What is the result of this calculation? 1/2 . 4/3 + 5/6 ÷ 7/8 =
A. 1 27/48
B. 1 13/21
C. 1 33/42
D. 1 19/48
To solve this calculation, you need to follow the order of operations, which is parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right).
First, let's simplify the expression within the parentheses.
5/6 ÷ 7/8 can be rewritten as (5/6) * (8/7) because dividing by a fraction is the same as multiplying by its reciprocal.
This simplifies to (40/42).
Now, let's simplify the multiplication part.
1/2 * 4/3 can be rewritten as (1/2) * (4/3) = (4/6) = (2/3).
Finally, let's add the two simplified fractions.
(2/3) + (40/42) can be rewritten with a common denominator of 42:
(28/42) + (40/42) = (68/42).
Now, let's convert the improper fraction (68/42) into a mixed number by dividing 68 by 42.
68 divided by 42 equals 1 with a remainder of 26.
So the mixed number is 1 26/42.
To simplify this mixed number, you need to find the greatest common divisor (GCD) of the numerator (26) and the denominator (42), which is 2.
Dividing both the numerator and denominator by the GCD:
26 divided by 2 equals 13, and 42 divided by 2 equals 21.
Therefore, the result of the calculation is 1 13/21.
The correct answer is B. 1 13/21.