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Study the pattern 1 multiply 8 plus 1 is equal to 9 1234 multiply 8 plus 4 is equal to 9876

Study the pattern :
1 \times 8 + 1 = 9                       1234 \times 8 + 4 = 9876
12 \times 8 + 2 = 98                   12345 \times 8 + 5 = 98765
123 \times 8 + 3 = 987               
Write the next two steps. Can you say how the pattern works?
(Hint: 12345 = 11111 + 1111 + 111 + 11 + 1).

Answers (1)
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123456 \times 8 + 6 = 987648 + 6 = 987654

1234567 \times 8 + 7 = 9876536 + 7 = 9876543

Yes, the pattern works.

As 123456 = 111111 + 11111 + 1111 + 111 + 11 + 1,

123456 \times 8 = (111111 + 11111 + 1111 + 111 + 11 + 1) \times 8

                   = 111111 \times 8 + 11111 \times 8 + 1111 \times 8 + 111 \times 8 + 11 \times 8 + 1  \times8

                   = 888888 + 88888 + 8888 + 888 + 88 + 8

                   = 987648

And,

123456 \times 8 + 6 = 987648 + 6 = 987648

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