EN हिं

NCERT Solutions for Class 5th Maths Chapter 6 Mili's father's method: multiplying with place values — Dairy Cooperative

Book page 81–83 Updated on2026-09-19

Q1.
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?
Answer

The dairy cooperative gets milk from at least 1,072 cows.

Each of the 268 villagers has at least 4 cows. So the smallest possible number of cows is 268 × 4.

Minimum cows = 268 × 4
Step 1. Split 268 into 200 + 60 + 8.
Step 2. 4 × 200 = 800
Step 3. 4 × 60 = 240
Step 4. 4 × 8 = 32
Step 5. 800 + 240 + 32 = 1,072 cows
Why "at least" matters: Some villagers may own 5 or 6 cows. But nobody owns fewer than 4. So 4 cows each gives the smallest total the cooperative could possibly have — the minimum.
Did you know? A dairy cooperative is a group of villagers who pool their milk and sell it together, so each family gets a fair price. Many are run by women, like Jamanaben Maganbhai Naku of Tuked village in Surat, who keeps 27 Gir cows.
Q2.
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)
Answer

In Mili's father's method you multiply one column at a time, from the right, and any extra tens or hundreds are carried to the next column — where they are added to the product, not to the original digit.

  1. Ones column. 4 × 8 = 32. That is 3 tens and 2 ones. Write 2 in the ones place and carry the 3 tens to the tens column.
  2. Tens column. 4 × 6 tens = 24 tens = 240. Now add the carried 3 tens: 240 + 30 = 270. Write 7 in the tens place and carry 2 hundreds.
  3. Hundreds column. 4 × 2 hundreds = 8 hundreds = 800. Add the carried 200: 800 + 200 = 1,000. Write 0 in the hundreds place and 1 in the thousands place.
  4. Read the answer. 1,072.
ThHTO 2 3 268 ×4 1072 The circled digits are the carries: 3 tens and 2 hundreds.
The carried 3 joins 4 × 60, not 60. The carried 2 joins 4 × 200, not 200.
The point to notice: The carried 3 is added after the multiplication of that column, not before. If you added 3 to the 6 first you would be working out 4 × 90, which is completely wrong. Multiply first, then add the carry.
Sample answer for the class discussion: We said each column is multiplied on its own, and whatever spills over goes next door. It is like filling small boxes of 10: when a box is full it moves up to the next shelf.
Q3.
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?
Answer

The cooperative receives 5,889 litres of milk from Gir cows every day.

Each Gir cow gives 13 litres. There are 453 of them.

Milk each day = 453 × 13
Step 1. Multiply by the 3 first.
3 × 400 = 1,200
3 × 50 = 150
3 × 3 = 9
Step 2. Add them: 1,200 + 150 + 9 = 1,359

Step 3. Now multiply by the 10.
10 × 400 = 4,000
10 × 50 = 500
10 × 3 = 30
Step 4. Add them: 4,000 + 500 + 30 = 4,530

Step 5. 1,359 + 4,530 = 5,889 litres
Why the second row ends in 0: The 1 of 13 stands for 1 ten. So 1 ten × 453 = 453 tens = 4,530. Forgetting that zero would make the answer ten times too small.
Did you know? The Gir is an Indian breed of cow from Gujarat. It is famous for giving a lot of milk and for coping well with heat.
Q4.
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?
Answer

The cooperative earns ₹71,750 in a month.

They sell 125 kg of ghee, and each kilogram brings ₹574.

Earnings = 574 × 125

Row 1 — multiply by 5
5 × 500 = 2,500
5 × 70 = 350
5 × 4 = 20
2,500 + 350 + 20 = 2,870

Row 2 — multiply by 20
20 × 500 = 10,000
20 × 70 = 1,400
20 × 4 = 80
10,000 + 1,400 + 80 = 11,480

Row 3 — multiply by 100
100 × 500 = 50,000
100 × 70 = 7,000
100 × 4 = 400
50,000 + 7,000 + 400 = 57,400

Add the three rows
2,870 + 11,480 + 57,400 = ₹71,750
Check it a quicker way: 125 is one eighth of 1,000. So 574 × 125 = 574 × 1,000 ÷ 8 = 574,000 ÷ 8 = 71,750 ✓
Why there are three rows: 125 has three digits — 100, 20 and 5. Each digit gets its own row, and each row must carry the right number of zeros.
Q5.
Discuss what the same coloured digits might mean. (in the 574 × 125 working)
Answer

The digits printed in the same colour are a carry and the place it lands in. A coloured digit above the line is the amount that spilled over from the column to its right.

  1. Every column can overflow. When a column's product is 10 or more, only the last digit stays. The rest must move one house to the left.
  2. The colour ties the two together. One coloured digit is the little number written above the next column. The matching coloured digit is the part of the product it came from.
  3. Example from the working. 2 tens × 574 gives 11,480. The 1 that appears above the thousands column is a carry, and it is the same colour as the digit that produced it.
  4. Reminder. A carry is always added after the next multiplication, never before it.
Why colours help: In a long multiplication there can be five or six carries floating about. Colouring them shows a learner where each one came from and where it must go, so no carry gets lost or used twice.
Sample answer for the class discussion: We said the colours are like labels on parcels. Each parcel of tens or hundreds has to be delivered to the correct column, and the colour tells you the address.
Was this helpful?