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Giải Bài 83 trang 27 sách bài tập Toán 6 - Cánh diều

a) Có bao nhiêu số tự nhiên có hai chữ số chia cho 3 dư 1? b) Có bao nhiêu số tự nhiên có ba chữ số chia cho 9 dư 2? c) Có bao nhiêu số tự nhiên có hai chữ số ab sao cho ab+ba chia hết cho 9?

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Đề bài

a)     Có bao nhiêu số tự nhiên có hai chữ số chia cho 3 dư 1? b)    Có bao nhiêu số tự nhiên có ba chữ số chia cho 9 dư 2? c)     Có bao nhiêu số tự nhiên có hai chữ số \(\overline {ab} \) sao cho \(\overline {ab}  + \overline {ba} \) chia hết cho 9?

Phương pháp giải - Xem chi tiết

Số có tổng các chữ số chia hết cho 9 thì chia hết cho 9 Tìm đặc điểm, quy luật của các số thỏa mãn yêu cầu. Có thể liệt kê và đi tính số các số thỏa mãn Số số hạng của dãy số cách đều = ( Số hạng cuối – số hạng đầu) : khoảng cách + 1

Lời giải chi tiết

a)     Các số tự nhiên có hai chữ số chia cho 3 dư 1 là: 10; 13;…; 94; 97.Số các số tự nhiên có hai chữ số chia cho 3 dư 1 là:(97 – 10 ):3 +1 = 30 (số)b)    Các số tự nhiên có hai chữ số chia cho 9 dư 2 là: 101; 110; …; 983; 992.Số các số tự nhiên có hai chữ số chia cho 9 dư 2 là:(992 – 101) : 9 +1 = 100 (số)c)     Ta có: \(\overline {ab}  + \overline {ba} \)= a.10+b+b.10+a=11.a +11.b=11.(a+b)Để \(\overline {ab}  + \overline {ba} \)chia hết cho 9 thì a+b phải chia hết cho 9 hay  \(\overline {ab} \) chia hết cho 9.Các số \(\overline {ab} \) thỏa mãn là 18;27;…;99. Chú ý điều kiện b \(\ne 0 \) . Vậy có 9 số tự nhiên thảo mãn điều kiện

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