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Number - Multiplication and division facts for 6 and 9

Grade 3Cambridge (IGCSE)

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

🔑Concepts

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Multiplication by 66: This involves skip-counting by 66 or doubling the 33 times table. The sequence is 6,12,18,24,30,36,42,48,54,606, 12, 18, 24, 30, 36, 42, 48, 54, 60.

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Multiplication by 99: This involves skip-counting by 99. The sequence is 9,18,27,36,45,54,63,72,81,909, 18, 27, 36, 45, 54, 63, 72, 81, 90.

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The 99 Times Table Pattern: For multiples of 99 (up to 9×109 \times 10), the tens digit increases by 11 and the ones digit decreases by 11. Also, the sum of the digits in the product always equals 99. For example, in 9×4=369 \times 4 = 36, 3+6=93 + 6 = 9.

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Inverse Operations: Multiplication and division are inverse (opposite) operations. If we know that 6×7=426 \times 7 = 42, we also know that 42÷6=742 \div 6 = 7 and 42÷7=642 \div 7 = 6.

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Relationship between 33, 66, and 99: Since 6=2×36 = 2 \times 3, any multiple of 66 is also a multiple of 33. Since 9=3×39 = 3 \times 3, any multiple of 99 is also a multiple of 33.

📐Formulae

a×b=p  ⟹  p÷a=ba \times b = p \implies p \div a = b

6×n=(5×n)+n6 \times n = (5 \times n) + n

9×n=(10×n)−n9 \times n = (10 \times n) - n

a×b=b×aa \times b = b \times a

💡Examples

Problem 1:

Find the product of 66 and 77.

Solution:

6×7=426 \times 7 = 42

Explanation:

You can use the strategy of 5×7=355 \times 7 = 35 and then add one more group of 77: 35+7=4235 + 7 = 42.

Problem 2:

Solve 54÷954 \div 9.

Solution:

54÷9=654 \div 9 = 6

Explanation:

To solve this division, think of the multiplication fact: what number multiplied by 99 gives 5454? Since 9×6=549 \times 6 = 54, then 54÷9=654 \div 9 = 6.

Problem 3:

A baker puts 66 cookies in each box. If he has 4848 cookies, how many boxes can he fill?

Solution:

48÷6=848 \div 6 = 8 boxes.

Explanation:

We need to find how many groups of 66 are in 4848. By skip-counting or using division facts, we find that 6×8=486 \times 8 = 48, so the answer is 88.

Problem 4:

What is 9×89 \times 8?

Solution:

9×8=729 \times 8 = 72

Explanation:

Using the 99 times table trick: the tens digit is one less than 88 (which is 77), and the sum of digits must be 99. Since 7+2=97 + 2 = 9, the answer is 7272. Alternatively, 10×8=8010 \times 8 = 80, and 80−8=7280 - 8 = 72.