Class 5 Exam > Class 5 Notes > Mathematics (Maths Mela) Class 5 - New NCERT > Important Formulas: The Dairy Farm
Important Formulas: The Dairy Farm | Mathematics (Maths Mela) Class 5 - New NCERT PDF Download
1. What is Multiplication?
Multiplication = making equal groups.
Example: 6 × 2 = 6 groups of 2 = 2 + 2 + 2 + 2 + 2 + 2 = 12.
It is faster than repeated addition.
2. Key Properties of Multiplication
1. Commutative Property
a × b = b × a
Example: 7 × 6 = 42 and 6 × 7 = 42
2. Multiplicative Identity
a × 1 = a
Example: 13 × 1 = 13
3. Multiplication by Zero
a × 0 = 0
Example: 9 × 0 = 0
4. Distributive Property
a × (b + c) = (a × b) + (a × c)
Example: 12 × (10 + 2) = (12 × 10) + (12 × 2) = 120 + 24 = 144
3. Multiplying by 10, 100, 1000…
When we multiply by 10, shift digits one place left, add 1 zero.
When we multiply by 100, shift digits two places left, add 2 zeros.
When we multiply by 1000, shift digits three places left, add 3 zeros.
Examples:
7 × 10 = 70
23 × 10 = 230
56 × 100 = 5600
8 × 1000 = 8000
4. Strategies to Multiply
Breaking into Parts (Distributive Law)
35 × 12 = (30 + 5) × (10 + 2)
= (30 × 10) + (30 × 2) + (5 × 10) + (5 × 2)
= 420
Nearest Multiple Method
19 × 4 = (20 × 4) – (1 × 4) = 80 – 4 = 76
Doubling & Halving
22 × 5 = (11 × 10) = 110
Splitting Numbers
18 × 5 = (10 × 5) + (8 × 5) = 50 + 40 = 90
Repeated Multiplication (Powers)
2 × 2 × 2 × 2 = 2⁴ = 16
5. Long Multiplication & Place Value
Always align digits by ones, tens, hundreds.
Put 0 when multiplying by tens, 00 for hundreds.
Carries belong to the next place value (not to small numbers).
Example:
268 × 4 = 1,072
453 × 13 = 5,889
6. Patterns in Multiplication
Numbers ending in 5:
(a5)² = a × (a+1) followed by 25
Example: 45² = (4×5)25 = 2025
All 1s squared:
11 × 11 = 121
111 × 111 = 12321
Multiplying by 11:
11 × ab = a (a+b) b (with carry if needed)
Example: 11 × 82 = 902
Pattern with 9s:
1 × 9 + 1 = 10
12 × 9 + 2 = 110
123 × 9 + 3 = 1110
7. Growth with Repeated Multiplication (King’s Reward Story)
Repeated multiplication grows numbers very fast.
Example: Minister 3 (×5 daily) → 78,125 coins after 7 days, biggest reward.
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FAQs on Important Formulas: The Dairy Farm - Mathematics (Maths Mela) Class 5 - New NCERT
| 1. What is multiplication and why is it important in mathematics? |  |
Ans. Multiplication is a mathematical operation that represents the repeated addition of a number. It is essential because it simplifies calculations, allows for the scaling of quantities, and is foundational for more advanced mathematical concepts such as algebra and geometry.
| 2. What are the key properties of multiplication? | |
Ans. The key properties of multiplication include commutative (a × b = b × a), associative ((a × b) × c = a × (b × c)), distributive (a × (b + c) = a × b + a × c), and the existence of an identity element (a × 1 = a). Understanding these properties helps in simplifying calculations and solving problems efficiently.
| 3. How does multiplying by 10, 100, and 1000 affect a number? | |
Ans. When multiplying a number by 10, 100, or 1000, the decimal point moves to the right by one, two, or three places, respectively. For example, multiplying 5 by 10 gives 50, by 100 gives 500, and by 1000 gives 5000. This pattern helps in quickly calculating large numbers and understanding place value.
| 4. What are some effective strategies for multiplying numbers? | |
Ans. Effective strategies for multiplying include using the distributive property to break down complex problems (e.g., for 12 × 15, think of it as (10 + 2) × 15), using arrays or models to visualize the multiplication, and practicing multiplication tables to increase speed and accuracy.
| 5. What is long multiplication and how does place value play a role in it? | |
Ans. Long multiplication is a method for multiplying larger numbers by breaking them down into manageable parts based on their place value. Each digit of the first number is multiplied by each digit of the second number, and the results are aligned according to place value before summing them up. This method ensures that each part of the number is accurately represented in the final product.
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The notes and questions for Important Formulas: The Dairy Farm have been prepared according to the Class 5 exam syllabus. Information about Important Formulas: The Dairy Farm covers topics
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