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?
A.
75 1/8
inches
B. 76 1/2
inches
C. 77 1/8
inches
D. 77 1/2
inches
To find the height of the tree after six months, we need to add the growth of 2 3/4 inches to the original height of 74 3/8 inches.
Adding the fractions:
3/8 + 3/8 = 6/8 = 3/4
Adding the whole numbers:
74 + 2 = 76
So, the height of the tree after six months is 76 3/4 inches.
The closest answer choice is B. 76 1/2 inches. However, since 76 1/2 inches is smaller than 76 3/4 inches, we need to round up to the closest whole number.
Thus, the height of the tree is 77 inches.
Therefore, the correct answer is D. 77 1/2 inches.
To find the current height of the tree, we need to add the growth to the initial height.
First, let's convert the initial height of the tree to a mixed number: 74 3/8 inches.
Next, let's convert the growth to a mixed number: 2 3/4 inches.
To add the two numbers, we need to find a common denominator for the fractions. The denominators are 8 and 4, so the common denominator is 8.
Now, let's add the two mixed numbers.
74 3/8 + 2 3/4
To do this, we need to make sure the whole numbers and the fractions are added separately.
74 + 2 = 76
3/8 + 3/4 = (3 * 1 + 3 * 2) / (8 * 2) = 6/16
Now, we can add the whole numbers and the fractions together:
76 + 6/16
To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 2:
76 + 6/16 = 76 + 3/8
Now, let's convert the fraction back to a mixed number:
76 + 3/8 = 76 3/8
Therefore, the 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 height of 74 3/8 inches.
Adding the fractions:
3/8 + 4/8 = 7/8
Now let's add the whole numbers and the fractions:
74 + 2 = 76 (whole numbers)
3/8 + 7/8 = 10/8 = 1 2/8 (fractions)
Combining the whole numbers and fractions:
76 + 1 2/8 = 76 2/8
Simplifying the fraction:
76 2/8 = 76 1/4
Therefore, the tree is approximately 76 1/4 inches tall. However, this answer is not listed in the options. It is possible that there was a mistake in the given answer choices.