(1)−150+250(2)635+2−12−6.6(3)(−512)×815÷(−32)(4)−8+4÷(−2)(5)−14−(1+0.5)×13÷(−4)(6)(14+56−12)×12(1)-150+250(2)6 \dfrac {3}{5}+2- \dfrac {1}{2}-6.6(3)(- \dfrac {5}{12})× \dfrac {8}{15}÷(- \dfrac {3}{2})(4)-8+4÷(-2)(5)-1^{4}-(1+0.5)× \dfrac {1}{3}÷(-4)(6)( \dfrac {1}{4}+ \dfrac {5}{6}- \dfrac {1}{2})×12.

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Worked solution

(1)

1. 计算两个有理数的和

−150+250=250−150=100-150 + 250 = 250 - 150 = 100

Answer

100

(2)

1. 将分数与小数进行统一转化并简便计算

将带分数 6356 \dfrac{3}{5} 转化为小数 6.66.6,原式可化为:
6.6+2−12−6.66.6 + 2 - \dfrac{1}{2} - 6.6

2. 利用加法交换律和结合律计算出最终结果

(6.6−6.6)+(2−12)=0+1.5=1.5=32(6.6 - 6.6) + \left(2 - \dfrac{1}{2}\right) = 0 + 1.5 = 1.5 = \dfrac{3}{2}

Answer

\frac{3}{2}

(3)

1. 确定积的符号,并将除法转化为乘法

两个负数相乘除,结果为正数。将除以 −32- \dfrac{3}{2} 转化为乘以 −23- \dfrac{2}{3}:
(−512)×815÷(−32)=512×815×23\left(-\dfrac{5}{12}\right) \times \dfrac{8}{15} \div \left(-\dfrac{3}{2}\right) = \dfrac{5}{12} \times \dfrac{8}{15} \times \dfrac{2}{3}

2. 进行分数乘法计算并约分

5×8×212×15×3=1×2×23×3×3=427\dfrac{5 \times 8 \times 2}{12 \times 15 \times 3} = \dfrac{1 \times 2 \times 2}{3 \times 3 \times 3} = \dfrac{4}{27}

Answer

\frac{4}{27}

(4)

1. 先计算除法运算

4÷(−2)=−24 \div (-2) = -2

2. 计算加法运算得到最终结果

−8+(−2)=−10-8 + (-2) = -10

Answer

-10

(5)

1. 计算乘方、括号内的加法以及将除法转化为乘法

−14=−1-1^{4} = -1, 且 1+0.5=1.5=321 + 0.5 = 1.5 = \dfrac{3}{2},除以 −4-4 转化为乘以 −14-\dfrac{1}{4}:
−14−(1+0.5)×13÷(−4)=−1−32×13×(−14)-1^{4}-(1+0.5) \times \dfrac{1}{3} \div (-4) = -1 - \dfrac{3}{2} \times \dfrac{1}{3} \times \left(-\dfrac{1}{4}\right)

2. 进行乘法计算并最后求和

−1−(−18)=−1+18=−78-1 - \left(-\dfrac{1}{8}\right) = -1 + \dfrac{1}{8} = -\dfrac{7}{8}

Answer

-\frac{7}{8}

(6)

1. 运用乘法分配律展开去括号

(14+56−12)×12=14×12+56×12−12×12\left(\dfrac{1}{4} + \dfrac{5}{6} - \dfrac{1}{2}\right) \times 12 = \dfrac{1}{4} \times 12 + \dfrac{5}{6} \times 12 - \dfrac{1}{2} \times 12

2. 计算乘法并进行有理数的加减混合运算

=3+10−6=7= 3 + 10 - 6 = 7

Answer

7

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