural Number
   (d) Cannot be determined
   
   
4. Dheeraj, a friend of Anuj's, came to the Durga Puja that Anuj hosted at his home. Dheeraj brought 1 kg of sweets having 28 pieces in the box. Anuj then distributed 19 pieces and so the amount of sweets distributed can be represented as 19/28. The type of number used for representing the amount of sweets distributed is a/an
   (a) Natural number
   (b) Whole number
   (c) Integer
   (d) Rational number
   
   
5. The Pushkar fair is one of India's largest camel, horse and cattle fairs having various kind of Ferris wheels.
   
   Each Ferris wheel has 24 passenger-carrying components. The first Ferris wheel is  filled while the second is  filled with passengers. If we look at these Ferris wheels, then which of the following is not true?
   (a) 
   (b) 
   (c) 
   (d) 
   
   
6. Keshav is going to her Uncle’s place and so will carry some toys with him. He checked the four drawers for the toys and noted down the number of toys each drawer has. The rational numbers formed by the three numbers are . Which of the following is correct?
   (a) 
   (b) 
   (c) 
   (d) 
   
   
7. Anurag made the decision to plant 8000 saplings with the aid of his friends in order to participate in the Green India Mission, which was introduced in 2014.
   
   
   He has finished planting 6834 young trees. The amount of saplings sown can now be expressed as . Divide this rational number by its multiplicative identity and then add additive identity to the result. What could be the reciprocal of the number obtained at the end?
   (a) 0
   (b) 1
   (c) 
   (d) 
   
   
8. Farmers are given seeds for their crops by a distributor. There are around 150 seeds in the box of type 1, of which 8 are not suitable for planting. However, the box of type 2 has around 100 seeds of which 6 are not suitable for planting. Add the amount of faulty plants in the two boxes and multiply the result with . The number obtained is equal to
   (a) 0
   (b) 1
   (c) 
   (d)  
   
   
9. Take a number say x and take its additive inverse. Add the two numbers and then multiply the result with its additive identity. Now, divide the result by the multiplicative identity and then take twice of the number obtained. What is the final result?
   (a) 0
   (b) 1
   (c) The same number
   (d) Twice the same number
   
   
10. Raghav ordered a wall shelf with 12 sections to display the show plants. Once the wall shelf was delivered, he placed the plants as shown below: 
    
    What is the amount of empty sections in the wall shelf?
    (a) 
    (b) 
    (c) 
    (d) 
    
    Subjective Questions
    
    
11. A game is played where every child has to identify a type of number out of the given numbers. If the child answers correctly, he/she receives a chocolate. Now, Chintu also participated in the game and he has to pick a number which is not rational out of the numbers given below:
    
    Chintu pick 4.9 and said this is not a rational number. Will Chintu get a chocolate? Explain your answer.
    
    
12. Som went on a holiday trip to Kedarnath. But when asked by his friend, he did not remember the time taken to reach their from Gholtir Railway Station. Now, as he knew the distance and speed of the car so, he tells that the time taken is . Which type of number is used to represent the time taken?
    
    
13. The amount of milk present in a cup  of its total capacity. There are two such cups. Now, if you notice, the amount represented is in the form of a rational number. So, when we add the amount of milk in the two cups, will the total amount be in rational number form? 
    
    
    
14. Daniel and his little brother Sam are going to take a bath. The bathtub is filled with  litres of water. When they come out after taking a bath, the tub is filled with  litres of water. Do the product of these two quantities of water be a rational number? Why or Why not?
    
    
    
15. A garden near the city has around 380 mango trees in it. The number of mangoes these trees together had is 38000. So, the average number of mangoes each tree had is given by 100. Represent the average number of mangoes each tree had in rational number form with denominator 380 if possible.
    
    
16. There are 7 members in a family. So, Shivi bought fruits for the entire 1 week. She bought 5 kg of grapes for Rs. 228 and 5 kg of apples for Rs. 484. Shivi subtracts price of 1 kg of grapes from the price 1 kg of apple and Ronny subtracts price of 1 kg of apple from the price of 1 kg of grapes. Will both get the same result? Explain your answer using commutative property.
    
    
17. Sandy made a fruit salad which contained  amount of apples,  amount of grapes,  amount of bananas and  amount of kiwi. Using properties of rational numbers, find the product of these numbers.
    
    
18. A house party arranged at Rohini’s house where she invited her friends, classmates, neighbours and sibling. The total number of guests who attended the party is 52 which include 20 friends, 22 classmates, 10 neighbours and no siblings. Using these numbers, form four different rational numbers whose denominator is 52. What is the product of the rational numbers formed?
    
    
19. Amar has got an assignment which he needs to submit the next day and so he takes help of his brother Ramesh. 
    Assignment: Find 
    Amar got the answer as  with the help of Ramesh. Is Amar correct?
    
    
20. Abhilash runs a cloth shop and maintains a record of various clothes sold every month. The sale made in October month is huge as Diwali is the next festival. The total number clothes sold is given by the expression . How many clothes were sold in the month of October?

Fill in the blanks Type Questions

1. A swimming pool in a society can accommodate up to 25 children at once. But only 4 children are in the pool in the afternoon due to the bright weather.
   
   The amount of pool occupied by people can be expressed as a/b. Now, if we multiply this number by its reciprocal and add the additive identity to the result, the number obtained at the end is ____________.
   
   Correct Answer: 1
   Solution:
   The amount of pool occupied by people can be expressed as
   Reciprocal of 
   Their product 
   Adding the additive identity which is 0, we get
   1 + 0 = 1
   Hence, the number obtained at the end is 1.
   
   
   Multiple Choice Questions
   
   
2. Arya peels off an orange and there are 8 carpels found. 
   
   She claims that one carpel is equivalent to the number 1/8. Name the type of number used to represent one carpel.
   (a) Integer
   (b) Whole Number
   (c) Natural Number
   (d) Rational Number
   
   Correct Option: (d) Rational number
   Solution:
   One carpel is represented as  which is a rational number
   
   
3. Bob was very thin and his mother started with a new diet for him. As a result, he gained  kg in first two months. In the next two months, he again gained kg.
   
   Thus, the total amount of weight acquired throughout the course of a new diet after four months will be a/an
   (a) Integer
   (b) Rational number
   (c) Natural Number
   (d) Cannot be determined
   
   Correct Option: (b) Rational number
   Solution:
   Weight gained in first two months is  kg and in the next two months is  kg
   Total weight gained kg
   As rational number is closed under addition.
   So, the result is a rational number.
   
   
4. Dheeraj, a friend of Anuj's, came to the Durga Puja that Anuj hosted at his home. Dheeraj brought 1 kg of sweets having 28 pieces in the box. Anuj then distributed 19 pieces and so the amount of sweets distributed can be represented as . The type of number used for representing the amount of sweets distributed is a/an
   (a) Natural number
   (b) Whole number
   (c) Integer
   (d) Rational number
   
   Correct Option: (d) Rational number
   Solution:
   The amount of sweets distributed can be represented as  which is a rational number.
   
   
5. The Pushkar fair is one of India's largest camel, horse and cattle fairs having various kind of Ferris wheels.
   
   Each Ferris wheel has 24 passenger-carrying components. The first Ferris wheel is  filled while the second is  filled with passengers. If we look at these Ferris wheels, then which of the following is not true?
   (a) 
   (b) 
   (c) 
   (d) 
   
   Correct Option: (c) 
   Solution:
   Using closure property, we know that the set of rational numbers is not closed under subtraction.
   So,  is not true.
   We can verify the same:
   
   
   
6. Keshav is going to her Uncle’s place and so will carry some toys with him. He checked the four drawers for the toys and noted down the number of toys each drawer has. The rational numbers formed by the three numbers are . Which of the following is correct?
   (a) 
   (b) 
   (c) 
   (d) 
   
   Correct Option: (c) 
   Solution:
   We know that for any three rational numbers a, b and c, 
   a + (b + c) = (a + b) + c
   a × (b × c) = (a × b) × c
   are not possible
    is not true as the rational numbers  are not same.
    is true using associative property.
   
   
7. Anurag made the decision to plant 8000 saplings with the aid of his friends in order to participate in the Green India Mission, which was introduced in 2014.
   
   
   He has finished planting 6834 young trees. The amount of saplings sown can now be expressed as . Divide this rational number by
   its multiplicative identity and then add additive identity to the result. What could be the reciprocal of the number obtained at the end?
   (a) 0
   (b) 1
   (c) 
   (d) 
   
   Correct Option: (d) 
   Solution:
   Number of saplings sown can now be expressed as .
   Its multiplicative identity is 1 and additive identity of any rational number is 0.
   
   Now, reciprocal of the number obtained which is 
   
   
8. Farmers are given seeds for their crops by a distributor. There are around 150 seeds in the box of type 1, of which 8 are not suitable for planting. However, the box of type 2 has around 100 seeds of which 6 are not suitable for planting. Add the amount of faulty plants in the two boxes and multiply the result with . The number obtained is equal to
   (a) 0
   (b) 1
   (c) 
   (d)  
   
   Correct Option: (d) 
   Solution:
   Amount of faulty seeds in the box of type 1 is 
   Amount of faulty seeds in the box of type 2 is 
   Amount of faulty seeds in the two boxes 
   Multiplying this by  gives us
   
   
   
9. Take a number say x and take its additive inverse. Add the two numbers and then multiply the result with its additive identity. Now, divide the result by the multiplicative identity and then take twice of the number obtained. What is the final result?
   (a) 0
   (b) 1
   (c) The same number
   (d) Twice the same number
   
   Correct Option: (a) 0
   Solution:
   Additive inverse of x is –x
   Now, x + (–x) = 0
   Multiply the result with its additive identity which is “0”
   0 × 0 = 0
   Divide the result by the multiplicative identity which is “1”
   =0
   Take twice of the number obtained
   2×0 = 0
   The final result = 0
   
   
10. Raghav ordered a wall shelf with 12 sections to display the show plants. Once the wall shelf was delivered, he placed the plants as shown below: 
    
    What is the amount of empty sections in the wall shelf?
    (a) 
    (b) 
    (c) 
    (d) 
    
    Correct Option: (b) 
    Solution:
    Out of 12 sections, 3 sections are empty.
    So, the amount of empty sections is=
    
    Subjective Questions
    
    
11. A game is played where every child has to identify a type of number out of the given numbers. If the child answers correctly, he/she receives a chocolate. Now, Chintu also participated in the game and he has to pick a number which is not rational out of the numbers given below:
    
    Chintu pick 4.9 and said this is not a rational number. Will Chintu get a chocolate? Explain your answer.
    
    Solution:
    
    This is in the form , where p and q are integers and q ≠ 0.
    So, it is a rational number.
    Hence, Chintu is incorrect and so he will not get a chocolate.
    
    
12. Som went on a holiday trip to Kedarnath. But when asked by his friend, he did not remember the time taken to reach their from Gholtir Railway Station. Now, as he knew the distance and speed of the car so, he tells that the time taken is . Which type of number is used to represent the time taken?
    
    Solution:
    The number  is in the form , where p and q are integers and q ≠ 0.
    So, it is a rational number.
    
    
13. The amount of milk present in a cup  of its total capacity. There are two such cups. Now, if you notice, the amount represented is in the form of a rational number. So, when we add the amount of milk in the two cups, will the total amount be in rational number form? 
    
    
    Solution:
    Amount of milk in the two cups is given by:
    
    We know that the sum of two rational numbers is always a rational number.
    So, the total amount of milk in the two cups will be in the form of a rational number.
    We can verify the same:
    
    
    
14. Daniel and his little brother Sam are going to take a bath. The bathtub is filled with  litres of water. When they come out after taking a bath, the tub is filled with  litres of water. Do the product of these two quantities of water be a rational number? Why or Why not?
    
    
    Solution:
    Product of the quantities of water 
    We know that the product of two rational numbers is always a rational number.
    So, the product of these two quantities of water will be a rational number.
    We can verify the same:
    
    
    
15. A garden near the city has around 380 mango trees in it. The number of mangoes these trees together had is 38000. So, the average number of mangoes each tree had is given by 100. Represent the average number of mangoes each tree had in rational number form with denominator 380 if possible.
    
    Solution:
    Average number of mangoes each tree had is given by 100.
    Total number of mangoes = 38000 and total number of trees = 380
    The average number of mangoes each tree had in rational number form is given as .
    
    
16. There are 7 members in a family. So, Shivi bought fruits for the entire 1 week. She bought 5 kg of grapes for Rs. 228 and 5 kg of apples for Rs. 484. Shivi subtracts price of 1 kg of grapes from the price 1 kg of apple and Ronny subtracts price of 1 kg of apple from the price of 1 kg of grapes. Will both get the same result? Explain your answer using commutative property.
    
    Solution:
    Price of 1 kg of grapes =
    Price of 1 kg of apple = 
    Shivi subtracts price of 1 kg of grapes from the price 1 kg of apple.
    The number Shivi get = 
    Ronny subtracts price of 1 kg of apple from the price of 1 kg of grapes
    The number Ronny get = 
    We know that subtraction is not commutative.
    Hence, Shivi and Ronny will get different results.
    
    
17. Sandy made a fruit salad which contained  amount of apples,  amount of grapes,  amount of bananas and  amount of kiwi. Using properties of rational numbers, find the product of these numbers.
    
    Solution:
    Product of these numbers
    
    
    
18. A house party arranged at Rohini’s house where she invited her friends, classmates, neighbours and sibling. The total number of guests who attended the party is 52 which include 20 friends, 22 classmates, 10 neighbours and no siblings. Using these numbers, form four different rational numbers whose denominator is 52. What is the product of the rational numbers formed?
    
    Solution:
    The four rational numbers are:
    
    Product of these rational numbers formed is
    
    
    
19. Amar has got an assignment which he needs to submit the next day and so he takes help of his brother Ramesh. 
    Assignment: Find 
    Amar got the answer as  with the help of Ramesh. Is Amar correct?
    Solution:
    
    So, Amar did not get the correct answer.
    
    
20. Abhilash runs a cloth shop and maintains a record of various clothes sold every month. The sale made in October month is huge as Diwali is the next festival. The total number clothes sold is given by the expression . How many clothes were sold in the month of October?
    
    Solution:
    Number of clothes sold
    
    = 22 × 15
    = 330
    Hence, the number of clothes sold in the month of October is 330.