Jake's measures the height of a tree to be 74 3/8 inches. Six months later, he measures the height again. He says the tree has grown 2 3/4 inches. How tall is the tree??

Question

75 1/8 inches
76 1/2 inches
77 1/8 inches
77 1/2 inches

Answer 1

To find the height of the tree after six months, we need to add the growth of 2 3/4 inches to the initial measurement of 74 3/8 inches.

First, let's convert the initial measurement to an improper fraction: 74 3/8 = (74 * 8 + 3) / 8 = 595 / 8

Now, let's convert the growth to an improper fraction: 2 3/4 = 2 + 3/4 = (2 * 4 + 3) / 4 = 11 / 4

Next, let's add the two fractions: (595 / 8) + (11 / 4) = (595 * 4 + 11 * 8) / (8 * 4) = 2380 + 88 / 32 = 2468 / 32

Finally, let's convert the result back to a mixed number: 2468 / 32 = (2468 / 32) / (4 / 4) = (2468 / 4) / (32 / 4) = 617 / 8

Therefore, the final height of the tree is 617 / 8 inches, which simplifies to 77 1/8 inches.

Therefore, the correct answer is 77 1/8 inches.