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Complete the additions using tokens: i) (-3) + (-2) ii) (+5) + (-7)

Mathematics

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Answers

2 parts
i
-5
ii
-2

Step-by-step solution

9 steps

Part i· 4 steps

  1. Start with (−3)+(−2)(-3) + (-2).

    Represent −3-3 using 3 negative tokens:

    −−−- \quad - \quad -

  2. Add −2-2 using 2 negative tokens

    −−- \quad -

  3. Combine all tokens

    −−−−−- \quad - \quad - \quad - \quad -

  4. Simplify

    5 negative tokens =−5= -5.
    −5\boxed{-5}

Part ii-2

  1. Start with (+5)+(−7)(+5) + (-7).

    Represent +5+5 using 5 positive tokens:

    ++++++ \quad + \quad + \quad + \quad +

  2. Add −7-7 using 7 negative tokens

    −−−−−−−- \quad - \quad - \quad - \quad - \quad - \quad -

  3. Combine all tokens

    +++++−−−−−−−+ \quad + \quad + \quad + \quad + \quad - \quad - \quad - \quad - \quad - \quad - \quad -

  4. Pair each positive token with a negative token (5 zero pairs)

    Remove 5(+)5(+) and 5(−)5(-), leaving:

    −−- \quad -

  5. Simplify

    2 negative tokens =−2= -2.
    −2\boxed{-2}

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