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 total height of the tree after six months, we need to add the initial height of the tree to the growth in height.
The initial height of the tree is 74 3/8 inches.
The growth in height is 2 3/4 inches.
To add these two values, we convert both to have the same denominator. The denominator that can be evenly divided by both 8 and 4 is 8.
Converting 74 3/8 to have a denominator of 8, we get 594/8.
Converting 2 3/4 to have a denominator of 8, we get 22/8.
Adding 594/8 and 22/8, we get 616/8.
To simplify the fraction, we divide both the numerator and the denominator by their greatest common divisor, which is 8.
So, 616/8 simplifies to 77/1.
Therefore, the total height of the tree after six months is 77 1/8 inches.
The answer is C) 77 1/8 inches.
12 - (-23)
To solve 12 - (-23), we need to perform the operation of subtracting a negative number, which is equivalent to adding.
So, 12 - (-23) is the same as 12 + 23.
Adding 12 and 23, we get 35.
Therefore, 12 - (-23) equals 35.
To find the height of the tree after the growth, we need to add the initial height of the tree with the growth that Jake measured.
Initial height of the tree = 74 3/8 inches
Growth measured by Jake = 2 3/4 inches
To add these two measurements, we need to find a common denominator for the fractions.
The common denominator for 3/8 and 4/4 is 8.
Converting the fractions to have a common denominator:
74 3/8 = 74 * 8/8 + 3/8 = 592/8 + 3/8 = 595/8
2 3/4 = 2 * 8/8 + 3/4 = 16/8 + 3/8 = 19/8
Adding the two measurements:
595/8 + 19/8 = (595 + 19) / 8 = 614/8 = 76 6/8 inches
Simplifying the mixed number:
76 6/8 = 76 + 6/8 = 76 3/4 inches
Therefore, the tree is 76 3/4 inches tall.