A man bought a cake and ate 1/7 from it immediately. Two hours later, hea ate 2/5 of the remainder and then gave 1/4 of the cake that is left to his cat. Calculate the fraction of the cake is left.
after first eating, 7/8 of cake is left
so he ate 2/5 of that, leaving (3/5)(7/8) or 21/40 of the cake.
he gave 1/4 of that to the cat, leaving him with
(3/4)(21/4) or ...... of the cake
To calculate the fraction of the cake that is left, we need to perform a series of calculations.
Step 1: Calculate the fraction of the cake the man ate initially.
The man ate 1/7 of the cake immediately. So, if the entire cake is represented by 1 (or 7/7), the fraction the man ate will be subtracted. Thus, the fraction left after the man ate part of the cake is 1 - 1/7 = 6/7.
Step 2: Calculate the fraction of the remaining cake the man ate after two hours.
The man ate 2/5 of the remaining cake. Since the remaining cake is represented by 6/7, we need to subtract 2/5 of 6/7. To do this, we can multiply 2/5 by 6/7, which gives us (2/5) * (6/7) = 12/35. Subtracting this fraction from the remaining cake, we have 6/7 - 12/35.
Step 3: Calculate the fraction of the cake the man gave to his cat.
The man gave 1/4 of the remaining cake to his cat. We need to subtract 1/4 of the fraction we obtained in Step 2 from the remaining cake. To do this, we can multiply 1/4 by (6/7 - 12/35), which gives us (1/4) * (6/7 - 12/35) = (1/4) * (30/35 - 12/35) = (1/4) * (18/35) = 18/140.
Step 4: Calculate the final fraction of the cake that is left.
To calculate the fraction of the cake that is left, we subtract the fraction we obtained in Step 3 from the remaining cake (6/7 - 12/35 - 18/140). We can find a common denominator of 140 for all three fractions and subtract them. After performing the subtraction, we get (840 - 48 - 18) / 140 = 774/140.
Therefore, the fraction of the cake that is left is 774/140, which can be further simplified if required.