What is the result of this calculation?
1/2 times 4/3 plus 5/6 divided by 7/8 equals
A. 1 27/48
B. 1 13/21
C. 1 33/42
D. 1 19/48
To solve this calculation, we need to follow the order of operations (also known as PEMDAS). We start by calculating the multiplication and division from left to right, and then add or subtract the results.
First, we can solve 1/2 times 4/3.
1/2 * 4/3 = (1*4)/(2*3) = 4/6.
Now, we solve 5/6 divided by 7/8.
5/6 ÷ 7/8 = (5/6) * (8/7) = (5*8)/(6*7) = 40/42.
Now, we add the results of the multiplication and division: 4/6 + 40/42.
To add these fractions, we need a common denominator. The least common multiple (LCM) of 6 and 42 is 42.
To convert 4/6 to a fraction with a denominator of 42, we multiply the numerator and denominator by 7:
4/6 * 7/7 = 28/42.
Now the two fractions have a common denominator, so we can add them:
28/42 + 40/42 = 68/42.
We can simplify this fraction by dividing numerator and denominator by their greatest common divisor (GCD) which is 2:
68 ÷ 2 / 42 ÷ 2 = 34/21.
Therefore, the result of the calculation 1/2 times 4/3 plus 5/6 divided by 7/8 is 34/21. This is equivalent to 1 13/21.
The correct answer is B. 1 13/21.