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
7518
inches
B
7612
inches
C
7718
inches
D
7712
inches
To find the current height of the tree, we need to add the growth to the initial height.
First, convert the height of the tree given initially from inches to a mixed number:
74 3/8 inches = 74 inches + 3/8 inches.
Next, add the growth of the tree:
74 inches + 3/8 inches + 2 3/4 inches.
Let's simplify the fractions:
3/8 + 4/4 = 7/8.
Now, add the whole numbers and fractions separately:
74 inches + 2 inches + 7/8 inches.
To add the whole numbers, we get:
74 inches + 2 inches = 76 inches.
Now, add the fractions:
7/8 inches.
Combine the whole number and the fraction:
76 inches + 7/8 inches.
To add the whole number and the fraction, we need to convert the whole number to a fraction with the same denominator as the fraction:
76 inches = 76/1 inches.
Now, add the fractions:
76/1 inches + 7/8 inches.
To add fractions, we need to have a common denominator. The least common multiple (LCM) of 1 and 8 is 8.
Converting the fraction with denominator 1 to a fraction with denominator 8:
76/1 inches x 8/8 = 608/8 inches.
Now, we can add the fractions:
608/8 inches + 7/8 inches = 615/8 inches.
To simplify the fraction, we divide the numerator by the denominator:
615 ÷ 8 = 76 remainder 7.
Therefore, the current height of the tree is 76 7/8 inches.
So, the correct answer is C) 7718 inches.
To find the height of the tree after it grew by 2 3/4 inches, we need to add this measurement to its initial height.
First, we need to convert the mixed numbers to improper fractions for easier calculations:
Initial height of the tree: 74 3/8 inches = 74 + 3/8 = (74 * 8 + 3) / 8 = 595 / 8 inches
Next, we add the growth of 2 3/4 inches to the initial height:
Total height of the tree = initial height + growth
Total height = 595/8 + 2 3/4
To add fractions, we need to find a common denominator. In this case, the common denominator is 8:
Total height = (595 + (8 * 2) + 3)/8
Total height = (595 + 16 + 3)/8
Total height = 614/8
Lastly, we simplify the fraction:
Total height = 76 6/8 inches
We can further simplify this fraction by dividing both the numerator and denominator by 2:
Total height = (76/2) / (6/2)
Total height = 38/3 inches
Therefore, the tree height after growing 2 3/4 inches is 38/3 inches, which is approximately 12 2/3 inches.
None of the given answer choices, A, B, C, or D, are equal to 12 2/3 inches.