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Perform the following operations: integer subtraction, simplifying expressions with double negatives, and comparing integers.

Mathematics

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Step-by-step solution

24 steps

4. Subtract the first integer from the second integer:

a) 6, 18

  1. Identify the first and second integers.

    First integer =6= 6
    Second integer =18= 18

  2. Subtract the first integer from the second.

    18−6=1218 - 6 = 12

    The result is 12\boxed{12}.

    b) -3, 6

  3. Identify the first and second integers.

    First integer =−3= -3
    Second integer =6= 6

  4. Subtract the first integer from the second.

    6−(−3)=6+3=96 - (-3) = 6 + 3 = 9

    The result is 9\boxed{9}.

    5. Find the value of:

    a) −37−(−15)−2-37 - (-15) - 2

  5. Simplify the double negative.

    −37−(−15)−2=−37+15−2-37 - (-15) - 2 = -37 + 15 - 2
  6. Perform the operations from left to right.

    −37+15=−22-37 + 15 = -22 −22−2=−24-22 - 2 = -24

    The value is −24\boxed{-24}.

    b) 16−[14−(−2)]16 - [14 - (-2)]

  7. Simplify the expression inside the innermost parentheses.

    14−(−2)=14+2=1614 - (-2) = 14 + 2 = 16
  8. Substitute this value back into the expression.

    16−[16]16 - [16]
  9. Perform the subtraction.

    16−16=016 - 16 = 0

    The value is 0\boxed{0}.

    6. Using >,<>, < or ==, fill in the boxes to make each statement true.

    a) (−1)+(−5)□(−7)−(−5)(-1) + (-5) \Box (-7) - (-5)

  10. Evaluate the left side.

    (−1)+(−5)=−1−5=−6(-1) + (-5) = -1 - 5 = -6
  11. Evaluate the right side.

    (−7)−(−5)=−7+5=−2(-7) - (-5) = -7 + 5 = -2
  12. Compare the two values.

    −6<−2-6 < -2

    The completed statement is (−1)+(−5)<(−7)−(−5)\boxed{(-1) + (-5) < (-7) - (-5)}.

    c) 6−(−2)+5□−1−(−2)−36 - (-2) + 5 \Box -1 - (-2) - 3

  13. Evaluate the left side.

    6−(−2)+5=6+2+5=8+5=136 - (-2) + 5 = 6 + 2 + 5 = 8 + 5 = 13
  14. Evaluate the right side.

    −1−(−2)−3=−1+2−3=1−3=−2-1 - (-2) - 3 = -1 + 2 - 3 = 1 - 3 = -2
  15. Compare the two values.

    13>−213 > -2

    The completed statement is 6−(−2)+5>−1−(−2)−3\boxed{6 - (-2) + 5 > -1 - (-2) - 3}.

    7. Use commutative and associative property of addition.

    c) 43+21+79=43 + 21 + 79 =

  16. Group numbers that are easy to add using the associative property.

    43+(21+79)43 + (21 + 79)
  17. Add the numbers in the parentheses.

    21+79=10021 + 79 = 100
  18. Add the remaining numbers.

    43+100=14343 + 100 = 143

    The sum is 143\boxed{143}.

    8. Verify:

    a) [(−18)+4]+6=(−18)+(6+4)[(-18) + 4] + 6 = (-18) + (6 + 4)

  19. Evaluate the left side.

    [(−18)+4]+6=[−14]+6=−8[(-18) + 4] + 6 = [-14] + 6 = -8
  20. Evaluate the right side.

    (−18)+(6+4)=(−18)+10=−8(-18) + (6 + 4) = (-18) + 10 = -8
  21. Compare both sides.

    −8=−8-8 = -8

    The statement is Verified\boxed{\text{Verified}}.

    c) (11+3)+(−9)=11+[3+(−9)](11 + 3) + (-9) = 11 + [3 + (-9)]

  22. Evaluate the left side.

    (11+3)+(−9)=14+(−9)=14−9=5(11 + 3) + (-9) = 14 + (-9) = 14 - 9 = 5
  23. Evaluate the right side.

    11+[3+(−9)]=11+[3−9]=11+[−6]=11−6=511 + [3 + (-9)] = 11 + [3 - 9] = 11 + [-6] = 11 - 6 = 5
  24. Compare both sides.

    5=55 = 5

    The statement is Verified\boxed{\text{Verified}}.

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