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

Answer 2

Let's break down the expression step by step:

1. First, simplify the fractions:
   • 5/6 can be expressed as 10/12
   • 4/13 remains as is

So, the expression becomes:

(3 10/12 : 1 4/13 - 1,1)² - 4 : 1/2

2. Now, simplify the mixed numbers:

3 10/12 = 3 5/6

So, the expression becomes:

(3 5/6 : 1 4/13 - 1,1)² - 4 : 1/2

3. Now, let's perform the operations inside the parentheses:

1 4/13 - 1,1 = 1 4/13 - 1 1/1 = (13/13) - (1/1) = 12/13

So, the expression becomes:

(3 5/6 : 12/13)² - 4 : 1/2

4. Perform the division inside the parentheses:

(3 5/6) ÷ (12/13) = (23/6) ÷ (12/13)

To divide fractions, multiply the first fraction by the reciprocal of the second:

(23/6) * (13/12)

Now, simplify this multiplication:

(23 * 13) / (6 * 12) = 299 / 72

So, the expression becomes:

(299/72)² - 4 : 1/2

5. Square the fraction:

(299/72)² = (299²) / (72²) = 89401 / 5184

6. Divide by 4:

(89401/5184) - 4

7. Divide by 1/2:

To divide by a fraction, multiply by its reciprocal:

(89401/5184) * (2/1) = (89401 * 2) / 5184 = 178802 / 5184

Now, if you want to simplify this fraction further, you can find the greatest common divisor (GCD) of the numerator and denominator and divide both by it. In this case, the GCD is 2:

(178802/2) / (5184/2) = 89401 / 2592

So, the final result is:

89401 / 2592