Operations with Signed Numbers: Problems with Solutions

Solution:
(+3) + (+4) = +7

Solution:
(-4) + (-3) = -7

Solution:
(+15) + (-7) = 15 - 7 = 8

Solution:
-(-10) = 10

Solution:
(+7) - (+4) = +3

Solution:
-17 - (-14) = -17 + 14 = -3

Solution:
(+5) ⋅ (-8) = -40

Solution:
-9 ⋅ (-9) = 81

Solution:
-6 ⋅ 5 = -30

Solution:
40 : (-8) = -5

Solution:
-24 : (-6) = 4

Solution:
0 : (-12) = 0

Solution:
[tex]-5 : \frac{1}{2} = -10[/tex]

Solution:
[tex]|a|[/tex] is the distance from [tex]a[/tex] to [tex]0[/tex] on the number line, so [tex]|a|\geq 0[/tex].
The smallest value is [tex]0[/tex], obtained only for [tex]a=0[/tex].
There is no largest value: [tex]|a|[/tex] can be as large as we like (for example, [tex]|1000|=1000[/tex], [tex]|-1000000|=1000000[/tex], …).

Solution:
[tex]-(-5)=5[/tex], [tex]|-5. 5|=5. 5[/tex]
[tex]5. 5\gt 5\gt 3\gt 0\gt -\frac{3}{4}\gt -5[/tex]
Of two negative numbers, the larger one is the one with the smaller absolute value: [tex]-\frac{3}{4}\gt -5[/tex].

Solution:
[tex]|6. 7|=6. 7[/tex]
Subtracting a negative number is the same as adding its opposite:
[tex]6. 7+4. 3+5=11+5=16[/tex]

Solution:
Group the terms conveniently: opposite numbers cancel, then add the negative and the positive numbers separately:
[tex](-3+3)+(-1. 5-2. 5-3. 5)+(4+8)=0+(-7. 5)+12=4. 5[/tex]

Solution:
[tex]|3-8|=|-5|=5[/tex], [tex]|5-4|=|1|=1[/tex]
[tex]M=-4\times 5-2\times 1=-20-2=-22[/tex]

Solution:
[tex]2^3=8[/tex], [tex]3^2=9[/tex]
[tex]8\div (-4)=-2[/tex], [tex]9\times (-5)=-45[/tex]
[tex]-2-(-45)=-2+45=43[/tex]

Solution:
Dividing by a fraction means multiplying by its reciprocal: [tex]-15\div \frac{1}{3}=-15\times 3=-45[/tex]
[tex]15\div |-5|=15\div 5=3[/tex]
[tex]-45+3=-42[/tex]

Solution:
[tex]2. 3\times (-2)=-4. 6[/tex]
[tex]4+(-4. 6)=-0. 6[/tex]
[tex]-0. 6\div 0. 3=-2[/tex]

Solution:
There are three negative factors (an odd number), so the product is negative. Group the factors conveniently:
[tex]-\left(3\times \frac{1}{3}\right)\times 9. 6\times 10=-1\times 96=-96[/tex]

Solution:
[tex](-52)\times \left(-\frac{3}{26}\right)=\frac{52\times 3}{26}=2\times 3=6[/tex]
[tex]|-5. 3|=5. 3[/tex]
[tex]6-5. 3=0. 7[/tex]