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Rational Number Computation

Directions: Using the digits -5 to 5 at most once each, write an expression that will have the greatest (or least) absolute value.

Hint

Hint

What kind of fraction produces larger (or smaller) numbers when multiplied by an integer other than 0? Which empty square in the expression has the greatest effect on the total? What does absolute value mean?

Answer

Answer

Greatest absolute value: |70| = |-70| = 70
Least absolute value: -4/2[-1 – (-2)] – 1[-5 – (-3)] = 0 (found by Jadine Louie)

Source: Michael Wiernicki

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9 comments

  1. Is the least absolute value here zero?
    -4/2[-1 – (-2)] – 1[-5 – (-3)]

    • Yes, your equation does have an absolute value of 0. Unfortunately though, it breaks the rule of using each number at most one time. Without that restriction, yours would definitely have a winner.

      • How does it break the rule? The numbers I’m seeing are -4, 2, -1, -2, 1, -5, and -3. Nothing was repeated or am I missing something?

      • I’m with Crystal. I don’t see which number was used twice either. There are 7 slots and only 6 ‘digits’ 0, 1, 2, 3, 4, 5 if you are not assuming -1 and 1 are different numbers. So exactly which number was used twice?

        • All of you were right and I was wrong. I don’t know what I was seeing. Yes, 0 is the least absolute value. I’ll correct the answer. Sorry!

  2. One of my students is wondering about this:

    5/.01(4 – (-5)) – -3(2 – (-4)= 4518 whose absolute value would be 4518.

    So, because the word “numbers” is used in the directions instead of digits, my student believes this solution is valid. Thoughts?

  3. I have an idea. You could have an absolute value of 0 if you did: -1/5(2 – -2) – 0(3 – -3)
    Although this may be wrong, seen as I also agree with Jadine’s equation. I see no repeated numbers in mine or Jadine’s though.

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