(1) (算理理解)在$◯$里填上运算符号,在$□$里填上数或字母,使运算简便。
$432 - 79 - 121 = 432◯(□◯□)$
$3.1÷2.5 = (3.1◯□)÷(2.5◯0.4)$
$4.5×198 = □◯□◯□◯□$
$a×99 + a = □×(□◯□)$
答案：1.(1) - 79 + 121 × 0.4 × 4.5 × 200 - 4.5 × 2 a 99 + 1
(2) 根据$22÷4 = 5.5$、$6×5.5 = 33$、$33 - 1.4 = 31.6$,列出一道综合算式为(
6 × (22 ÷ 4) - 1.4 = 31.6
)。
答案：1.(2) 6 × (22 ÷ 4) - 1.4 = 31.6
(3) 已知$A = 48×52$,$B = 49×51$,要比较$A$和$B$的大小,可以用以下方法:
$A = 48×52 = 48×(51 + 1) = 48×51 +$(
48
)$×1$。
$B = 49×51 = (48 + 1)×51 = 48×51 + 1×$(
51
)。
所以$A$和$B$相比,(
B
)$＞$(
A
)。
答案：1.(3) 48 51 B A
(4) 用$1$、$3$、$6$、$9$这四个数及运算符号和括号,写出两道不同的算式,使结果都是$24$:(
答案不唯一,如(9 ÷ 3 + 1) × 6 = 24
)、(
(6 - 3) × (9 - 1) = 24
)。
答案：1.(4) 答案不唯一,如(9 ÷ 3 + 1) × 6 = 24 (6 - 3) × (9 - 1) = 24
解析：
(9 ÷ 3 + 1) × 6 = 24；(6 - 3) × (9 - 1) = 24
(5) 在算式$\frac{1}{4}÷\frac{7}{6}×\frac{5}{2}÷\frac{3}{8}×\frac{7}{5} = \frac{8}{25}$中,有一个运算符号写错了,把它改成正确的算式为(
$\frac {1}{4} ÷ \frac {7}{6} ÷ \frac {5}{2} \frac {3}{8} × \frac {7}{5} = \frac {8}{25}$
)。
答案：$1.(5) \frac {1}{4} ÷ \frac {7}{6} ÷ \frac {5}{2} \frac {3}{8} × \frac {7}{5} = \frac {8}{25}$
(1) (算法探究)$3600÷25$能用简便方法计算,下面运用简便方法错误的是(
D
)。
A.$3000÷25 + 600÷25$
B.$3600÷5÷5$
C.$(3600×4)÷(25×4)$
D.$3600÷100÷4$
答案：2.(1) D
(2) 已知$6.4×\triangle + 3.6×\triangle = 32.8$,则$\triangle$表示(
B
)。
A.$0.328$
B.$3.28$
C.$328$
D.$32.8$
答案：2.(2) B
解析：
$6.4×\triangle + 3.6×\triangle = 32.8$
$(6.4 + 3.6)×\triangle = 32.8$
$10×\triangle = 32.8$
$\triangle = 32.8÷10$
$\triangle = 3.28$
B
3. 计算下面各题,能简算的要简算。
$\frac{9}{10}÷[\frac{1}{2}×(\frac{6}{5} - \frac{7}{10})]$
$\frac{14}{15}×(\frac{5}{14} + \frac{5}{21}) + \frac{2}{3}$
$\frac{4}{11}×\frac{5}{19} + \frac{5}{11}×\frac{7}{19}$
$(\frac{1}{16} + \frac{3}{49})×16 + \frac{1}{49}$
$2.5×7.2×0.4$
$375 - 47 + 25 - 153$
$42×\frac{42}{43}$
$8×(\frac{1}{4} + \frac{2}{9})×9$
答案：$3. \frac {9}{10} ÷ [ \frac {1}{2} × ( \frac {6}{5} - \frac {7}{10} ) ] \frac {14}{15} × ( \frac {5}{14} + \frac {5}{21} ) + \frac {2}{3}$
$ = \frac {9}{10} ÷ [ \frac {1}{2} × ( \frac {12}{10} - \frac {7}{10} ) ] = \frac {14}{15} × \frac {5}{14} + \frac {14}{15} × \frac {5}{21} + \frac {2}{3}$
$ = \frac {9}{10} ÷ [ \frac {1}{2} × \frac {5}{10} ] = \frac {1}{3} + \frac {2}{9} + \frac {2}{3}$
$ = \frac {9}{10} ÷ \frac {1}{4} = ( \frac {1}{3} + \frac {2}{3} ) + \frac {2}{9}$
$ = \frac {9}{10} × 4 = 1 + \frac {2}{9}$
$ = \frac {18}{5} = \frac {11}{9}$
$ \frac {4}{11} × \frac {5}{19} + \frac {5}{11} × \frac {7}{19} ( \frac {1}{16} + \frac {3}{49} ) × 16 + \frac {1}{49}$
$ = \frac {5}{11} × \frac {4}{19} + \frac {5}{11} × \frac {7}{19} = \frac {1}{16} × 16 + \frac {3}{49} × 16 + \frac {1}{49}$
$ = \frac {5}{11} × ( \frac {4}{19} + \frac {7}{19} ) = 1 + \frac {48}{49} + \frac {1}{49}$
$ = \frac {5}{11} × \frac {11}{19} = 1 + ( \frac {48}{49} + \frac {1}{49} )$
$ = \frac {5}{19} = 1 + 1$
= 2
2.5 × 7.2 × 0.4 375 - 47 + 25 - 153
= (2.5 × 0.4) × 7.2 = (375 + 25) - (47 + 153)
= 1 × 7.2 = 400 - 200
= 7.2 = 200
$ 42 × \frac {42}{43} 8 × ( \frac {1}{4} + \frac {2}{9} ) × 9$
$= (43 - 1) × \frac {42}{43} = 8 × \frac {1}{4} × 9 + 8 × \frac {2}{9} × 9$
$= 43 × \frac {42}{43} - 1 × \frac {42}{43} = 18 + 16$
$= 42 - \frac {42}{43} = 34$
$= 41 \frac {1}{43}$
4. 给下面的算式添上括号,使等式成立。
$6 + 36÷3 - 2×4 - 1 = 5$
$6 + 36÷3 - 2×4 - 1 = 63$
$6 + 36÷3 - 2×4 - 1 = 18$
答案：4.(6 + 36) ÷ 3 - 2 × 4 - 1 = 5 (6 + 36 ÷ 3 - 2) × 4 - 1 = 63 6 + 36 ÷ [ (3 - 2) × (4 - 1) ] = 18(最后一道算式答案不唯一)
解析：
$(6 + 36) ÷ 3 - 2 × 4 - 1 = 5$
$(6 + 36 ÷ 3 - 2) × 4 - 1 = 63$
$6 + 36 ÷ [(3 - 2) × (4 - 1)] = 18$
5. 简便计算:$3\frac{3}{5}×27\frac{4}{5} + 40\frac{3}{10}×6\frac{2}{5}$。
答案：$5.3 \frac {3}{5} × 27 \frac {4}{5} + 40 \frac {3}{10} × 6 \frac {2}{5} = 3.6 × 27.8 + 40.3 × 6.4$
= 3.6 × 27.8 + (27.8 + 12.5) × 6.4 = 3.6 × 27.8 + 27.8 × 6.4 + 12.5 × 6.4 = (3.6 + 6.4) × 27.8 + 12.5 × 0.8 × 8 = 278 + 80 = 358
