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Tables and Shares - Multiplication Tables

Grade 4CBSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Multiplication as Repeated Addition: Multiplication is a shortcut for adding the same number multiple times. For example, 4×34 \times 3 means adding 3 four times: 3+3+3+3=123 + 3 + 3 + 3 = 12. Visually, this can be seen as 4 groups with 3 stars in each group, totaling 12 stars.

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Array Representation: Objects arranged in rows and columns form an array. In a 5×25 \times 2 array, there are 5 horizontal rows and 2 vertical columns. The total number of objects in this rectangular shape represents the product, which is 10.

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Building Tables by Splitting: You can create a new multiplication table by adding the results of two smaller tables. For example, to find the table of 7, you can add the products of the table of 2 and the table of 5. Visually, imagine a large grid of 7×47 \times 4 being split into two smaller grids of 2×42 \times 4 and 5×45 \times 4.

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Concept of Sharing (Division): Sharing means distributing a total quantity into equal groups. If you have 20 marbles and want to share them equally among 4 friends, each friend gets 5 marbles. This is written as 20÷4=520 \div 4 = 5.

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The Inverse Relationship: Multiplication and division are opposite operations. If you know that 6×4=246 \times 4 = 24, you also know the division facts: 24÷6=424 \div 6 = 4 and 24÷4=624 \div 4 = 6. They belong to the same 'fact family'.

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Multiplying by 10 and 100: When a number is multiplied by 10, the digits shift one place to the left and a zero is placed in the ones column. For example, 8×10=808 \times 10 = 80. Similarly, 8×100=8008 \times 100 = 800.

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Doubling to Find Tables: You can find the table of 4 by doubling the answers from the table of 2. For instance, since 2×7=142 \times 7 = 14, then 4×74 \times 7 is double 14, which is 28. Visually, this is like placing two identical 2×72 \times 7 grids next to each other to form a 4×74 \times 7 grid.

📐Formulae

Total Quantity=Number of Groups×Number of Items in each Group\text{Total Quantity} = \text{Number of Groups} \times \text{Number of Items in each Group}

a×b=b×aa \times b = b \times a (Commutative Property)

Dividend÷Divisor=Quotient\text{Dividend} \div \text{Divisor} = \text{Quotient}

Dividend=Divisor×Quotient+Remainder\text{Dividend} = \text{Divisor} \times \text{Quotient} + \text{Remainder}

a×(b+c)=(a×b)+(a×c)a \times (b + c) = (a \times b) + (a \times c) (Distributive Property for splitting tables)

💡Examples

Problem 1:

Rohan wants to find the value of 13×613 \times 6. He knows the tables of 10 and 3. How can he calculate the answer?

Solution:

  1. Split 13 into 10+310 + 3. \n2. Multiply both parts by 6: \n 10×6=6010 \times 6 = 60 \n 3×6=183 \times 6 = 18 \n3. Add the two results together: 60+18=7860 + 18 = 78. \nTherefore, 13×6=7813 \times 6 = 78.

Explanation:

This approach uses the distributive property where a larger number is broken into easier parts (10 and 3) to multiply them separately and then combine the results.

Problem 2:

A gardener has 48 flowers. She wants to arrange them in 6 equal rows. How many flowers will be in each row?

Solution:

  1. Total flowers = 48. \n2. Number of rows = 6. \n3. To find the flowers per row, use division: 48÷648 \div 6. \n4. Recall the multiplication table of 6: 6×8=486 \times 8 = 48. \n5. So, 48÷6=848 \div 6 = 8. \nEach row will have 8 flowers.

Explanation:

This problem demonstrates sharing as division. By knowing the multiplication fact 6×8=486 \times 8 = 48, we can easily find the missing factor in the division equation.