Question

multiples
a multiple is the product of a given whole number and another whole number.
\\(1 \times 6 = 6\\)
\\(2 \times 6 = 12\\)
\\(3 \times 6 = 18\\)
\\(4 \times 6 = 24\\)
\\(5 \times 6 = 30\\)
\\(6 \times 6 = 36\\)
\\(6 \times 7 = 42\\)
\\(6 \times 8 = 48\\)
\\(6 \times 9 = 54\\)
and so on...
what are the first 6 multiples of 6? 6, 12, 18, 24, 30, and 36

1. what are the first 4 multiples of 9?

\\(\underline{\quad\quad}\\), \\(\underline{\quad\quad}\\), \\(\underline{\quad\quad}\\), and \\(\underline{\quad\quad}\\).

1. circle the numbers that are multiples of 7.

cross out the numbers that are not multiples of 7.
1, 7, 14, 17, 21, 27, 35

1. circle the numbers that are multiples of 8.

cross out the numbers that are not multiples of 8.
38, 40, 45, 49, 64, 72, 81

1. are multiples of 4 always even? explain.

1. are multiples of 3 always odd? explain.

a multiple is a number that can be made out of adding groups of another number together.

1. write down the first 6 multiples of each of these numbers.

number | 1st | 2nd | 3rd | 4th | 5th | 6th
6 | 6 | 12 | 18 | 24 | 30 | 36
20 | | | | | |
4 | | | | | |
11 | | | | | |
15 | | | | | |

1. which of the groups of numbers below are multiples of 5?

4, 10, 13, 17 | 7, 27, 37, 47 | 20, 15, 40, 25 | 53, 55, 58, 51 | 50, 20, 80, 10

1. which groups of numbers below are multiples of 3?

35, 32, 38, 30 | 24, 15, 30, 9 | 13, 43, 23, 53 | 27, 36, 9, 18 | 14, 21, 28, 35

1. i am a multiple of 3. i am between 40 and 50. who could i be?

3 possibilities

1. i am a multiple of 8. i am between 50 and 70. who could i be?

2 possibilities

1. i am a multiple of 6. i am also a multiple of 4. i am less than 30. who am i?

2 possibilities

1. write down a multiple of both 7 and 3 that is less than 50.

Explanation:

🆕 New Concept Discovered: Multiples and Common Multiples
Finding numbers in skip-counting patterns and shared lists.

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Step 1: Complete the Multiples Table (Question 1)

To find the first 6 multiples of a number, we multiply that number by 1, 2, 3, 4, 5, and 6.

• For 20:
• \(20 \times 1 = 20\)
• \(20 \times 2 = 40\)
• \(20 \times 3 = 60\)
• \(20 \times 4 = 80\)
• \(20 \times 5 = 100\)
• \(20 \times 6 = 120\)
• For 4:
• \(4 \times 1 = 4\)
• \(4 \times 2 = 8\)
• \(4 \times 3 = 12\)
• \(4 \times 4 = 16\)
• \(4 \times 5 = 20\)
• \(4 \times 6 = 24\)
• For 11:
• \(11 \times 1 = 11\)
• \(11 \times 2 = 22\)
• \(11 \times 3 = 33\)
• \(11 \times 4 = 44\)
• \(11 \times 5 = 55\)
• \(11 \times 6 = 66\)
• For 15:
• \(15 \times 1 = 15\)
• \(15 \times 2 = 30\)
• \(15 \times 3 = 45\)
• \(15 \times 4 = 60\)
• \(15 \times 5 = 75\)
• \(15 \times 6 = 90\)

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Step 2: Identify Groups of Multiples of 5 (Question 2)

A number is a multiple of 5 if it ends in 0 or 5. Let's check each group:

• \(4, 10, 13, 17\): No (only 10 ends in 0).
• \(7, 27, 37, 47\): No.
• \(20, 15, 40, 25\): Yes (all numbers end in 0 or 5).
• \(53, 55, 58, 51\): No.
• \(50, 20, 80, 10\): Yes (all numbers end in 0).

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Step 3: Identify Groups of Multiples of 3 (Question 3)

A number is a multiple of 3 if the sum of its digits is divisible by 3, or if it appears in the 3 times table. Let's check each group:

• \(35, 32, 38, 30\): No (35, 32, and 38 are not multiples of 3).
• \(24, 15, 30, 9\): Yes (\(24 = 3 \times 8\), \(15 = 3 \times 5\), \(30 = 3 \times 10\), \(9 = 3 \times 3\)).
• \(13, 43, 23, 53\): No.
• \(27, 36, 9, 18\): Yes (\(27 = 3 \times 9\), \(36 = 3 \times 12\), \(9 = 3 \times 3\), \(18 = 3 \times 6\)).
• \(14, 21, 28, 35\): No.

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Step 4: Solve Riddle 4

• Clues: Multiple of 3, strictly between 40 and 50.
• Numbers between 40 and 50: 41, 42, 43, 44, 45, 46, 47, 48, 49.
• Multiples of 3 in this range:
• \(42 \div 3 = 14\)
• \(45 \div 3 = 15\)
• \(48 \div 3 = 16\)
• Possibilities: 42, 45, 48.

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Step 5: Solve Riddle 5

• Clues: Multiple of 8, strictly between 50 and 70.
• Multiples of 8 in this range:
• \(8 \times 7 = 56\)
• \(8 \times 8 = 64\)
• Possibilities: 56, 64.

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Step 6: Solve Riddle 6

• Clues: Multiple of 6, also a multiple of 4, less than 30.
• Multiples of 6 less than 30: 6, 12, 18, 24.
• Which of these are also multiples of 4?
• 12 (\(4 \times 3\))
• 24 (\(4 \times 6\))
• Possibilities: 12 or 24.

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Step 7: Solve Riddle 7

• Clues: Multiple of both 7 and 3, less than 50.
• Common multiples of 7 and 3 are multiples of \(7 \times 3 = 21\).
• Multiples of 21 less than 50:
• \(21 \times 1 = 21\)
• \(21 \times 2 = 42\)
• Answer: 21 or 42 (either is correct).

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Answer:

1) Multiples Table:

• 20: 20, 40, 60, 80, 100, 120
• 4: 4, 8, 12, 16, 20, 24
• 11: 11, 22, 33, 44, 55, 66
• 15: 15, 30, 45, 60, 75, 90

2) Groups of numbers that are multiples of 5:

• \(20, 15, 40, 25\)
• \(50, 20, 80, 10\)

3) Groups of numbers that are multiples of 3:

• \(24, 15, 30, 9\)
• \(27, 36, 9, 18\)

Riddles:

• 4) 42, 45, 48
• 5) 56, 64
• 6) 12 or 24
• 7) 21 (or 42)