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Solve the following problems involving addition and subtraction of integers using number lines and direct calculation.

Mathematics

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39 steps

Here are the solutions to the problems:

1. Add using a number line.

a)

  1. Start at −3-3 and move 4 units to the left.

    (−3)+(−4)=−7(-3) + (-4) = -7

    b)

  2. Start at 1 and move 8 units to the left.

    1+(−8)=−71 + (-8) = -7

    c)

  3. Start at 2 and move 2 units to the left.

    2+(−2)=02 + (-2) = 0

    d)

  4. Start at 12 and move 7 units to the left.

    12−7=512 - 7 = 5

    2. Add.

    a)

  5. Add the numbers.

    25+(−11)=25−11=1425 + (-11) = 25 - 11 = 14

    b)

  6. Add the numbers.

    23+(−19)=23−19=423 + (-19) = 23 - 19 = 4

    c)

  7. Add the numbers.

    24+(−12)=24−12=1224 + (-12) = 24 - 12 = 12

    d)

  8. Add the numbers.

    (−71)+71=0(-71) + 71 = 0

    e)

  9. Add the numbers.

    −12+(−17)=−12−17=−29-12 + (-17) = -12 - 17 = -29

    f)

  10. Add the numbers.

    58+(−91)=58−91=−3358 + (-91) = 58 - 91 = -33

    g)

  11. Add the numbers.

    −6+11=5-6 + 11 = 5

    h)

  12. Add the numbers.

    67+(−66)=67−66=167 + (-66) = 67 - 66 = 1

    i)

  13. Add the numbers.

    15+14=2915 + 14 = 29

    j)

  14. Add the numbers.

    90+(−97)=90−97=−790 + (-97) = 90 - 97 = -7

    3. Subtract.

    a)

  15. Subtract the numbers.

    (−95)−54=−149(-95) - 54 = -149

    b)

  16. Change subtraction of a negative to addition.

    77−(−29)=77+29=10677 - (-29) = 77 + 29 = 106

    c)

  17. Subtract the numbers.

    (−75)−18=−93(-75) - 18 = -93

    d)

  18. Subtract the numbers.

    (−83)−65=−148(-83) - 65 = -148

    e)

  19. Change subtraction of a negative to addition.

    (−33)−(−80)=−33+80=47(-33) - (-80) = -33 + 80 = 47

    f)

  20. Subtract the numbers.

    (−13)−60=−73(-13) - 60 = -73

    g)

  21. Change subtraction of a negative to addition.

    89−(−52)=89+52=14189 - (-52) = 89 + 52 = 141

    h)

  22. Subtract the numbers.

    14−95=−8114 - 95 = -81

    i)

  23. Subtract the numbers.

    (−47)−25=−72(-47) - 25 = -72

    j)

  24. Change subtraction of a negative to addition.

    (−10)−(−50)=−10+50=40(-10) - (-50) = -10 + 50 = 40

    4. Simplify.

    a)

  25. Combine the numbers.

    10+(−11)+5+(−5)=10−11+5−5=−1+0=−110 + (-11) + 5 + (-5) = 10 - 11 + 5 - 5 = -1 + 0 = -1

    b)

  26. Combine the numbers.

    (−2)+11+4=9+4=13(-2) + 11 + 4 = 9 + 4 = 13

    c)

  27. Combine the numbers.

    2+10+(−10)+10=2+10−10+10=2+0+10=122 + 10 + (-10) + 10 = 2 + 10 - 10 + 10 = 2 + 0 + 10 = 12

    d)

  28. Combine the numbers.

    (−5)+(−8)+(−2)+1=−5−8−2+1=−13−2+1=−15+1=−14(-5) + (-8) + (-2) + 1 = -5 - 8 - 2 + 1 = -13 - 2 + 1 = -15 + 1 = -14

    e)

  29. Combine the numbers.

    (−1)+11+5=10+5=15(-1) + 11 + 5 = 10 + 5 = 15

    f)

  30. Combine the numbers.

    9+(−12)+(−6)+(−2)=9−12−6−2=−3−6−2=−9−2=−119 + (-12) + (-6) + (-2) = 9 - 12 - 6 - 2 = -3 - 6 - 2 = -9 - 2 = -11

    5. Solve the following.

    a)

  31. Represent "14 degrees below zero" as −14∘C-14^\circ \text{C}.

  32. Represent "dropped 24 degrees" as subtracting 24∘C24^\circ \text{C}.

  33. Calculate the new temperature.

    −14∘C−24∘C=−38∘C-14^\circ \text{C} - 24^\circ \text{C} = -38^\circ \text{C}

    The new temperature is -38 degrees\boxed{\text{-38 degrees}}.

    b)

  34. The mountain climber's altitude is 3625 metres.

  35. The scuba diver's altitude is −609-609 metres.

  36. Find the difference by subtracting the lower altitude from the higher altitude.

    Difference=3625 m−(−609 m)\text{Difference} = 3625 \text{ m} - (-609 \text{ m}) Difference=3625 m+609 m\text{Difference} = 3625 \text{ m} + 609 \text{ m} Difference=4234 m\text{Difference} = 4234 \text{ m}

    The difference in their altitudes is 4234 metres\boxed{\text{4234 metres}}.

    Subtract 1092 from 0.

  37. Perform the subtraction.

    0−1092=−10920 - 1092 = -1092

    The result is -1092\boxed{\text{-1092}}.

    From the sum of -19 and -43, subtract 17.

  38. Find the sum of −19-19 and −43-43.

    Sum=(−19)+(−43)=−19−43=−62\text{Sum} = (-19) + (-43) = -19 - 43 = -62

  39. Subtract 17 from the sum.

    Result=−62−17=−79\text{Result} = -62 - 17 = -79

    The result is -79\boxed{\text{-79}}.

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