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Integer Sums and Differences

Directions: Using the integers -3 to 3, at most one time each, fill in the blanks to make each equation true.

Hint

Hint

What do you know about adding and subtracting integers?

Answer

Answer

There are many possibilities. 2 + -3 = -1 and 1 – 3 = -2; 1 + 2 = 3 and -3 – (-1) = -2

Source: Jeanmarie Mullen

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11 comments

  1. The second solution is incorrect. -3 – 1 = -4
    It should read -3 – (-1) = -2

  2. zero is part of the integer set. Should the directions also state that zero can’t be used?

    • I let them use zero. Solutions like -2 + 1 = -1 and 0 – (-3) = 3 were found. Made for some good discussion about the meaning of 0.

  3. I really like this activity. Thank you for coming up with it. It is fun and challenging

  4. -1+-2= -3

    3-2=1
    Does this work?

  5. 3+-3=0
    1+-2=-1

  6. 2+-3=-1
    1 -3=-2

  7. Richard Buettner

    I believe this is an exhaustive list of answers.

    -3 + 1 = -2 and 2 – -1 = 3
    -3 + 1 = -2 and 2 – 3 = -1
    -3 + 2 = -1 and 1 – -2 = 3
    -3 + 2 = -1 and 1 – 3 = -2
    -3 + 3 = 0 and -1 – -2 = 1
    -3 + 3 = 0 and -1 – 1 = -2
    -3 + 3 = 0 and 1 – -1 = 2
    -3 + 3 = 0 and 1 – 2 = -1
    -2 + -1 = -3 and 3 – 1 = 2
    -2 + -1 = -3 and 3 – 2 = 1
    -2 + 1 = -1 and 0 – -3 = 3
    -2 + 1 = -1 and 0 – 3 = -3
    -2 + 3 = 1 and -1 – -3 = 2
    -2 + 3 = 1 and -1 – 2 = -3
    -1 + -2 = -3 and 3 – 1 = 2
    -1 + -2 = -3 and 3 – 2 = 1
    -1 + 2 = 1 and 0 – -3 = 3
    -1 + 2 = 1 and 0 – 3 = -3
    -1 + 3 = 2 and -2 – -3 = 1
    -1 + 3 = 2 and -2 – 1 = -3
    1 + -3 = -2 and 2 – -1 = 3
    1 + -3 = -2 and 2 – 3 = -1
    1 + -2 = -1 and 0 – -3 = 3
    1 + -2 = -1 and 0 – 3 = -3
    1 + 2 = 3 and -3 – -2 = -1
    1 + 2 = 3 and -3 – -1 = -2
    2 + -3 = -1 and 1 – -2 = 3
    2 + -3 = -1 and 1 – 3 = -2
    2 + -1 = 1 and 0 – -3 = 3
    2 + -1 = 1 and 0 – 3 = -3
    2 + 1 = 3 and -3 – -2 = -1
    2 + 1 = 3 and -3 – -1 = -2
    3 + -3 = 0 and -1 – -2 = 1
    3 + -3 = 0 and -1 – 1 = -2
    3 + -3 = 0 and 1 – -1 = 2
    3 + -3 = 0 and 1 – 2 = -1
    3 + -2 = 1 and -1 – -3 = 2
    3 + -2 = 1 and -1 – 2 = -3
    3 + -1 = 2 and -2 – -3 = 1
    3 + -1 = 2 and -2 – 1 = -3

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