Three boys are sharing a cake. Joey ate 2/5 of the cake, Billy ate 1/3 of it, and Matt ate the remaining piece. What is the ratio of Joey's piece to Billy's piece to Matt's piece?
(2/5) : (1/3) : (1 - 2/5 - 1/3)
1 : 6/5 : 3/2
Hmmm. I think I mean
1 : 5/6 : 2/3
To find the ratio of their portions, we first need to determine the fraction of the cake that each boy ate. Let's calculate it step by step:
1. Joey ate 2/5 of the cake.
2. Billy ate 1/3 of the cake.
3. To find Matt's portion, we need to subtract Joey and Billy's portions from the whole cake. Since the cake is being shared among three boys, Matt's portion is equal to 1 - (2/5 + 1/3).
To simplify the calculation, we can find a common denominator for 5 and 3, which is 15.
Now let's calculate their portions:
1. Joey's portion: (2/5) * 15/15 = 30/75 = 2/5 (multiplied the numerator and denominator by 3 to get 15 in the denominator)
2. Billy's portion: (1/3) * 15/15 = 15/45 = 1/3 (multiplied the numerator and denominator by 5 to get 15 in the denominator)
3. Matt's portion: 1 - (2/5 + 1/3) = 1 - (6/15 + 5/15) = 1 - (11/15) = 15/15 - 11/15 = 4/15
The ratio of Joey's portion to Billy's portion to Matt's portion is 2/5 : 1/3 : 4/15.
To simplify the ratio, we can multiply all the fractions by the least common multiple (LCM) of the denominators, which is 15:
Joey's portion: (2/5) * 15/15 = 6/15
Billy's portion: (1/3) * 15/15 = 5/15
Matt's portion: (4/15) * 15/15 = 4/15
The simplified ratio is now 6 : 5 : 4.