Class 5 Exam > Class 5 Notes > Mathematics (Maths Mela) Class 5 - New NCERT > Important Formulas: Coconut Farm
Important Formulas: Coconut Farm | Mathematics (Maths Mela) Class 5 - New NCERT PDF Download
Multiplication Basics
Multiplication = repeated addition (same number added many times).
Notation:
×(times).Numbers multiplied = factors.
Result = product.
Example: 2 × 4 = 8
→ factors = 2, 4
→ product = 8.
Daily Life Uses: Counting baskets of apples, chairs in rows, or boxes in stacks.
Division Basics
Division = sharing equally OR grouping equally.
Notation:
÷or/.Parts of division:
Dividend = number being divided.
Divisor = number of groups / how many in each group.
Quotient = result of division.
Remainder = what is left.
Formula: Dividend = (Divisor × Quotient) + Remainder
Example: 122 ÷ 5 = 24 remainder 2.
Daily Life Uses: Sharing chocolates, splitting money, forming equal teams.
Arrays – Link Between Multiplication & Division
Arrays = arrangement of objects in rows × columns.
From one multiplication fact, we can write two division facts.
Example: 5 × 7 = 35 →
35 ÷ 7 = 5
35 ÷ 5 = 7
Relation Between Multiplication & Division
Multiplication: factors → product.
Division: product ÷ one factor → gives the other factor.
Patterns in Division
Dividing by 10, 100, 1000 → number becomes smaller by 10, 100, 1000.
Place value rule:
÷10 → digits move 1 place right.
÷100 → digits move 2 places right.
÷1000 → digits move 3 places right.
Example:
1000 ÷ 10 = 100
3300 ÷ 300 = 11
Division Strategies
Mental Division
Break into parts (64 ÷ 4 → 60 ÷ 4 + 4 ÷ 4 = 15 + 1 = 16).
Halving: ÷4 → halve twice; ÷8 → halve thrice.
Use multiplication tables to check.
Estimate first, then calculate.
Partial Quotients Method
Subtract big groups of divisor repeatedly.
Faster if large multiples are used.
Example: 582 ÷ 6 → quotient = 97.
Remainders Rule
Always smaller than divisor.
If remainder = 0 → exact division.
If remainder ≠ 0 → leftover exists.
Formula check: N = (D × Q) + R.
Example: 902 ÷ 16 → Q = 56, R = 6 → 902 = (16 × 56) + 6.
Division Using Place Value
Write the problem:
Dividend = 100, Divisor = 7 → 100 ÷ 7
- Look at the first digit (1):
1 ÷ 7 is not possible. So, we look at the first two digits together (10).
- Divide 10 by 7:
7 goes into 10 only 1 time.
Write 1 on top.
Multiply 7 × 1 = 7.
Subtract 10 – 7 = 3.
- Bring down the next digit (0):
Now we have 30.
- Divide 30 by 7:
7 goes into 30 - 4 times (because 7 × 4 = 28).
Write 4 on top.
Subtract 30 – 28 = 2.
- Final Answer:
Quotient = 14
Remainder = 2
So, 100 ÷ 7 = 14 remainder 2.
Applications of Division
Distance & time: Find per day/hour values.
Capacity & packing: Bags, boxes, bottles.
Sharing equally: Money, food, resources.
Data handling: Complete tables by dividing totals by units.
Special Tricks & Observations
Multiplication & division are inverse operations.
Patterns with 10, 100, 1000 → digit shifts.
Large number division = easier with estimation + partial quotients.
Remainder concept important in practical life (e.g., leftover items).
The document Important Formulas: Coconut Farm | Mathematics (Maths Mela) Class 5 - New NCERT is a part of the Class 5 Course Mathematics (Maths Mela) Class 5 - New NCERT.
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FAQs on Important Formulas: Coconut Farm - Mathematics (Maths Mela) Class 5 - New NCERT
| 1. What are the basic principles of multiplication and division? |  |
Ans. Multiplication is the process of adding a number to itself a certain number of times. For example, 4 multiplied by 3 (4 x 3) means adding 4 three times: 4 + 4 + 4 = 12. Division, on the other hand, is the process of distributing a number into equal parts. For instance, dividing 12 by 3 (12 ÷ 3) means finding out how many times 3 fits into 12, which equals 4.
| 2. How are arrays used to connect multiplication and division? | |
Ans. Arrays are visual representations of multiplication and division concepts. For example, an array with 3 rows and 4 columns represents 3 x 4 = 12. It shows that there are 12 items arranged in groups. Conversely, if we have 12 items and want to divide them into groups of 3, we can use an array to see that there are 4 groups (12 ÷ 3 = 4). This illustrates the relationship between the two operations.
| 3. What is the relationship between multiplication and division? | |
Ans. Multiplication and division are inverse operations. This means that if you know one operation, you can easily find the other. For example, if 5 x 6 = 30, then dividing 30 by 6 gives you 5, and dividing 30 by 5 gives you 6. Understanding this relationship helps in solving problems efficiently.
| 4. What are some effective strategies for division? | |
Ans. Some effective strategies for division include using repeated subtraction, estimating the quotient, and breaking down larger numbers into smaller, more manageable parts. For example, if you need to divide 48 by 4, you can subtract 4 repeatedly (4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48) until you reach zero, counting how many times you subtracted (which is 12).
| 5. How do remainders work in division, and what is the Remainders Rule? | |
Ans. A remainder is what is left over when a number cannot be evenly divided by another. For example, in 13 ÷ 4, 4 goes into 13 three times (which makes 12), leaving a remainder of 1. The Remainders Rule states that when dividing, if the dividend (the number being divided) is smaller than the divisor (the number you are dividing by), the remainder is the dividend itself. Understanding remainders is crucial for solving real-life problems involving division.
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Sep 19, 2025
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