11. 若$| a - \frac{1}{2} | + | b + \frac{1}{3} | + | c - \frac{1}{4} | = 0$,求$b - a + c$的值.
答案：$-\frac{7}{12}$
解析：
因为$|a - \frac{1}{2}| + |b + \frac{1}{3}| + |c - \frac{1}{4}| = 0$，且绝对值具有非负性，所以$a - \frac{1}{2} = 0$，$b + \frac{1}{3} = 0$，$c - \frac{1}{4} = 0$。
解得$a = \frac{1}{2}$，$b = -\frac{1}{3}$，$c = \frac{1}{4}$。
则$b - a + c = -\frac{1}{3} - \frac{1}{2} + \frac{1}{4}$
$= -\frac{4}{12} - \frac{6}{12} + \frac{3}{12}$
$= -\frac{7}{12}$。
$-\frac{7}{12}$
解得$a = \frac{1}{2}$，$b = -\frac{1}{3}$，$c = \frac{1}{4}$。
则$b - a + c = -\frac{1}{3} - \frac{1}{2} + \frac{1}{4}$
$= -\frac{4}{12} - \frac{6}{12} + \frac{3}{12}$
$= -\frac{7}{12}$。
$-\frac{7}{12}$
12. 数轴上,在$-7和29$之间插入三个数,使这$5$个数中每相邻的两个数之间的距离相等,这三个数分别是
2
,11
,20
.答案：2,11,20
若$| \frac{1}{2} - 1 | = 1 - \frac{1}{2}$,$| \frac{1}{3} - \frac{1}{2} | = \frac{1}{2} - \frac{1}{3}$,$| \frac{1}{4} - \frac{1}{3} | = \frac{1}{3} - \frac{1}{4}$,…,照此规律：
(1)计算：$| \frac{1}{19} - \frac{1}{18} | = $
(2)计算：$| \frac{1}{2} - 1 | + | \frac{1}{3} - \frac{1}{2} | + | \frac{1}{4} - \frac{1}{3} | + | \frac{1}{5} - \frac{1}{4} |$；
(3)计算：$| \frac{1}{3} - 1 | + | \frac{1}{5} - \frac{1}{3} | + | \frac{1}{7} - \frac{1}{5} | + … + | \frac{1}{2025} - \frac{1}{2023} |$.
(1)计算：$| \frac{1}{19} - \frac{1}{18} | = $
$\frac{1}{18}$
$-$$\frac{1}{19}$
；(2)计算：$| \frac{1}{2} - 1 | + | \frac{1}{3} - \frac{1}{2} | + | \frac{1}{4} - \frac{1}{3} | + | \frac{1}{5} - \frac{1}{4} |$；
(3)计算：$| \frac{1}{3} - 1 | + | \frac{1}{5} - \frac{1}{3} | + | \frac{1}{7} - \frac{1}{5} | + … + | \frac{1}{2025} - \frac{1}{2023} |$.
（2）原式$=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}=1-\frac{1}{5}=\frac{4}{5}$；（3）原式$=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\cdots+\frac{1}{2023}-\frac{1}{2025}=1-\frac{1}{2025}=\frac{2024}{2025}$
答案：（1）$\frac{1}{18};\frac{1}{19}$ （2）原式$=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}=1-\frac{1}{5}=\frac{4}{5}$；（3）原式$=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\cdots+\frac{1}{2023}-\frac{1}{2025}=1-\frac{1}{2025}=\frac{2024}{2025}$
1. 式子$-6 - (-4) + (+7) - (-3)$写成和的形式是(
A.$-6 + (+4) + (+7) + (-3)$
B.$-6 + (-4) + (+7) + (-3)$
C.$-6 + (+4) + (+7) + (+3)$
D.$-6 + (-4) + (+7) + (+3)$
C
)A.$-6 + (+4) + (+7) + (-3)$
B.$-6 + (-4) + (+7) + (-3)$
C.$-6 + (+4) + (+7) + (+3)$
D.$-6 + (-4) + (+7) + (+3)$
答案：C
解析：
$-6 - (-4) + (+7) - (-3) = -6 + (+4) + (+7) + (+3)$
C
C
2. 有人用$600$元买了一匹马,又以$700$元的价钱卖了出去；然后,他再用$800$元把它买回来,最后以$900$元的价格卖出,在这桩马的交易中,他(
A.收支平衡
B.赚了$100$元
C.赚了$300$元
D.赚了$200$元
D
)A.收支平衡
B.赚了$100$元
C.赚了$300$元
D.赚了$200$元
答案：D
解析：
第一次交易：$700 - 600 = 100$元
第二次交易：$900 - 800 = 100$元
总利润：$100 + 100 = 200$元
D
第二次交易：$900 - 800 = 100$元
总利润：$100 + 100 = 200$元
D
3. 下列各式中,与式子$-1 - 2 + 3$不相等的是(
A.$(-1) + (-2) + (+3)$
B.$(-1) - 2 + (+3)$
C.$(-1) + (-2) - (-3)$
D.$(-1) - (-2) - (-3)$
D
)A.$(-1) + (-2) + (+3)$
B.$(-1) - 2 + (+3)$
C.$(-1) + (-2) - (-3)$
D.$(-1) - (-2) - (-3)$
答案：D
解析：
$-1 - 2 + 3 = -3 + 3 = 0$
A.$(-1) + (-2) + (+3) = -3 + 3 = 0$
B.$(-1) - 2 + (+3) = -3 + 3 = 0$
C.$(-1) + (-2) - (-3) = -3 + 3 = 0$
D.$(-1) - (-2) - (-3) = -1 + 2 + 3 = 4$
D
A.$(-1) + (-2) + (+3) = -3 + 3 = 0$
B.$(-1) - 2 + (+3) = -3 + 3 = 0$
C.$(-1) + (-2) - (-3) = -3 + 3 = 0$
D.$(-1) - (-2) - (-3) = -1 + 2 + 3 = 4$
D
4. 算式$8 - 7 + 3 - 6$正确的读法是(
A.$8$、$7$、$3$、$6$的和
B.正$8$、负$7$、正$3$、负$6$的和
C.$8减7加正3减负6$
D.$8减7加3减6$的和
B
)A.$8$、$7$、$3$、$6$的和
B.正$8$、负$7$、正$3$、负$6$的和
C.$8减7加正3减负6$
D.$8减7加3减6$的和
答案：B
5. 计算：$( + 1\frac{1}{5}) - ( - \frac{2}{5}) + ( - \frac{3}{5}) = $
1
.答案：1
解析：
$(+1\frac{1}{5}) - (-\frac{2}{5}) + (-\frac{3}{5})$
$=1\frac{1}{5} + \frac{2}{5} - \frac{3}{5}$
$=\frac{6}{5} + \frac{2}{5} - \frac{3}{5}$
$=\frac{8}{5} - \frac{3}{5}$
$=\frac{5}{5}$
$=1$
$=1\frac{1}{5} + \frac{2}{5} - \frac{3}{5}$
$=\frac{6}{5} + \frac{2}{5} - \frac{3}{5}$
$=\frac{8}{5} - \frac{3}{5}$
$=\frac{5}{5}$
$=1$