NCERT Revision Notes for Class 5 Maths Chapter 6: The Dairy Farm – Free PDF Download

Chapter 6 of Class 5 Maths, The Dairy Farm, uses milk collection and distribution at a dairy as its setting to build multiplication skills – multiplying 2-digit and 3-digit numbers, understanding multiplication as repeated addition and as arrays, and solving word problems that involve multiplying quantities and rates.

Key Concepts

Multiplication as Repeated Addition

Multiplying a number by another means adding that number to itself repeatedly. If a dairy collects 45 litres of milk from each of 6 farmers, the total is 45 + 45 + 45 + 45 + 45 + 45, or more simply, 45 × 6.

Multiplying by a 2-Digit Number

To multiply a number by a 2-digit number (like 23), break the 2-digit number into tens and ones, multiply separately, then add: 45 × 23 = 45 × 20 + 45 × 3 = 900 + 135 = 1,035. This is the idea behind the standard column multiplication method.

Column (Standard) Multiplication Method

Write the numbers in columns aligned by place value, multiply the top number first by the ones digit of the bottom number, then by the tens digit (shifting one place left), and add the two partial products together.

Multiplication as an Array

An array arranges objects in equal rows and columns, so multiplication can be pictured as the total number of objects – 6 rows of 8 milk cans is 6 × 8 = 48 cans in total.

Estimating a Product

Round each number before multiplying to get a rough check of the final answer – 38 × 19 is close to 40 × 20 = 800, so an exact answer very far from 800 signals an error.

Word Problems Involving Rate

Many dairy-themed problems use a “rate” – an amount per unit, like litres per cow per day, or price per litre – and multiplying the rate by the number of units (cows, days, litres) gives the total.

Worked Examples

Example 1: 2-Digit Multiplication

A dairy collects 36 litres of milk daily from a farmer. How much milk is collected in 28 days?
36 × 28 = 36 × 20 + 36 × 8 = 720 + 288 = 1,008 litres.

Example 2: Rate Word Problem

Milk is sold at Rs 42 per litre. What is the cost of 15 litres?
42 × 15 = 42 × 10 + 42 × 5 = 420 + 210 = 630 rupees.

Example 3: Array Multiplication

Milk cans are stacked in 7 rows of 12 cans each. How many cans in total?
7 × 12 = 84 cans.

Quick Recap

• Multiplication is repeated addition of the same number.
• Break a 2-digit multiplier into tens and ones, multiply each part, then add (the basis of column multiplication).
• An array (rows × columns) is a visual way to picture and check a multiplication.
• Estimate first by rounding both numbers, to catch major calculation errors.
• A “rate” word problem multiplies a per-unit amount by the number of units to find a total.

Common Mistakes to Avoid

• Forgetting to shift the second partial product one place left when doing column multiplication by a 2-digit number.
• Adding the two partial products incorrectly after multiplying by tens and ones separately.
• Confusing rows and columns when reading an array, though the total is the same either way.
• Skipping estimation and not catching an answer that is ten times too big or too small.
• Misreading a rate problem and adding instead of multiplying (or vice versa).

Home Practice Tips

• Use egg cartons, ice-cube trays, or a chocolate bar’s grid of squares as ready-made arrays to practise multiplication facts.
• Create simple rate problems from home shopping, like the cost of several kilograms of rice at a given price per kg.
• Practise 2-digit by 2-digit multiplication by breaking numbers into tens and ones out loud before writing the column method.
• Estimate the answer to a multiplication problem before solving it exactly, and compare afterward.
• Turn a milk delivery or water bottle delivery scenario into a repeated-addition versus multiplication comparison.

Frequently Asked Questions

Q1. Why does column multiplication involve shifting the second row of digits?
Because multiplying by the tens digit of the bottom number actually means multiplying by a multiple of ten, so the partial product represents tens, not ones, and must be shifted one place left before adding.

Q2. How is an array different from just repeated addition?
An array shows the same total visually as equal rows and columns, which helps see multiplication as area or grouping rather than only as adding the same number over and over.

Q3. What is a “rate” in a multiplication word problem?
A rate is an amount that applies to each single unit, like rupees per litre or litres per day, and multiplying it by the number of units gives the total amount.

Q4. Why is estimating useful before doing an exact multiplication?
It gives a ballpark figure to compare the exact answer against, making it much easier to spot an error like a missing digit or a misplaced decimal.

Q5. Can multiplication word problems involve more than one step?
Yes – for example, finding a daily total first, then multiplying again by the number of days, or by the number of farmers, requires two multiplication steps done in the correct order.

Full walkthrough: Chapter 6 Solutions · Extra Questions.

Written by Satish

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