(1) (-8)-(-1);(2) 45+(-30);(3) (-1.5)-(-11.5);(4) (-(1)/(4))-(-(1)/(2));(5) 15-[1-(-20-4)];(6) (-40)-28-(-19)+(-24);(7) 7.5+(-4.4)+(-2.5)+4.4;(8) ((2)/(3)-(1)/(2))-((1)/(3)-(5)/(6));(9) 2.4-(-(3)/(5))+(-3.1)+(4)/(5);(10) (-(6)/(13))+(-(7)/(13))-(-2);(11) (3)/(4)-(-(11)/(6))+(-(7)/(3));(12) 11+(-22)-3times(-11);
(1) $(-8)-(-1)$; (2) $45+(-30)$; (3) $(-1.5)-(-11.5)$; (4) $(-\frac{1}{4})-(-\frac{1}{2})$; (5) $15-[1-(-20-4)]$; (6) $(-40)-28-(-19)+(-24)$; (7) $7.5+(-4.4)+(-2.5)+4.4$; (8) $(\frac{2}{3}-\frac{1}{2})-(\frac{1}{3}-\frac{5}{6})$; (9) $2.4-(-\frac{3}{5})+(-3.1)+\frac{4}{5}$; (10) $(-\frac{6}{13})+(-\frac{7}{13})-(-2)$; (11) $\frac{3}{4}-(-\frac{11}{6})+(-\frac{7}{3})$; (12) $11+(-22)-3\times(-11)$;
题目解答
答案
我们来逐题解答这些有理数的加减运算题,注意每一步的符号变化和运算顺序。
(1) $(-8) - (-1)$
减去一个负数,等于加上它的相反数:
$(-8) - (-1) = -8 + 1 = -7$
答案: $\boxed{-7}$
(2) $45 + (-30)$
正数加负数,相当于减法:
$45 + (-30) = 45 - 30 = 15$
答案: $\boxed{15}$
(3) $(-1.5) - (-11.5)$
减去一个负数,等于加上它的相反数:
$(-1.5) - (-11.5) = -1.5 + 11.5 = 10$
答案: $\boxed{10}$
(4) $(-\frac{1}{4}) - (-\frac{1}{2})$
同样,减负变加:
$(-\frac{1}{4}) - (-\frac{1}{2}) = -\frac{1}{4} + \frac{1}{2}$
通分计算:
$-\frac{1}{4} + \frac{2}{4} = \frac{1}{4}$
答案: $\boxed{\frac{1}{4}}$
(5) $15 - [1 - (-20 - 4)]$
先算括号内的:
$-20 - 4 = -24$
代入:
$1 - (-24) = 1 + 24 = 25$
再代入原式:
$15 - 25 = -10$
答案: $\boxed{-10}$
(6) $(-40) - 28 - (-19) + (-24)$
逐步化简:
先去掉括号,注意符号变化:
$= -40 - 28 + 19 - 24$
从左到右计算:
$-40 - 28 = -68 \\ -68 + 19 = -49 \\ -49 - 24 = -73$
答案: $\boxed{-73}$
(7) $7.5 + (-4.4) + (-2.5) + 4.4$
重新排列组合,便于抵消:
$(7.5 - 2.5) + (-4.4 + 4.4) = 5 + 0 = 5$
答案: $\boxed{5}$
(8) $(\frac{2}{3} - \frac{1}{2}) - (\frac{1}{3} - \frac{5}{6})$
先分别计算括号内:
第一个括号:$\frac{2}{3} - \frac{1}{2}$
通分(最小公倍数为6):
$\frac{4}{6} - \frac{3}{6} = \frac{1}{6}$
第二个括号:$\frac{1}{3} - \frac{5}{6}$
$\frac{2}{6} - \frac{5}{6} = -\frac{3}{6} = -\frac{1}{2}$
原式变为:
$\frac{1}{6} - (-\frac{1}{2}) = \frac{1}{6} + \frac{1}{2}$
通分:
$\frac{1}{6} + \frac{3}{6} = \frac{4}{6} = \frac{2}{3}$
答案: $\boxed{\frac{2}{3}}$
(9) $2.4 - (-\frac{3}{5}) + (-3.1) + \frac{4}{5}$
先统一形式,把分数转为小数:
$\frac{3}{5} = 0.6,\quad \frac{4}{5} = 0.8$
代入原式:
$2.4 + 0.6 - 3.1 + 0.8$
从左到右计算:
$2.4 + 0.6 = 3.0 \\ 3.0 - 3.1 = -0.1 \\ -0.1 + 0.8 = 0.7$
答案: $\boxed{0.7}$
(10) $(-\frac{6}{13}) + (-\frac{7}{13}) - (-2)$
前两项相加:
$-\frac{6}{13} - \frac{7}{13} = -\frac{13}{13} = -1$
然后:
$-1 - (-2) = -1 + 2 = 1$
答案: $\boxed{1}$
(11) $\frac{3}{4} - (-\frac{11}{6}) + (-\frac{7}{3})$
先去括号,注意符号:
$= \frac{3}{4} + \frac{11}{6} - \frac{7}{3}$
找最小公倍数:4, 6, 3 的最小公倍数是 12
通分:
$\frac{3}{4} = \frac{9}{12},\quad \frac{11}{6} = \frac{22}{12},\quad \frac{7}{3} = \frac{28}{12}$
代入:
$\frac{9}{12} + \frac{22}{12} - \frac{28}{12} = \frac{31}{12} - \frac{28}{12} = \frac{3}{12} = \frac{1}{4}$
答案: $\boxed{\frac{1}{4}}$
(12) $11 + (-22) - 3 \times (-11)$
注意运算顺序:先乘法,后加减。
先算乘法:
$3 \times (-11) = -33$
但前面是减号:
$- 3 \times (-11) = -(-33) = +33$
原式变为:
$11 - 22 + 33$
计算:
$11 - 22 = -11 \\ -11 + 33 = 22$
答案: $\boxed{22}$
最终答案汇总:
- $-7$
- $15$
- $10$
- $\frac{1}{4}$
- $-10$
- $-73$
- $5$
- $\frac{2}{3}$
- $0.7$
- $1$
- $\frac{1}{4}$
- $22$
所有题目解答完毕。