To find the first 5 multiples of any number, multiply it by 1, 2, 3, 4, and 5 sequentially. For example, for 9, the products are 9 × 1 = 9, 9 × 2 = 18, 9 × 3 = 27, 9 × 4 = 36, and 9 × 5 = 45. This systematic multiplication yields the required lists for each given number.

To find the first 5 multiples of any number, multiply it by 1, 2, 3, 4, and 5 sequentially. For example, for 9, the products are 9 × 1 = 9, 9 × 2 = 18, 9 × 3 = 27, 9 × 4 = 36, and 9 × 5 = 45. This systematic multiplication yields the required lists for each given number.

In the diagram, each corner number is obtained by multiplying the center number 12 by the inner triangular number adjacent to that corner. For the top-left, 12 × 9 = 108. Therefore, the top-right corner is 12 × 4 = 48. For the bottom-right corner, the outer value 72 gives the bottom inner value as 72 ÷ 12 = 6. Finally, the bottom-left corner is 12 × 8 = 96.

In the diagram, each corner number is obtained by multiplying the center number 12 by the inner triangular number adjacent to that corner. For the top-left, 12 × 9 = 108. Therefore, the top-right corner is 12 × 4 = 48. For the bottom-right corner, the outer value 72 gives the bottom inner value as 72 ÷ 12 = 6. Finally, the bottom-left corner is 12 × 8 = 96.

From the given list 56, 43, 50, 24, 40, 47, 32, 72, the numbers that are divisible by 8 without remainder are 56 (8 × 7), 24 (8 × 3), 40 (8 × 5), 32 (8 × 4), and 72 (8 × 9). For the days problem, an exact number of weeks means the number must be a multiple of 7. From the list, 7 = 7 × 1, 14 = 7 × 2, and 28 = 7 × 4 represent exact weeks.

From the given list 56, 43, 50, 24, 40, 47, 32, 72, the numbers that are divisible by 8 without remainder are 56 (8 × 7), 24 (8 × 3), 40 (8 × 5), 32 (8 × 4), and 72 (8 × 9). For the days problem, an exact number of weeks means the number must be a multiple of 7. From the list, 7 = 7 × 1, 14 = 7 × 2, and 28 = 7 × 4 represent exact weeks.

2. Find the first five multiples of: a. $9$ b. $7$ c. $8$ d. $12$ e. $15$ g. $20$ h. $19$ i. $10$ j. $16$ k. $17$ 3. Write 'T' for true and 'F' for false: a. $38$ is a multiple of $5$ . b. $45$ is a multiple of $9$ . c. $72$ is a multiple of $8$ . d. $84$ is a multiple of $8$ . 4. Magic Multiples: a. A square divided into regions. In the center is a circle containing the number $12$ . Around the circle are four triangular regions with numbers $9$ (top), $4$ (right), $?$ (bottom), and $8$ (left). At the four corners of the square are triangular outer regions with numbers: top-left has $108$ , top-right has $?$ , bottom-right has $72$ , and bottom-left has $?$ . b. A $5 \times 5$ grid of numbers: $\begin{array}{|c|c|c|c|c|} \hline 5 & 4 & 3 & 2 & 1 \\ \hline 10 & 8 & 6 & 4 & 2 \\ \hline 15 & 12 & 9 & 6 & 3 \\ \hline 20 & 16 & 12 & 8 & 4 \\ \hline 25 & 20 & 15 & 10 & 5 \\ \hline \end{array}$ 5. Encircle the multiples of $8$ : $56, 43, 50, 24, 40, 47, 32, 72$ Think and Answer There are $7$ days in a week. Which of the following number of days are an exact number of weeks? $7, 10, 13, 14, 20, 23, 28, 31$ . COMMON MULTIPLES Look at the multiples of $2$ and $3$ on the number line and fill in the blanks: [A number line is shown with markings from $0$ onwards, with arcs showing multiples of $2$ and $3$ .]

Answer: 2. Multiples: 9: 9, 18, 27, 36, 45; 7: 7, 14, 21, 28, 35; 8: 8, 16, 24, 32, 40; 12: 12, 24, 36, 48, 60; 15: 15, 30, 45, 60, 75; 20: 20, 40, 60, 80, 100; 19: 19, 38, 57, 76, 95; 10: 10, 20, 30, 40, 50; 16: 16, 32, 48, 64, 80; 17: 17, 34, 51, 68, 85. 3. a. F, b. T, c. T, d. F. 4. Magic Multiples: top-right = 48, bottom inner = 6, bottom-left = 96. 5. Multiples of 8: 56, 24, 40, 32, 72. Think and Answer: 7, 14, 28.

Step-by-step solution

Step 1: Find the first five multiples

To find the first 5 multiples of any number, multiply it by 1, 2, 3, 4, and 5 sequentially. For example, for 9, the products are $9 \times 1 = 9$ , $9 \times 2 = 18$ , $9 \times 3 = 27$ , $9 \times 4 = 36$ , and $9 \times 5 = 45$ . This systematic multiplication yields the required lists for each given number.

Step 2: Evaluate True or False statements

A number is a multiple of another if it divides completely with a remainder of 0. Since 38 divided by 5 leaves a remainder of 3, 38 is not a multiple of 5, making statement a False. Statement b is True since $9 \times 5 = 45$ , statement c is True since $8 \times 9 = 72$ , and statement d is False since 84 leaves a remainder of 4 when divided by 8.

Step 3: Solve Magic Multiples (Part 4a)

In the diagram, each corner number is obtained by multiplying the center number 12 by the inner triangular number adjacent to that corner. For the top-left, $12 \times 9 = 108$ . Therefore, the top-right corner is $12 \times 4 = 48$ . For the bottom-right corner, the outer value 72 gives the bottom inner value as $72 \div 12 = 6$ . Finally, the bottom-left corner is $12 \times 8 = 96$ .

Step 4: Identify multiples of 8 and complete the Think and Answer

From the given list $56, 43, 50, 24, 40, 47, 32, 72$ , the numbers that are divisible by 8 without remainder are 56 ( $8 \times 7$ ), 24 ( $8 \times 3$ ), 40 ( $8 \times 5$ ), 32 ( $8 \times 4$ ), and 72 ( $8 \times 9$ ). For the days problem, an exact number of weeks means the number must be a multiple of 7. From the list, $7 = 7 \times 1$ , $14 = 7 \times 2$ , and $28 = 7 \times 4$ represent exact weeks.

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