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Grade 6 puzzle 3: Halfway = average

A free grade 6 math puzzle that teaches Halfway = average. Try it first — the hint and the full solution open when you are ready.

Problem 3 · Halfway = average · 3 points

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Which fraction is exactly halfway between 1/3 and 1/2?

Illustration for problem 3
  1. 1/4
  2. 3/8
  3. 5/12
  4. 2/5
  5. 4/10
Show a hint
  • Think of halfway as a distance: find the gap between the two fractions, then move half that gap from the smaller fraction.
  • The gap is 1/2 − 1/3 = 1/6. Split that gap in half, then add it to 1/3.
Show the answer and solution

Answer: C — 5/12

Half of the gap 1/6 is 1/12, so the halfway point is 1/3 + 1/12 = 4/12 + 1/12 = 5/12. The fraction 2/5 is between 1/3 and 1/2, but it is not halfway: it is 1/15 above 1/3 and 1/10 below 1/2.

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