1.(2024·潮州模拟)计算 $2-(-3)×4$ 的结果是 (
A.20
B.-10
C.14
D.-20
C
)A.20
B.-10
C.14
D.-20
答案：C
解析：
$2-(-3)×4$
$=2+12$
$=14$
C
$=2+12$
$=14$
C
2. 计算 $-3×2-8÷(-2)$ 的结果是 (
A.2
B.-2
C.-10
D.7
B
)A.2
B.-2
C.-10
D.7
答案：B
解析：
$-3×2-8÷(-2)$
$=-6+4$
$=-2$
B
$=-6+4$
$=-2$
B
3. 计算:(1) $(-4+2)÷(-1)= $
2
；(2) $-8+4÷(-2)= $-10
.答案：(1)2；(2)-10
解析：
(1) $(-4+2)÷(-1)=(-2)÷(-1)=2$；
(2) $-8+4÷(-2)=-8+(-2)=-10$
(2) $-8+4÷(-2)=-8+(-2)=-10$
4. 计算:
(1) $2×(-7)-6×(-9)$； (2) $(-28)÷(+7)-(-3)×(-2)$；
(3) $42×(-\frac{2}{3})+(-\frac{3}{4})÷(-0.25)$； (4) $\frac{2}{3}×(-6)-(-\frac{10}{7})÷(-\frac{5}{21})$.
(1) $2×(-7)-6×(-9)$； (2) $(-28)÷(+7)-(-3)×(-2)$；
(3) $42×(-\frac{2}{3})+(-\frac{3}{4})÷(-0.25)$； (4) $\frac{2}{3}×(-6)-(-\frac{10}{7})÷(-\frac{5}{21})$.
答案：(1)40；(2)-10；(3)-25；(4)-10
解析：
(1) $2×(-7)-6×(-9)$
$=-14 + 54$
$=40$
(2) $(-28)÷(+7)-(-3)×(-2)$
$=-4 - 6$
$=-10$
(3) $42×(-\frac{2}{3})+(-\frac{3}{4})÷(-0.25)$
$=-28 + 3$
$=-25$
(4) $\frac{2}{3}×(-6)-(-\frac{10}{7})÷(-\frac{5}{21})$
$=-4 - 6$
$=-10$
$=-14 + 54$
$=40$
(2) $(-28)÷(+7)-(-3)×(-2)$
$=-4 - 6$
$=-10$
(3) $42×(-\frac{2}{3})+(-\frac{3}{4})÷(-0.25)$
$=-28 + 3$
$=-25$
(4) $\frac{2}{3}×(-6)-(-\frac{10}{7})÷(-\frac{5}{21})$
$=-4 - 6$
$=-10$
5. 计算:
(1) $2\frac{1}{4}×(-\frac{6}{7})÷(\frac{1}{2}-2)$； (2) $(3-3\frac{2}{3})÷4×\frac{1}{2}$；
(3) $-3\frac{1}{3}÷(-\frac{4}{45})÷(-6\frac{3}{4})÷(-3\frac{1}{3})$；(4) $3\frac{1}{7}×(3\frac{1}{7}-7\frac{1}{3})×\frac{7}{22}÷1\frac{1}{21}$；
(5) $-\frac{5}{4}×\frac{4}{5}÷\frac{4}{5}×(-\frac{5}{4})$； (6) $(-\frac{7}{8})÷(\frac{7}{8}-\frac{7}{12})-(\frac{7}{12}-\frac{7}{8})÷\frac{7}{8}$.
(1) $2\frac{1}{4}×(-\frac{6}{7})÷(\frac{1}{2}-2)$； (2) $(3-3\frac{2}{3})÷4×\frac{1}{2}$；
(3) $-3\frac{1}{3}÷(-\frac{4}{45})÷(-6\frac{3}{4})÷(-3\frac{1}{3})$；(4) $3\frac{1}{7}×(3\frac{1}{7}-7\frac{1}{3})×\frac{7}{22}÷1\frac{1}{21}$；
(5) $-\frac{5}{4}×\frac{4}{5}÷\frac{4}{5}×(-\frac{5}{4})$； (6) $(-\frac{7}{8})÷(\frac{7}{8}-\frac{7}{12})-(\frac{7}{12}-\frac{7}{8})÷\frac{7}{8}$.
答案：(1)$\frac{9}{7}$；(2)$-\frac{1}{12}$；(3)$\frac{5}{3}$；(4)-4；(5)$\frac{25}{16}$；(6)$-2\frac{2}{3}$
解析：
(1) $2\frac{1}{4}×(-\frac{6}{7})÷(\frac{1}{2}-2)$
$=\frac{9}{4}×(-\frac{6}{7})÷(-\frac{3}{2})$
$=\frac{9}{4}×(-\frac{6}{7})×(-\frac{2}{3})$
$=\frac{9}{4}×\frac{12}{21}$
$=\frac{9}{7}$
(2) $(3 - 3\frac{2}{3})÷4×\frac{1}{2}$
$=(-\frac{2}{3})÷4×\frac{1}{2}$
$=(-\frac{2}{3})×\frac{1}{4}×\frac{1}{2}$
$=-\frac{2}{24}$
$=-\frac{1}{12}$
(3) $-3\frac{1}{3}÷(-\frac{4}{45})÷(-6\frac{3}{4})÷(-3\frac{1}{3})$
$=(-\frac{10}{3})×(-\frac{45}{4})÷(-\frac{27}{4})÷(-\frac{10}{3})$
$=(-\frac{10}{3})×(-\frac{45}{4})×(-\frac{4}{27})×(-\frac{3}{10})$
$=(\frac{10}{3}×\frac{3}{10})×(\frac{45}{4}×\frac{4}{27})$
$=1×\frac{45}{27}$
$=\frac{5}{3}$
(4) $3\frac{1}{7}×(3\frac{1}{7}-7\frac{1}{3})×\frac{7}{22}÷1\frac{1}{21}$
$=\frac{22}{7}×(\frac{22}{7}-\frac{22}{3})×\frac{7}{22}×\frac{21}{22}$
$=\frac{22}{7}×\frac{7}{22}×(\frac{22}{7}-\frac{22}{3})×\frac{21}{22}$
$=1×[22×(\frac{1}{7}-\frac{1}{3})]×\frac{21}{22}$
$=22×(-\frac{4}{21})×\frac{21}{22}$
$=-4$
(5) $-\frac{5}{4}×\frac{4}{5}÷\frac{4}{5}×(-\frac{5}{4})$
$=(-\frac{5}{4}×\frac{4}{5})×(\frac{5}{4}×\frac{5}{4})$
$=(-1)×(-\frac{25}{16})$
$=\frac{25}{16}$
(6) $(-\frac{7}{8})÷(\frac{7}{8}-\frac{7}{12}) - (\frac{7}{12}-\frac{7}{8})÷\frac{7}{8}$
$=(-\frac{7}{8})÷(\frac{21}{24}-\frac{14}{24}) - (-\frac{7}{24})×\frac{8}{7}$
$=(-\frac{7}{8})÷\frac{7}{24} + \frac{1}{3}$
$=(-\frac{7}{8})×\frac{24}{7} + \frac{1}{3}$
$=-3 + \frac{1}{3}$
$=-2\frac{2}{3}$
$=\frac{9}{4}×(-\frac{6}{7})÷(-\frac{3}{2})$
$=\frac{9}{4}×(-\frac{6}{7})×(-\frac{2}{3})$
$=\frac{9}{4}×\frac{12}{21}$
$=\frac{9}{7}$
(2) $(3 - 3\frac{2}{3})÷4×\frac{1}{2}$
$=(-\frac{2}{3})÷4×\frac{1}{2}$
$=(-\frac{2}{3})×\frac{1}{4}×\frac{1}{2}$
$=-\frac{2}{24}$
$=-\frac{1}{12}$
(3) $-3\frac{1}{3}÷(-\frac{4}{45})÷(-6\frac{3}{4})÷(-3\frac{1}{3})$
$=(-\frac{10}{3})×(-\frac{45}{4})÷(-\frac{27}{4})÷(-\frac{10}{3})$
$=(-\frac{10}{3})×(-\frac{45}{4})×(-\frac{4}{27})×(-\frac{3}{10})$
$=(\frac{10}{3}×\frac{3}{10})×(\frac{45}{4}×\frac{4}{27})$
$=1×\frac{45}{27}$
$=\frac{5}{3}$
(4) $3\frac{1}{7}×(3\frac{1}{7}-7\frac{1}{3})×\frac{7}{22}÷1\frac{1}{21}$
$=\frac{22}{7}×(\frac{22}{7}-\frac{22}{3})×\frac{7}{22}×\frac{21}{22}$
$=\frac{22}{7}×\frac{7}{22}×(\frac{22}{7}-\frac{22}{3})×\frac{21}{22}$
$=1×[22×(\frac{1}{7}-\frac{1}{3})]×\frac{21}{22}$
$=22×(-\frac{4}{21})×\frac{21}{22}$
$=-4$
(5) $-\frac{5}{4}×\frac{4}{5}÷\frac{4}{5}×(-\frac{5}{4})$
$=(-\frac{5}{4}×\frac{4}{5})×(\frac{5}{4}×\frac{5}{4})$
$=(-1)×(-\frac{25}{16})$
$=\frac{25}{16}$
(6) $(-\frac{7}{8})÷(\frac{7}{8}-\frac{7}{12}) - (\frac{7}{12}-\frac{7}{8})÷\frac{7}{8}$
$=(-\frac{7}{8})÷(\frac{21}{24}-\frac{14}{24}) - (-\frac{7}{24})×\frac{8}{7}$
$=(-\frac{7}{8})÷\frac{7}{24} + \frac{1}{3}$
$=(-\frac{7}{8})×\frac{24}{7} + \frac{1}{3}$
$=-3 + \frac{1}{3}$
$=-2\frac{2}{3}$
6.(2024秋·福田区期中)定义新运算“*”: $a*b= 1-3ab$,如 $5*(-1)= 1-3×5×(-1)= 16$. 请利用此定义计算 $2*[(-1)*3]= $ (
A.-61
B.-59
C.59
D.61
B
)A.-61
B.-59
C.59
D.61
答案：B
解析：
先计算$(-1)*3$：
$(-1)*3 = 1 - 3×(-1)×3 = 1 + 9 = 10$
再计算$2*10$：
$2*10 = 1 - 3×2×10 = 1 - 60 = -59$
B
$(-1)*3 = 1 - 3×(-1)×3 = 1 + 9 = 10$
再计算$2*10$：
$2*10 = 1 - 3×2×10 = 1 - 60 = -59$
B