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To locate the average (halfway point) between two fractions, change them both to equivalent fractions: fractions with a common denominator. The LCM is best, or you can multiply the denominators together to find a common one. Then add the fractions together and divide by 2.

If the numerator of the sum is odd, divide by two by multiplying the denominator by 2.

examples:

1/5 and 3/5 -- the average (halfway point) is obviously 2/5

1/3 and 2/3 -- the sum is 3/3 = 1, so the midway point is 1/2

(you can see that the midway point between 2/6 and 4/6 is 3/6)

1/5 and 3/7 -- 7/35 + 15/35 = 22/35 and the halfway point is 11/35

(the midway point between 7 and 15 is 11)

1/6 and 5/11 -- 11/66 + 30/66 = 41/66 and the halfway point is 41/132

Checking:

1/6 = 22/132 and 5/11 = 60/132 --

the midpoint 41/132 is 19/132 more than 1/6 and 19/132 less than 5/11

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Q: How do you work out a number halfway between two fractions?
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