Operations with Signed Numbers: Difficult Problems with Solutions

Solution:
(-12) + (+11) + (-8) + (+39) = (-1) + (-8) + (+39) = (-9) + (+39) = +30

Solution:
-20 - 22 ⋅ (-1) = -20 + 22 = 2

Solution:
(-6) - (+6) - (-8) = -12 - (-8) = -12 + 8 = -4

Solution:
(-5) ⋅ (-4) + (+3) ⋅ (-2) = 20 + (-6) = 14

Solution:
(-15) ⋅ [-3 + (-15)] : (+5) = -15 ⋅ (-18) : 5 = (-15 : 5) ⋅ (-18) = -3 ⋅ (-18) = 54

Solution:
-18 : [-20 - (30 - 56)] = -18 : [-20 - (-26)] = -18 : (-20 + 26) = -18 : 6 = -3

Solution:
-2 ⋅ (-4.5) ⋅ (-5) = 9 ⋅ (-5) = -45

Solution:
[tex](-1) - \left(-5\frac{1}{2}\right) \cdot \frac{4}{11} = -1 - \left(-\frac{11}{2}\right)\cdot \frac{4}{11} =[/tex]
[tex]-1 - (-2) = -1 + 2 = 1[/tex]

Solution:
|-8| - |-5| + |1| = 8 - 5 + 1 = 4

Solution:
[tex]x=-|-2|=-2[/tex]
[tex]|x+1|=|-1|=1[/tex], [tex]|x-3|=|-5|=5[/tex], [tex]|-x|=|2|=2[/tex]
[tex]5\times 1-2\times 5-4\div 2=5-10-2=-7[/tex]

Solution:
The new product is the old one multiplied by [tex]-\frac{1}{4}[/tex] four times:
[tex]\left(-\frac{1}{4}\right)^4=\frac{1}{256}[/tex]
[tex]-512\times \frac{1}{256}=-2[/tex]

Solution:
[tex]5\div \left(-6\frac{2}{3}\right)=5\div \left(-\frac{20}{3}\right)=-5\times \frac{3}{20}=-\frac{3}{4}[/tex]
[tex](-4. 5)\times \left(-\frac{1}{3}\right)=1. 5[/tex]
[tex]7\frac{1}{2}-\left(-\frac{3}{4}\right)+1. 5=7. 5+0. 75+1. 5=9. 75[/tex]

Solution:
[tex]\left|-1\frac{1}{4}\right|=1\frac{1}{4}[/tex]
[tex]2\times \left(-1\frac{1}{8}\right)=2\times \left(-\frac{9}{8}\right)=-\frac{9}{4}=-2\frac{1}{4}[/tex]
[tex]-70+1\frac{1}{4}-\left(-2\frac{1}{4}\right)=-70+1\frac{1}{4}+2\frac{1}{4}=-70+3\frac{1}{2}=-66\frac{1}{2}[/tex]