What is the result of this calculation?
1/2 . 4/3 + 5/6 dived 7/8
A.1 27/48
B.1 13/21
C.1 33/42
The result of the calculation is:
(1/2 * 4/3) + (5/6 divided by 7/8)
First, simplify the multiplication: 1/2 * 4/3 = 4/6 = 2/3
Then, simplify the division: 5/6 divided by 7/8 = 5/6 * 8/7 = 40/42 = 20/21
Finally, add the two simplified fractions: 2/3 + 20/21 = (2*21 + 20*3)/(3*21) = (42 + 60)/63 = 102/63
The simplified fraction is 102/63, which cannot be further simplified.
Therefore, the answer is C. 1 33/42.
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To find the result of the calculation, we need to simplify the given expression step-by-step.
1/2 * 4/3 + 5/6 ÷ 7/8
First, let's simplify the division:
5/6 ÷ 7/8
To divide fractions, we need to multiply the first fraction by the reciprocal of the second fraction:
5/6 * 8/7
Next, let's simplify the multiplication:
(5 * 8) / (6 * 7) = 40/42
Now, let's simplify the addition:
1/2 * 4/3 + 40/42
We can find a common denominator for the fractions:
1/2 * 14/14 + 40/42
Next, we multiply the numerators and denominators:
14/28 + 40/42
To add fractions, we need to have a common denominator:
(14 * 42) / (28 * 42) + (40 * 28) / (42 * 28)
Simplifying:
588/1176 + 1120/1176
Now, we can add the fractions:
(588 + 1120) / 1176 = 1708/1176
However, the fraction can be simplified further:
1708/1176 = 427/294
Therefore, the result of the calculation is:
B. 1 13/21
To solve this calculation, we need to follow the correct order of operations (PEMDAS/BODMAS).
First, let's simplify the multiplication: 1/2 * 4/3. To multiply fractions, you can simply multiply the numerators together, and then multiply the denominators together. So, we have (1 * 4)/(2 * 3), which equals 4/6.
Next, let's simplify the division: 5/6 divided by 7/8. To divide fractions, we can multiply the first fraction by the reciprocal of the second fraction. So, we have (5/6) * (8/7). Multiplying across gives us (5 * 8)/(6 * 7), which is equal to 40/42.
Now, let's add the results together: 4/6 + 40/42. In order to add fractions, we need to find a common denominator. The smallest number that both 6 and 42 divide into evenly is 42. So, we need to convert both fractions so they have a denominator of 42.
For the first fraction, we can multiply the numerator and denominator by 7, since 6 * 7 = 42. This gives us (4 * 7)/42 = 28/42.
For the second fraction, we can multiply the numerator and denominator by 1, since 42 * 1 = 42. This gives us (40 * 1)/42 = 40/42.
Now that both fractions have a common denominator of 42, we can add them together: 28/42 + 40/42. To add the fractions, we add the numerators together and keep the denominator the same: (28 + 40)/42 = 68/42.
Finally, we can simplify the fraction 68/42 by finding the greatest common divisor (GCD) of the numerator and denominator, and then dividing both by that value. The GCD of 68 and 42 is 2, so we can divide both by 2: (68/2)/(42/2) = 34/21.
So, the final result of the calculation is 34/21, which corresponds to option B.