1. 用多种方法将下面各组数组成得数是 24 的算式。
(1) $2 3 4 6$
(2) $3 4 5 7$
(1) $2 3 4 6$
(2) $3 4 5 7$
答案:
1.
(1) 2 3 4 6
4 × 6 × (3 - 2) = 24
2 × 6 + 3 × 4 = 24
3 × 6 + 2 + 4 = 24
(2) 3 4 5 7
3 × (7 - 5) × 4 = 24
3 × (7 + 5 - 4) = 24
3 × 4 + 7 + 5 = 24
(1) 2 3 4 6
4 × 6 × (3 - 2) = 24
2 × 6 + 3 × 4 = 24
3 × 6 + 2 + 4 = 24
(2) 3 4 5 7
3 × (7 - 5) × 4 = 24
3 × (7 + 5 - 4) = 24
3 × 4 + 7 + 5 = 24
2. 先用计算器分别计算每组前 4 式的得数,发现规律后,写出后 3 式的得数,再用计算器验算。
(1) $9×9 + 7 =$
$98×9 + 6 =$
$987×9 + 5 =$
$9876×9 + 4 =$
$98765×9 + 3 =$
$987654×9 + 2 =$
$9876543×9 + 1 =$
(2) $1234567×9 + 8 =$
$123456×9 + 7 =$
$12345×9 + 6 =$
$1234×9 + 5 =$
$123×9 + 4 =$
$12×9 + 3 =$
$1×9 + 2 =$
(1) $9×9 + 7 =$
$98×9 + 6 =$
$987×9 + 5 =$
$9876×9 + 4 =$
$98765×9 + 3 =$
$987654×9 + 2 =$
$9876543×9 + 1 =$
(2) $1234567×9 + 8 =$
$123456×9 + 7 =$
$12345×9 + 6 =$
$1234×9 + 5 =$
$123×9 + 4 =$
$12×9 + 3 =$
$1×9 + 2 =$
答案:
2.
(1)
9 × 9 + 7 = 88
98 × 9 + 6 = 888
987 × 9 + 5 = 8888
9876 × 9 + 4 = 88888
98765 × 9 + 3 = 888888
987654 × 9 + 2 = 8888888
9876543 × 9 + 1 = 88888888
(2)
1234567 × 9 + 8 = 11111111
123456 × 9 + 7 = 1111111
12345 × 9 + 6 = 111111
1234 × 9 + 5 = 1111
123 × 9 + 4 = 1111
12 × 9 + 3 = 111
1 × 9 + 2 = 11
(1)
9 × 9 + 7 = 88
98 × 9 + 6 = 888
987 × 9 + 5 = 8888
9876 × 9 + 4 = 88888
98765 × 9 + 3 = 888888
987654 × 9 + 2 = 8888888
9876543 × 9 + 1 = 88888888
(2)
1234567 × 9 + 8 = 11111111
123456 × 9 + 7 = 1111111
12345 × 9 + 6 = 111111
1234 × 9 + 5 = 1111
123 × 9 + 4 = 1111
12 × 9 + 3 = 111
1 × 9 + 2 = 11
3. 根据前面两个算式,推算出各式的结果。
$9×9 + 9 = 90$
$99×99 + 99 = 9900$
$999×999 + 999 =$
$9999×9999 + 9999 =$
$99999×99999 + 99999 =$
$999999×999999 + 999999 =$
$9999999×9999999 + 9999999 =$
$99999999×99999999 + 99999999 =$
$999999999×999999999 + 999999999 =$
说一说你是怎样推算的。
$9×9 + 9 = 90$
$99×99 + 99 = 9900$
$999×999 + 999 =$
$9999×9999 + 9999 =$
$99999×99999 + 99999 =$
$999999×999999 + 999999 =$
$9999999×9999999 + 9999999 =$
$99999999×99999999 + 99999999 =$
$999999999×999999999 + 999999999 =$
说一说你是怎样推算的。
答案:
3.
9 × 9 + 9 = 90
99 × 99 + 99 = 9900
999 × 999 + 999 = 999000
9999 × 9999 + 9999 = 99990000
99999 × 99999 + 99999 = 9999900000
999999 × 999999 + 999999 = 999999000000
9999999 × 9999999 + 9999999 = 99999990000000
99999999 × 99999999 + 99999999 = 9999999900000000
999999999 × 999999999 + 999999999 = 999999999000000000
说一说你是怎样推算的。
每增加1个9和0,结果中的9和0也相应增加1个。
9 × 9 + 9 = 90
99 × 99 + 99 = 9900
999 × 999 + 999 = 999000
9999 × 9999 + 9999 = 99990000
99999 × 99999 + 99999 = 9999900000
999999 × 999999 + 999999 = 999999000000
9999999 × 9999999 + 9999999 = 99999990000000
99999999 × 99999999 + 99999999 = 9999999900000000
999999999 × 999999999 + 999999999 = 999999999000000000
说一说你是怎样推算的。
每增加1个9和0,结果中的9和0也相应增加1个。
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