Question

(3 5/6:1 4/13-1,1)²-4:1/2

Answer 1

Ответ:

Fraction Subtraction and Simplification

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(3 5/6:1 4/13-1,1)²-4:1/2

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Let's break down the expression step by step:

3 5/6: This is a mixed number, which is equivalent to 23/6 when converted to an improper fraction.

1 4/13: Similarly, this mixed number is equivalent to 17/13 as an improper fraction.

Now, let's calculate each part of the expression:

23/6 - 17/13: To subtract these fractions, you need a common denominator, which is 78. So, (23/6) - (17/13) = (23/6)(13/13) - (17/13)(6/6) = (299/78) - (102/78) = 197/78.

(197/78)²: To square this fraction, you square the numerator and denominator separately. (197²)/(78²) = 38809/6084.

4:1/2: This is 4 divided by 1/2, which is equivalent to 4*2 = 8.

Now, we have (38809/6084) - 8.

To subtract a whole number (8) from a fraction, you can convert 8 to a fraction with the same denominator as the fraction: 8 = 8/1.

Now, subtract the fractions: (38809/6084) - (8/1).

To subtract fractions, you need a common denominator, which is 6084 in this case.

Now, calculate the final result:

(38809/6084) - (8/1) = (38809/6084) - (48672/6084) = (38809 - 48672)/6084 = -9863/6084.

So, the final result is -9863/6084