Answer: -11/40
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Step-by-step explanation
Convert the mixed number 4 & 1/8 to the improper fraction 33/8 due to this formula
a & b/c = (a*c + b)/c
We then divide the 33/8 cups among the 15 cakes.
(33/8) ÷ 15 = (33/8) ÷ (15/1)
(33/8) ÷ 15 = (33/8) × (1/15)
(33/8) ÷ 15 = 33/120
(33/8) ÷ 15 = 11/40
Each cake is short 11/40 of a cup of frosting.
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Another approach
4 & 1/8 really means 4 + (1/8). She is short 4 full cups and 1/8 of an extra cup added on.
Let's divide this over 15 cakes.
(4 + 1/8) ÷ 15 = 4/15 + (1/8)÷(15/1)
(4 + 1/8) ÷ 15 = 4/15 + (1/8)×(1/15)
(4 + 1/8) ÷ 15 = 4/15 + 1/120
(4 + 1/8) ÷ 15 = 32/120 + 1/120
(4 + 1/8) ÷ 15 = 33/120
(4 + 1/8) ÷ 15 = 11/40