Question

× 7 4 1 5 3 9 8 6 0 2
4
9
2
5
3
7
0
6
1
8

Explanation:

Step1: Fill row 4 (multiplier 4)

For each column (multiplicand \( x \)): \( 4\times7 = 28 \), \( 4\times4 = 16 \), \( 4\times1 = 4 \), \( 4\times5 = 20 \), \( 4\times3 = 12 \), \( 4\times9 = 36 \), \( 4\times8 = 32 \), \( 4\times6 = 24 \), \( 4\times0 = 0 \), \( 4\times2 = 8 \).

Step2: Fill row 9 (multiplier 9)

\( 9\times7 = 63 \), \( 9\times4 = 36 \), \( 9\times1 = 9 \), \( 9\times5 = 45 \), \( 9\times3 = 27 \), \( 9\times9 = 81 \), \( 9\times8 = 72 \), \( 9\times6 = 54 \), \( 9\times0 = 0 \), \( 9\times2 = 18 \).

Step3: Fill row 2 (multiplier 2)

\( 2\times7 = 14 \), \( 2\times4 = 8 \), \( 2\times1 = 2 \), \( 2\times5 = 10 \), \( 2\times3 = 6 \), \( 2\times9 = 18 \), \( 2\times8 = 16 \), \( 2\times6 = 12 \), \( 2\times0 = 0 \), \( 2\times2 = 4 \).

Step4: Fill row 5 (multiplier 5)

\( 5\times7 = 35 \), \( 5\times4 = 20 \), \( 5\times1 = 5 \), \( 5\times5 = 25 \), \( 5\times3 = 15 \), \( 5\times9 = 45 \), \( 5\times8 = 40 \), \( 5\times6 = 30 \), \( 5\times0 = 0 \), \( 5\times2 = 10 \).

Step5: Fill row 3 (multiplier 3)

\( 3\times7 = 21 \), \( 3\times4 = 12 \), \( 3\times1 = 3 \), \( 3\times5 = 15 \), \( 3\times3 = 9 \), \( 3\times9 = 27 \), \( 3\times8 = 24 \), \( 3\times6 = 18 \), \( 3\times0 = 0 \), \( 3\times2 = 6 \).

Step6: Fill row 7 (multiplier 7)

\( 7\times7 = 49 \), \( 7\times4 = 28 \), \( 7\times1 = 7 \), \( 7\times5 = 35 \), \( 7\times3 = 21 \), \( 7\times9 = 63 \), \( 7\times8 = 56 \), \( 7\times6 = 42 \), \( 7\times0 = 0 \), \( 7\times2 = 14 \).

Step7: Fill row 0 (multiplier 0)

All products: \( 0\times x = 0 \) for any \( x \), so all cells in this row are \( 0 \).

Step8: Fill row 6 (multiplier 6)

\( 6\times7 = 42 \), \( 6\times4 = 24 \), \( 6\times1 = 6 \), \( 6\times5 = 30 \), \( 6\times3 = 18 \), \( 6\times9 = 54 \), \( 6\times8 = 48 \), \( 6\times6 = 36 \), \( 6\times0 = 0 \), \( 6\times2 = 12 \).

Step9: Fill row 1 (multiplier 1)

\( 1\times x = x \), so cells are \( 7, 4, 1, 5, 3, 9, 8, 6, 0, 2 \) respectively.

Step10: Fill row 8 (multiplier 8)

\( 8\times7 = 56 \), \( 8\times4 = 32 \), \( 8\times1 = 8 \), \( 8\times5 = 40 \), \( 8\times3 = 24 \), \( 8\times9 = 72 \), \( 8\times8 = 64 \), \( 8\times6 = 48 \), \( 8\times0 = 0 \), \( 8\times2 = 16 \).

Answer:

The completed multiplication table (rows are multipliers, columns are multiplicands):

×	7	4	1	5	3	9	8	6	0	2
9	63	36	9	45	27	81	72	54	0	18
2	14	8	2	10	6	18	16	12	0	4
5	35	20	5	25	15	45	40	30	0	10
3	21	12	3	15	9	27	24	18	0	6
7	49	28	7	35	21	63	56	42	0	14
0	0	0	0	0	0	0	0	0	0	0
6	42	24	6	30	18	54	48	36	0	12
1	7	4	1	5	3	9	8	6	0	2
8	56	32	8	40	24	72	64	48	0	16