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??
75 1/8 inches
76 1/2 inches
77 1/8 inches
77 1/2 inches
To find the total height of the tree after the growth, we need to add the initial height of the tree to the growth.
The initial height of the tree is 74 3/8 inches.
The growth of the tree is 2 3/4 inches.
To add the two measurements together, we need to make sure they have the same denominator.
Converting 74 3/8 to have a denominator of 8 gives us 74 24/8 inches.
Adding 74 24/8 inches to 2 3/8 inches gives us a total of 76 27/8 inches.
To simplify this fraction, we divide the numerator by the denominator: 27/8 = 3 and 3/8 inches.
Therefore, the total height of the tree is 76 3/8 inches.
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.
To find the height of the tree after six months, we need to add the growth of 2 3/4 inches to the initial height of 74 3/8 inches.
Let's add the two measurements:
74 3/8 inches + 2 3/4 inches
To add fractions, we first need to find a common denominator. In this case, the denominator of 3/8 is 8, and the denominator of 3/4 is 4. The least common multiple of 8 and 4 is 8, so we'll convert the fractions to have a denominator of 8:
74 6/8 inches + 2 6/8 inches
Now we can add the fractions:
76 12/8 inches
Simplifying the fraction, we have:
76 1/2 inches
Therefore, the tree is 76 1/2 inches tall after six months.