NCERT Solutions for Class 5 Maths Chapter 6 the Dairy Farm (PDF) – 2026-27

NCERT Solutions for Class 5 Maths Chapter 6 the Dairy Farm provide clear, step-by-step answers to every exercise and in-text question from the chapter the Dairy Farm of the NCERT textbook Math Mela. Prepared by subject experts as per the latest NCERT (CBSE) syllabus for 2026-27, these NCERT Solutions for Class 5 Maths help you understand each concept, write exam-ready answers, and check your own solutions. You can read them online below or download the free Class 5 Maths Chapter 6 question-answer PDF.

NCERT Solutions for Class 5 Maths Chapter 6 the Dairy Farm

• Class: Class 5
• Subject: Maths
• Chapter: Chapter 6 – the Dairy Farm
• Textbook: Math Mela (NCERT)
• Study material: NCERT Solutions – questions with answers, free PDF

These solutions answer all the exercise questions of Chapter 6 the Dairy Farm — including the in-text questions, short-answer and long-answer questions, and activities — with complete explanations so you can follow the method, not just the final answer. Read the full solutions below.

NCERT Solutions Class 5 Maths Chapter 6 the Dairy Farm View Download

NCERT Solutions for Class 5 Maths Chapter 6 PDF Download

You can read the NCERT Solutions for Class 5 Maths Chapter 6 online above, or download the complete question-answer PDF to study the Dairy Farm offline at any time.

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NCERT Solutions for Class 5 Maths Chapter 6 PDF Download Link – Click Here to Download Solutions PDF

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Questions Covered in This Chapter

These NCERT Solutions answer all 95 questions of this chapter. The questions solved are:

1. The given shapes stand for numbers between 1 and 24. The same shape denotes the same number across all problems. Find the numbers hiding in all the shapes. a)×=d)×=b)×=e)×=c)×=f)×=×The six shape problems printed on page 70. The same shape always stands for the same number.
2. Place the digits 2, 5, and 3 appropriately to get a product close to 100. Share your reasoning in class.
3. A dairy has packed butter milk pouches in the following manner. Find the number of pouches kept in each arrangement. One is done for you. (First arrangement: 30 × 2 = 60.)
4. What other groups can you make? (with the butter milk pouches)
5. Which number am I? I am a two-digit number. Find me with the help of the following clues. (a) I am greater than 8. (b) I am not a multiple of 4. (c) I am a multiple of 9. (d) I am an odd number. (e) I am not a multiple of 11. (f) I am less than 50. (g) My ones digit is even. (h) My tens digit is odd.
6. Did you use all the clues to find the number? Which clues did not help you in finding the number?
7. Make your own numbers. Choose any two numbers and one operation from the grid. Try to make all the numbers between 0 and 20. For example, 2 can be formed as 4 – 2. Could you make all the numbers? 100255102361243−×+÷The number grid and the four operation cards printed on page 71.
8. Which numbers could you not make? Is it possible to make these numbers using three numbers? You can use two operations, if needed.
9. Which numbers between 0–20 can you get in more than one way?
10. Daljeet Kaur runs a milk processing unit. She has arranged the butter packets in the following ways. Find the number of butter packets in each case. What pattern do you notice (or observe)? Discuss in class. (a) 2 × 3 and 3 × 2 (b) 5 × 8 and 8 × 5, then 6 × 13 and 13 × 6, (e) 10 × 5 and 5 × 10 (f) 8 × 20 and 20 × 8 (g) 12 × 9 and 9 × 12
11. What is 9 × 0? 0 × 9? Is this true for the product of any two numbers? Discuss in class.
12. Let us revise multiplication by 10s and 100s. a) 4 × 10 = ___ b) 20 × 10 = ___ c) 10 × 40 = ___ d) 10 × 10 = 100 e) 20 × 50 = ___ f) 80 × 10 = ___ g) 3 × 100 = 100 × 3 = 300 h) 8 × 100 = ___ = ___ i) 10 × 100 = ___ = ___
13. Find answers to the following questions. 100 × 90 = __,000; 400 × 10 = ___; 60 × 50 = ____; 30 × 20 = 600; 700 × 4 = _,_00; 10 × 45 = ____
14. How should we write 450 in the table below? ProblemThHTO10 × 45 =    30 × 20 = 600400 × 10 =    700 × 8 =    100 × 90 =9000The place value table printed on page 73. Two rows are already filled in.
15. Fill in the table. Describe the pattern. ProblemThHTO10 × 45 =    30 × 20 = 600400 × 10 =    700 × 8 =    100 × 90 =9000The place value table printed on page 73. Two rows are already filled in.
16. Fill in the tables. Describe the pattern. Discuss in class. ProblemThHTO60 × 50 =    220 × 20 =    11 × 300 =    ProblemThHTO80 × 90 =    10 × 63 =    40 × 12 =    The two place value tables printed on page 73.
17. What will happen if we multiply numbers by 1,000? 2 × 1,000 = ; 5 × 1,000 = ; 10 × 1,000 = ; 20 × 1,000 =
18. Let us fill in the table and observe the patterns. ProblemTThThHTO2 × 1,000 = 20005 × 1,000 = 500010 × 1,000 =1000020 × 1,000 =200003 × 5,000 =     8 × 3,000 =     5 × 7,000 =     The first table printed on page 74. The first four rows are already filled in.
19. Fill in the table. ProblemTThThHTO20 × 100 =     40 × 500 =     60 × 300 =     600 × 30 =     80 × 900 =     70 × 600 =     5 × 7,000 =     The second table printed on page 74.
20. What is 18 × 5?
21. Do you think they are all correct? Why do you think so?
22. Butter packets are arranged in the following ways. (a) 3 × 18: Double one, halve the other, to get 6 × 9 = 54. Discuss why these are the same.
23. (b) 22 × 5: fill in ___ × ___ = ____
24. (c) Solve the following problems like the previous ones (fill in the Half and Double boxes): 14 × 3 = , 38 × 5 = , 16 × 4 = , 35 × 14 =
25. This halving and doubling strategy works well when we have to multiply with numbers like 5 and 25. Discuss why?
26. (d) Find the product by halving and doubling either the multiplier or the multiplicand. 1) 5 × 18 2) 50 × 28 3) 15 × 22 4) 25 × 12 5) 12 × 45 6) 16 × 45
27. (e) Give 5 examples of multiplication problems where halving and doubling will help in finding the product easily. Find the products as well.
28. (a) 4 × 19. Observe the picture and find why we need to subtract 4. The picture for 4 × 19 printed on page 76. Each small square is one item.
29. (b) 14 × 21. Observe the picture and find why we need to add 14. The picture for 14 × 21 printed on page 76. Each small square is one item.
30. (c) Give 5 examples of problems where you can use the nearest multiple to find the product easily. Find the products as well.
31. (d) Find the products of the following numbers by finding the nearest multiple. 1) 7 × 52 2) 12 × 28 3) 75 × 31 4) 99 × 15 5) 8 × 25 6) 22 × 42
32. A school has an auditorium with 35 rows, with 42 seats in each row. How many people can sit in this auditorium?
33. Priya jogs 4 kilometres every day. How many kilometers will she jog in 31 days?
34. A school has received 36 boxes of books with 48 books in each box. How many total books did the school receive in the boxes?
35. Priya uses 16 metres of cloth to make 4 kurtas. How much cloth would she need to make 8 kurtas?
36. Gollappa has 29 cows on his farm. Each cow produces 5 litres of milk per day. How many litres of milk do the cow produce in total, each day?
37. Maska Cow Farm has 297 cows. Each cow requires 18 kg of fodder per day. How much total fodder is needed to feed 297 cows every day?
38. A family of 4 produces around 35 kg of kitchen waste in a month. How much waste will the family produce in a year? The family produces _____ kg of waste in a year.
39. Kanti and John tried to solve it in the following ways. How are these solutions same or different? Discuss in class.
40. The family regularly composts the collected waste. They get around 150 kg of compost each year, which they use in their garden. 1 kg of compost is often sold in the market at ₹24. By creating their own compost, how much money have they saved in a year?
41. (a) 32 × 8. Fill the grid and complete the two column methods. ×3028    32 (30 + 2)×8____ (8 × 2)__0 (8 × 30)25632 (30 + 2)× 8____0 + 16 = 256The grid and the two column methods printed on page 79. Some numbers are already filled in.
42. (b) 69 × 45. Fill the grid and complete the column methods. ×60940  5   2700405 310569 (60 + 9)× 45 (40 + 5)45 (5 × 9)___0 (5 × 60)___0 (40 × 9)__00 (40 × 60)3,10569 (60 + 9)× 45 (40 + 5)300 + __ = 345 (5 × 69)____ + ___ = 2760 (40 × 69)= 3,105The grid and the two column methods printed on page 79. Some numbers are already filled in.
43. Solve the following problems like Nida did (using a grid). a) 78 × 4 b) 83 × 9 c) 67 × 28 d) 53 × 37
44. Solve the following problems like Kanti. a) 94 × 5 b) 49 × 6 c) 37 × 53 d) 28 × 79
45. Solve the following problems like John. a) 86 × 3 b) 72 × 7 c) 94 × 36 d) 66 × 22
46. (a) A movie theater has 8 rows of seats, and each row has 12 seats. If half the seats are filled, how many people are watching the movie? If 3 more rows get filled, how many total people will be there?
47. (b) In a test match between India and West Indies, the Indian team hit twenty-four 4s and eighteen 6s across the two innings. How many runs were scored in 4s and 6s each? 234 runs were made by running between the wickets. If 23 runs were extras, how many runs were scored by Indian team in the two innings?
48. (c) Anjali buys 15 bulbs and 12 tube lights from Sudha Electricals. Each bulb costs ₹25 and each tube light costs ₹34. How much money should Anjali give to the shopkeeper?
49. (d) A shopkeeper sold 28 bags of rice. Each bag costs ₹350. How much money did he earn by selling rice bags?
50. (e) A school library has 86 shelves and each shelf has 162 books. Find the number of books in the library.
51. A dairy cooperative in a small town gets its milk from 268 villagers. Each villager has at least 4 milk-giving cows. What is the minimum number of cows the dairy cooperative gets its milk from?
52. Discuss how this multiplication is being carried out! (Mili’s father’s method for 268 × 4, with 30 added to 4 × 60 and 200 added to 4 × 200)
53. The villagers rear various breeds of cows. Among the villagers, there are 453 Gir cows. Each of these cows give 13 litres of milk each day. How many litres of milk does the dairy cooperative receive from Gir cows everyday?
54. The dairy cooperative sells 1 kg cow ghee for ₹574. The cooperative is able to produce around 125 kg of ghee in a month. How much do they earn by selling ghee in a month?
55. Discuss what the same coloured digits might mean. (in the 574 × 125 working)
56. Solve the following problems like Nida. a) 548 × 6 b) 682 × 3 c) 324 × 18 d) 507 × 23 e) 190 × 65
57. Solve the following problems like John. a) 123 × 84 b) 368 × 32 c) 159 × 324 d) 239 × 401 e) 592 × 5 f) 101 × 22
58. Let us solve a few questions like Mili’s father: 806 × 9, 455 × 26, and 143 × 208 (fill the boxes and circles).
59. Now use Mili’s father’s method to solve the following questions. (a) 807 × 5 (b) 143 × 28 (c) 309 × 9
60. (d) 450 × 38 (e) 584 × 23 (f) 302 × 13
61. (g) 604 × 54 (h) 112 × 23 (i) 237 × 19
62. Check if Asma’s solution is correct. Asma’s solution for 46 × 59: 2,000 + 300 + 360 + 54 = 2,714. If correct, explain why. If incorrect, identify the error and correct the solution.
63. Check if Pankaj’s solution is correct. Pankaj’s solution for 203 × 54: 80 + 12 = 92; 100 + 15 = 115; = 135. If incorrect, identify the error and correct the solution.
64. Check if Lado’s solution is correct. Lado’s solution for 38 × 150: 1,500 + 400 = 1,900; 3,000 + 800 = 3,800; = 5,700.
65. Check if Kira’s solution is correct. Kira’s solution for 193 × 272: 200 + 180 + 6 = 386; 700 + 630 + 21 = 1,351; 20,000 + 18,000 + 600 = 38,600; = 40,337.
66. Check if Asher’s solution is correct. Asher’s solution for 626 × 323 gives the rows 1878, 1252, 1878 and a total of 5,018.
67. Identify the problems that have the same answer as the one given at the top of each box. Do not calculate. (12 × 17; 26 × 11; 18 × 4; 55 × 9; 101 × 42; 247 × 8; 1001 × 5; 1999 × 2)
68. Find easy ways of solving these problems. (a) 16 × 25 (b) 12 × 125 (c) 24 × 250
69. (d) 36 × 25 (e) 28 × 75 (f) 300 × 15
70. (g) 50 × 78 (h) 199 × 63 (i) 128 × 35
71. Write 5 other examples for which you can find easy ways of getting products.
72. Find the answers to the following questions based on the given information. (a) 17 × 23 = 391 (b) 17 × 24 = ___ (c) 17 × 22 = ___ (d) 16 × 23 = ___
73. (e) 8 × 9 = 72 (f) 18 × 9 = ___ (g) 28 × 9 = ___ (h) 108 × 9 = ___ (i) 18 × 23 = ___
74. To find 17 × 24, how much is to be added to 17 × 23 — 17 or 23?
75. To find 18 × 23, how much is to be added to 17 × 23 — 17 or 23?
76. Find the possible values of the coloured boxes in each of the following problems. The same colour indicates the same number in a problem. Some problems can have more than one answer. a) (2-digit) × 3 = (2-digit) b) (3-digit) × 3 = (3-digit) c) (4-digit) × 3 = (4-digit)
77. d) (2 boxes) × 5 = 1 (box) 0 e) (3 boxes, first two same colour) × 5 = (2 same-colour boxes) 0 f) (4 boxes, first three same colour) × 5 = 1 (3 same-colour boxes) 0
78. g) (3 boxes, first and third same colour) × 9 = (4 boxes, alternating two colours) h) (3 boxes) × (box, same colour as the last one) = 5,999 i) (3 boxes) × (box, same colour as the middle one) = 2,000
79. Estimate the products on the left and match them to the numbers given on the right. (25 × 31, 132 × 19, 101 × 11, 248 × 49, 12 × 25) with (2,600; 12,500; 300; 750; 1,000). Discuss how you estimated.
80. Which of the rewards would you have chosen?
81. After a week, the 3 ministers were surprised at the final amount of gold coins. Guess who received the most gold coins? Calculate how much gold coins each minister received.
82. Notice how the multiplier, multiplicand, and products are changing. What is the relationship of the new product with the original product? a) 16 × 44 = 704; 1) 8 × 88 = 704; 2) 8 × 22 = 176; 3) 16 × 22 = ___; 4) 32 × 44 = ___
83. b) 12 × 32 = 384; 1) 6 × 16 = ___; 2) 24 × 16 = ___; 3) 24 × 64 = ___; 4) 12 × 16 = ___
84. Observe and complete the given pattern: 1 × 1 = 1; 11 × 11 = 121; 111 × 111 = 12,321; 1111 × 1111 = ___
85. Observe and complete: 11 × 12 = 132; 11 × 34 = 374; 11 × 56 = 616; 11 × 78 = 858; 11 × 54 = ___; 11 × 82 = ___
86. Observe and complete: 5 × 5 = 25; 15 × 15 = 225; 25 × 25 = 625; 35 × 35 = 1,225; 45 × 45 = ___; 55 × 55 = ___
87. Observe and complete: 1 × 9 + 1 = 10; 12 × 9 + 2 = 110; 123 × 9 + 3 = 1,110; 1,234 × 9 + 4 = ___
88. Here are some numbers (8, 35, 75 / 32, 62, 13 / 66, 11, 14). Any two adjacent numbers in a row or a column are number pairs. Can you identify the pair whose product is the smallest and another pair whose product is the largest? Do you need to find every product or can you find this by looking at the numbers?
89. Mala went to a book exhibition and bought 18 books. The shop was selling 3 books for ₹150. After buying the books, she still had ₹20 left. How much money did Mala have at the beginning?
90. A village sports club organises a women’s football tournament. They sold 57 tickets for ₹115 each. They had 3 teams joining the tournament, with each team paying a participation fee of ₹1,599. (a) How much money did the club collect in total from ticket sales and team participation fees?
91. (b) The teams paid ₹1,750 in total to rent the football ground and ₹1,129 for food and water. What were the total expenses on renting the ground and food and water?
92. Ananya is watching Republic Day celebrations on the city’s public ground. There are 12 rows of students sitting in front of her and 17 rows behind her. There are 18 students to her right and 22 students to her left. (a) How many rows of students are there in total? (b) How many students are there in Ananya’s row? (c) What is the total number of students on the ground?
93. Multiply. (a) 67 × 78 (b) 34 × 56 (c) 45 × 263 (d) 86 × 542 (e) 432 × 107 (f) 310 × 120
94. If 67 × 67 = 4489, without multiplication find 67 × 68.
95. If 99 × 100 = 9900, without multiplication find 99 × 99.

Chapter at a Glance

• Order does not change a product. Daljeet Kaur puts 6 groups of 13 butter packets on a tray. Turn the tray sideways and it becomes 13 groups of 6. The packets did not move, so the total is the same: 6 × 13 = 13 × 6 = 78. This is true for every pair of numbers.
• Multiplying by 10, 100 and 1,000. Multiply by 10 and every digit shifts one place to the left, so a zero appears at the end: 45 × 10 = 450. Multiply by 100 and the digits shift two places: 8 × 100 = 800. Multiply by 1,000 and they shift three: 5 × 1,000 = 5,000. That is why 30 × 20 is easy — think 3 × 10 × 2 × 10 = 6 × 100 = 600.
• Doubling and halving. A block of butter packets 3 rows deep and 18 across can be cut in half and the two pieces stacked. Now it is 6 rows deep and 9 across. Nothing was added or thrown away, so 3 × 18 = 6 × 9 = 54. Double one number, halve the other, and the product stays the same. This is a gift when one number is 5 or 25, because doubling 5 gives 10 and doubling 25 twice gives 100.
• Nearest multiple. 4 × 19 is hard, but 4 × 20 is easy. Draw 4 rows of 20 and rub out one column of 4: 4 × 19 = 80 − 4 = 76. The same trick works upwards. 14 × 21 is one extra column of 14 more than 14 × 20, so 14 × 21 = 280 + 14 = 294.
• Breaking a number into place values. 35 is 30 + 5 and 12 is 10 + 2. So 35 × 12 has four small pieces: 10 + 60 + 50 + 300 = 420. Kanti writes all four pieces. John collects them into two rows: 2 × 35 = 70 and 10 × 35 = 350, then 70 + 350 = 420. Nida draws the same idea as a grid. Three pictures, one answer.
• Mili’s father’s method. This is the short column method with carrying. In 268 × 4, the ones give 4 × 8 = 32. The 30 in that 32 is 3 tens, so it is added to 4 × 60 = 240, not to 60. Keeping track of what each carried digit is worth is the whole secret: 268 × 4 = 1,072.
• Estimating. You do not always need the exact answer. 248 × 49 is close to 250 × 50 = 12,500. 25 × 31 is close to 25 × 30 = 750. Rounding each number to a friendly one gives an answer that is near enough to check your work against.
• Patterns are shortcuts you can see. Halve one number and the product halves: 16 × 22 is half of 16 × 44. Double one number and the product doubles. Double both and the product becomes four times as big. And a chain like 1 × 1 = 1, 11 × 11 = 121, 111 × 111 = 12,321 lets you write the next answer without multiplying at all.
• Multiplying again and again grows very fast. The king offers 5 coins doubled daily, 3 coins tripled daily, or 1 coin multiplied by 5 daily, each for 7 days. Starting biggest does not win. After 7 days the three ministers hold 640, 6,561 and 78,125 coins. The one who started with a single coin ends up richest by far.

How to Download NCERT Solutions for Class 5 Maths Chapter 6 PDF

Follow these simple steps to get the the Dairy Farm questions-and-answers PDF from Math Mela.

1. Search NCERT Solutions for Class 5 Maths Chapter 6 aglasem and open this page.
2. Read the exercise questions with answers for the Dairy Farm shown above.
3. Click the Download PDF link to save the the Dairy Farm solutions to your device.

NCERT Solutions for Class 5 Maths – All Chapters

There are more chapters to study besides the Dairy Farm in Maths. Here are the NCERT Solutions for all chapters of Class 5 Maths.

• Chapter 1 We the Travellers I
• Chapter 2 Fractions
• Chapter 3 Angles As Turns
• Chapter 4 We the Travellers Ii
• Chapter 5 Far and Near
• Chapter 6 the Dairy Farm
• Chapter 7 Shapes and Patterns
• Chapter 8 Weight and Capacity
• Chapter 9 Coconut Farm
• Chapter 10 Symmetrical Designs
• Chapter 11 Grandmother s Quilt
• Chapter 12 Racing Seconds
• Chapter 13 Animal Jumps
• Chapter 14 Maps and Locations
• Chapter 15 Data Through Pictures

NCERT Solutions for Class 5 – All Subjects

Just like Chapter 6 of Maths, you can get the exercise questions with answers for every other subject of Class 5. Here are the NCERT Solutions for all subjects of Class 5.

• English
• Hindi
• Maths
• The World Around Us

NCERT Solutions for Class 5 Maths Chapter 6 – An Overview

The key highlights of this study material are as follows.

Aspects	Details
Class	Class 5
Subject	Maths
Chapter Number	Chapter 6
Chapter Name	the Dairy Farm
Book Name	Math Mela
Book By	NCERT (National Council of Educational Research and Training)
Educational Resource Here	NCERT Solutions of Class 5 Maths Chapter 6 for all exercises
More Questions Answers of This Subject	NCERT Solutions for Class 5 Maths
Download Book Chapter	NCERT Book Class 5 Maths
All Questions Answers For This Class	NCERT Solutions for Class 5
Complete Solutions	NCERT Solutions

NCERT Solutions for Class 5 Maths Chapter 6 the Dairy Farm – FAQs

What are the NCERT Solutions for Class 5 Maths Chapter 6 the Dairy Farm?

They are the complete, step-by-step answers to all the exercise and in-text questions of Chapter 6 the Dairy Farm from the NCERT Class 5 Maths textbook Math Mela, written by experts as per the latest NCERT syllabus.

How can I download the Class 5 Maths Chapter 6 solutions PDF for free?

Open this page on aglasem, read the the Dairy Farm questions with answers, and click the “Download Solutions PDF” link. The Class 5 Maths Chapter 6 NCERT Solutions PDF is completely free to download.

Are these NCERT Solutions as per the latest 2026-27 syllabus?

Yes. The NCERT Solutions for Class 5 Maths Chapter 6 are based on the latest NCERT textbook Math Mela and the current 2026-27 CBSE syllabus, so the questions and answers match what you study in class.

Where can I get NCERT Solutions for the other chapters of Class 5 Maths?

You can find the answers to every chapter on the NCERT Solutions for Class 5 Maths page, and solutions for every subject on the NCERT Solutions for Class 5 page.

How do NCERT Solutions help in exam preparation?

They show the correct method to solve each question, help you write answers the way they are expected in exams, let you check and correct your own work, and save revision time — which together improve your marks in Class 5 Maths.

If you have any queries on NCERT Solutions for Class 5 Maths Chapter 6 the Dairy Farm, then please ask in the comments below.