z - x/y = (zy - x)/y

x = fraction's numerator; y = fraction's denominator; z = the integer you're subtracting from

1 - 5/7 = 7/7 - 5/7 = 2/7

2 - 8/9 = 18/9 - 8/9 = 10/9 or 1 + 1/9

3 - 17/25 = 75/25 - 17/25 = 58/25 or 2 + 8/25

4 - 50/101 = 404/101 - 50/101 = 354/101 or 3 + 51/101

5 - 125/289 = 1445/289 - 125/289 = 1320/289 or 4 + 169/289

100 - 117/100 = 10,000/100 - 117/100 = 9,883/100 or 98 + 83/100

(117/100 = 1 + 17/100)

100 - 999,999/1,000 = 1000,000/1,000 - 999,999/1,000 = -899,999/1,000 or -(899 + 999/1,000)

(999,999/1,000 = 999 + 999/1,000)

x/x = 1 if x ≠ zero(0)

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© Derek Cumberbatch