Problem 2 · 2020 Math Kangaroo
Easy
Fractions, Decimals & Percents
careful-counting
Using the numbers 1, 2, 3 and 4, we can write several fractions whose value is less than 1, for example, 13. How many different values, beyond the example, can be obtained?
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Answer: B — 4
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Hint 1 of 2
List every fraction (one number over another) you can build that is below 1, then drop repeats.
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Hint 2 of 2
Two different fractions can have the same value, like 2/4 and 1/2 — count values, not fractions.
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Approach: list the proper fractions and remove equal values
- Using two of 1,2,3,4 with value < 1 gives 1/2, 1/3, 1/4, 2/3, 3/4 and 2/4.
- But 2/4 equals 1/2, so the distinct values are 1/2, 1/3, 1/4, 2/3, 3/4 — five in all.
- The example 1/3 is one of them, so beyond it there are 5 − 1 = 4 other values.
- The answer is B.
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