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Solutions

Overview

Step-by-step NCERT solutions for The Dairy Farm (Chapter 6, NCERT Class 5 Mathematics) — every question and answer worked out in full, not just the final result. You can also read the The Dairy Farm textbook chapter.

Solved

What these solutions cover

All 45 questions in The Dairy Farm are solved in the PDF. Here's what's inside, exercise by exercise:

Let Us Think — Shape puzzles and Buttermilk Arrangements (p. 70–71)

  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) blue rectangle x pink circle = purple triangle b) blue rectangle x blue rectangle = white rectangle c) yellow parallelogram x orange diamond = purple triangle d) orange diamond x green pentagon = orange diamond e) yellow parallelogram x…
  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 buttermilk pouches in the following manner. Find the number of pouches kept in each arrangement. One is done for you. Arrangement 1: 30 x 2 = 60 (given) Arrangement 2: ___ x ___ = 60 Arrangement 3: ___ x ___ = 60 Arrangement 4: ___ x ___ = 60 What other groups can you make?
  4. 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. Did you use all the clues to find the number? Which clues did not help you?
  5. Make your own numbers. Choose any two numbers and one operation from the grid (numbers: 100, 25, 5, 10, 2, 36, 12, 4, 3; operations: -, x, +, ÷) to make all numbers between 0 and 20. For example, 2 can be formed as 4 - 2. Which numbers could you not make? Which numbers between 0-20 can you get in more than one way?

Order of Numbers in Multiplication (p. 72)

  1. Daljeet Kaur has arranged butter packets in the following ways. Find the number of butter packets in each case and notice the pattern. a) 2 x 3 = ___ and 3 x 2 = ___ b) 8 x 5 = ___ and 5 x 8 = ___ e) 10 x 5 = ___ and 5 x 10 = ___ f) 8 x 20 = ___ and 20 x 8 = ___ g) 12 x 9 = ___ and 9 x 12 = ___ (Also: 6 x 13 = ___ and 13 x 6 = ___) What is 9 x 0? 0 x 9?

Patterns in Multiplication by 10s and 100s — Q1 (p. 72)

  1. Let us revise multiplication by 10s and 100s. Fill in the blanks. a) 4 x 10 = ___ b) 20 x 10 = ___ c) 10 x 40 = ___ d) 10 x 10 = 100 (given) e) 20 x 50 = ___ f) 80 x 10 = ___ g) 3 x 100 = 100 x 3 = 300 (given) h) 8 x 100 = ___ = ___ i) 10 x 100 = ___ = ___

Patterns in Multiplication by 10s and 100s — Q2 Tables (p. 73)

  1. Find answers to the following. Fill in the place-value tables and describe the pattern. 100 x 90 = __,000 400 x 10 = ___ 60 x 50 = ____ 30 x 20 = 600 (given) 700 x 4 = _,_00 10 x 45 = ____ Also fill in the tables for: 60 x 50 = ___ | 220 x 20 = ___ | 11 x 300 = ___ 80 x 90 = ___ | 10 x 63 = ___ | 40 x 12 = ___
  2. Fill in the place-value table for multiplying by 1,000. 2 x 1,000 = ___ | 20 x 100 = ___ | 40 x 500 = ___ 5 x 1,000 = ___ | 60 x 300 = ___ | 600 x 30 = ___ 10 x 1,000 = ___ | 80 x 900 = ___ | 70 x 600 = ___ 20 x 1,000 = ___ | 3 x 5,000 = ___ 8 x 3,000 = ___ | 5 x 7,000 = ___

Doubling and Halving (p. 75)

  1. Solve 22 x 5 by doubling and halving. (c) Solve the following problems by doubling and halving: 14 x 3 = ___ 38 x 5 = ___ 16 x 4 = ___ 35 x 14 = ___ (d) Find the product by halving and doubling either the multiplier or the multiplicand: 1) 5 x 18 2) 50 x 28 3) 15 x 22 4) 25 x 12 5) 12 x 45 6) 16 x 45 (e) Give 5 examples of multiplication problems where halving and doubling will help. Find the…

Nearest Multiple (p. 76)

  1. Give 5 examples of problems where you can use the nearest multiple to find the product easily. Find the products. (d) Find the products by finding the nearest multiple: 1) 7 x 52 2) 12 x 28 3) 75 x 31 4) 99 x 15 5) 8 x 25 6) 22 x 42

Let Us Solve — Flexible Strategies (p. 77)

  1. A school has an auditorium with 35 rows, with 42 seats in each row. How many people can sit in this auditorium?
  2. Priya jogs 4 kilometres every day. How many kilometres will she jog in 31 days?
  3. A school has received 36 boxes of books with 48 books in each box. How many total books did the school receive?
  4. Priya uses 16 metres of cloth to make 4 kurtas. How much cloth would she need to make 8 kurtas?
  5. Gollappa has 29 cows on his farm. Each cow produces 5 litres of milk per day. How many litres of milk do the cows produce in total, each day?
  6. 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?

Waste and Composting (p. 77–78)

  1. A family of 4 produces around 35 kg of kitchen waste in a month. How much waste will the family produce in a year?
  2. 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 Rs 24. By creating their own compost, how much money have they saved in a year?

Let Us Do

  1. Solve the following problems like Nida did (using a grid/box method). a) 78 x 4 b) 83 x 9 c) 67 x 28 d) 53 x 37
  2. Solve the following problems like Kanti (vertical partial products, each part on its own line). a) 94 x 5 b) 49 x 6 c) 37 x 53 d) 28 x 79
  3. Solve the following problems like John (group partial products by each digit of multiplier). a) 86 x 3 b) 72 x 7 c) 94 x 36 d) 66 x 22
  4. Solve the following word problems:
    • (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?
    • (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…

Dairy Cooperative (p. 81–83)

  1. 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?
  2. Among the villagers, there are 453 Gir cows. Each of these cows gives 13 litres of milk each day. How many litres of milk does the dairy cooperative receive from Gir cows every day?
  3. The dairy cooperative sells 1 kg cow ghee for Rs 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?

Let Us Solve — Large Multiplication Practice (p. 83–84)

  1. Solve the following problems like Nida. a) 548 x 6 b) 682 x 3 c) 324 x 18 d) 507 x 23 e) 190 x 65
  2. Solve the following problems like John. a) 123 x 84 b) 368 x 32 c) 159 x 324 d) 239 x 401 e) 592 x 5 f) 101 x 22
  3. Use Mili's father's method (standard algorithm with place values) to solve the following.
    • (a) 807 x 5
    • (b) 143 x 28
    • (c) 309 x 9
    • (d) 450 x 38
    • (e) 584 x 23
    • (f) 302 x 13
    • (g) 604 x 54
    • (h) 112 x 23
    • (i) 237 x 19

Check, Check! — Find and Fix Errors (p. 85)

  1. Check if each child's solution is correct. If incorrect, find the error and correct it. a) Asma's solution for 46 x 59: 46 x 59: 2,000 + 300 + 360 + 54 = 2,714 b) Pankaj's solution for 203 x 54: 203 x 54: 80 + 12 = 92; 100 + 15 = 115; total = 135 c) Lado's solution for 38 x 150: 38 x 150: 1,500 + 400 = 1,900; 3,000 + 800 = 3,800; total = 5,700 d) Kira's solution for 193 x 272: 193 x 272…

Let Us Do — Same-Answer Identification and Easy Multiplication (p. 86)

  1. Identify the problems that have the same answer as the one given at the top of each box. Do not calculate. 12 x 17: options — 11 x 18, 6 x 34 26 x 11: options — (26 x 10 and 26 x 1), (20 x 11 and 6 x 11) 18 x 4: options — 9 x 8, 20 x 4 - 8 55 x 9: options — (50 x 9 and 5 x 9), 54 x 10, 55 x 10 - 55 101 x 42: options — (100 x 42 and 100), (100 x 42 and 42) 247 x 8: options — 250 x 8 - 24, 247 x…
  2. Find easy ways of solving these problems.
    • (a) 16 x 25
    • (b) 12 x 125
    • (c) 24 x 250
    • (d) 36 x 25
    • (e) 28 x 75
    • (f) 300 x 15
    • (g) 50 x 78
    • (h) 199 x 63
    • (i) 128 x 35
  3. Write 5 other examples for which you can find easy ways of getting products.
  4. Find the answers to the following questions based on the given information.
    • (a) 17 x 23 = 391 (given)
    • (b) 17 x 24 = ___
    • (c) 17 x 22 = ___
    • (d) 16 x 23 = ___
    • (e) 8 x 9 = 72 (given)
    • (f) 18 x 9 = ___
    • (g) 28 x 9 = ___
    • (h) 108 x 9 = ___
    • (i) 18 x 23 = ___

Let Us Think — Coloured Box Puzzles and Estimation (p. 87–88)

  1. 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) [A][A] x 3 = [B][B] (2-digit same-digit x 3 = 2-digit same-digit) b) [A][A][A] x 3 = [B][B][B] c) [A][A][A][A] x 3 = [B][B][B][B] d) [A][B] x 5 = 1[C]0 (result starts with 1, ends with 0) e) [A][B][C] x 5 =…
  2. Estimate the products on the left and match them to the numbers given on the right. 25 x 31 -> ? 132 x 19 -> ? 101 x 11 -> ? 248 x 49 -> ? 12 x 25 -> ? Options: 2,600 | 12,500 | 300 | 750 | 1,000

The King's Reward (p. 88–89)

  1. A king offered three ministers their choice: Choice 1: Start with 5 gold coins, double every day for 7 days. Choice 2: Start with 3 gold coins, triple every day for 7 days. Choice 3: Start with 1 gold coin, multiply by 5 every day for 7 days. Which choice gives the most coins? Calculate how many gold coins each minister received after 7 days.

Multiplication Patterns (p. 89–90)

  1. Notice how the multiplier, multiplicand, and products are changing. What is the relationship of the new product with the original product? a) 16 x 44 = 704 (given), 8 x 88 = 704 (given), 8 x 22 = 176 (given) 3) 16 x 22 = ___ 4) 32 x 44 = ___ b) 12 x 32 = 384 (given) 1) 6 x 16 = ___ 2) 24 x 16 = ___ 3) 24 x 64 = ___ 4) 12 x 16 = ___
  2. Observe and complete the given patterns.
    • (i) 1x1=1; 11x11=121; 111x111=12,321; 1111x1111=___
    • (ii) 5x5=25; 15x15=225; 25x25=625; 35x35=1,225; 45x45=___; 55x55=___
    • (iii) 11x12=132; 11x34=374; 11x56=616; 11x78=858; 11x54=___; 11x82=___
    • (iv) 1x9+1=10; 12x9+2=110; 123x9+3=1,110; 1234x9+4=___
    • (v) Number pairs grid: 8,35,75 / 32,62,13 / 66,11,14. Find the adjacent pair with the smallest product and the…

Let Us Solve — Final Word Problems (p. 91)

  1. Mala went to a book exhibition and bought 18 books. The shop was selling 3 books for Rs 150. After buying the books, she still had Rs 20 left. How much money did Mala have at the beginning?
  2. A village sports club organises a women's football tournament. They sold 57 tickets for Rs 115 each. They had 3 teams joining, each paying a participation fee of Rs 1,599. The teams paid Rs 1,750 to rent the football ground and Rs 1,129 for food and water.
    • (a) How much money did the club collect in total from ticket sales and team participation fees?
    • (b) What were the total expenses on renting…
  3. 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?
  4. Multiply.
    • (a) 67 x 78
    • (b) 34 x 56
    • (c) 45 x 263
    • (d) 86 x 542
    • (e) 432 x 107
    • (f) 310 x 120
  5. If 67 x 67 = 4,489, without multiplication find 67 x 68.
  6. If 99 x 100 = 9,900, without multiplication find 99 x 99.
Sample

Worked examples

3 questions from The Dairy Farm, solved step by step.

Let Us Think — Shape puzzles and Buttermilk Arrangements (p. 70–71)

Place the digits 2, 5, and 3 appropriately to get a product close to 100. Share your reasoning in class.

We have digits 2, 5, 3 to form a 2-digit number x 1-digit number.

Possible arrangements:

25 x 3 = 75

32 x 5 = 160

35 x 2 = 70

52 x 3 = 156

53 x 2 = 106

23 x 5 = 115

Closest to 100: 53 x 2 = 106 (only 6 away) or 23 x 5 = 115 (15 away).

Best answer: 53 x 2 = 106.

Answer: 53 x 2 = 106 is closest to 100. (Accept any well-reasoned arrangement.)

Nearest Multiple (p. 76)

Give 5 examples of problems where you can use the nearest multiple to find the product easily. Find the products. (d) Find the products by finding the nearest multiple: 1) 7 x 52 2) 12 x 28 3) 75 x 31 4) 99 x 15 5) 8 x 25 6) 22 x 42

(c) Nearest-multiple examples:

5 x 19 = 5 x 20 - 5 = 100 - 5 = 95

6 x 31 = 6 x 30 + 6 = 180 + 6 = 186

4 x 49 = 4 x 50 - 4 = 200 - 4 = 196

8 x 21 = 8 x 20 + 8 = 160 + 8 = 168

7 x 29 = 7 x 30 - 7 = 210 - 7 = 203

(d)

1) 7 x 52 = 7 x 50 + 7 x 2 = 350 + 14 = 364

2) 12 x 28 = 12 x 30 - 12 x 2 = 360 - 24 = 336

3) 75 x 31 = 75 x 30 + 75 = 2,250 + 75 = 2,325

4) 99 x 15 = 100 x 15 - 1 x 15 = 1,500 - 15 = 1,485

5) 8 x 25 = 200 (exact, no nearest-multiple needed)

6) 22 x 42 = 22 x 40 + 22 x 2 = 880 + 44 = 924

Answer: (c) Examples: 5x19=95, 6x31=186, 4x49=196, 8x21=168, 7x29=203. (d) 1)364 2)336 3)2,325 4)1,485 5)200 6)924.

Waste and Composting (p. 77–78)

A family of 4 produces around 35 kg of kitchen waste in a month. How much waste will the family produce in a year?

Waste in 12 months = 12 x 35 kg.

12 x 35 = 12 x 30 + 12 x 5 = 360 + 60 = 420 kg.

(Nida's grid: 10x30=300, 10x5=50, 2x30=60, 2x5=10; total=300+50+60+10=420.)

Answer: 420 kg.

All 45 questions in The Dairy Farm are solved step by step in the Solutions PDF above.

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