Question

( 1/2 + 1/3 + 1/6 ) * 24 : 5 - 9/22 : 15/121

Answer 1

Ответ:

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Answer 2

To simplify the given expression, let's break it down step by step:

1. Simplify the terms in the first set of parentheses: (1/2 + 1/3 + 1/6). LCM of 2, 3, and 6 is 6. 1/2 = 3/6 1/3 = 2/6

   So, (1/2 + 1/3 + 1/6) = (3/6 + 2/6 + 1/6) = 6/6 = 1.

2. Simplify the second set of parentheses: (9/22 : 15/121).

   To divide fractions, you invert the second fraction and multiply:

   (9/22 : 15/121) = (9/22) * (121/15)

   Now, simplify this multiplication:

   (9/22) * (121/15) = (9 * 121) / (22 * 15) = 1089 / 330.

3. Now, the expression becomes: (1 * 24/5 - 1089/330).

4. Let's simplify further:

   (24/5) can be written as (24/5) * (66/66) to have the same denominator as 330:

   (24/5) * (66/66) = (24 * 66) / (5 * 66) = 1584 / 330.

5. Now the expression is: (1584/330 - 1089/330).

6. Subtract the fractions:

   (1584/330 - 1089/330) = (1584 - 1089) / 330 = 495/330.

7. Finally, simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 165:

   (495/330) = (495/165) / (330/165) = 3/2.

So, the final simplified value of the expression is 3/2.