Question

6th grade fractions...

Answer 1

The last pair of numbers bracket the point 3/7.

12/32 = 3/8 < 3/7

15/18 = 5/6 > 3/7

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3/7 ≈ 0.428571... (repeating), so will be larger than 3/8 = 0.375, 12/32 = 3/8, and 4/10. That is, 3/7 is larger than the largest number of each pair except the last.

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You can always compare two fractions to see which is larger by cross-multiplying. That is a/b vs c/d gives the same result as ad vs bc. (Put the product on the numerator side of the comparison.)

Here, that would mean comparing 12/32 vs 3/7, we would get 12·7 vs 3·32, or 84 vs 96. The fraction on the left is smaller.

Comparing 3/7 vs 15/18, we would get 3·18 vs 7·15, or 54 vs 105. The fraction on the right is larger.