Question

7/9 ÷9+5/9*1/9-1/3*1/9 рациональным способом

Answer 1

7/9 ÷ 9 +1/9×(5/9 - 1/3) = 7/9 ×1/9 + 1/9 ×2/9 = 1/9×(7/9 + 2/9) = 1/9 × 1 = 1/9
Ответ: 1/9.

Answer 2

To simplify the expression using rational methods, follow the order of operations (PEMDAS/BODMAS):

1. Parentheses/Brackets
2. Exponents/Orders
3. Multiplication and Division (from left to right)
4. Addition and Subtraction (from left to right)

Let's simplify the expression step-by-step:

1. There are no parentheses or exponents, so we can move to the next step.

2. Perform multiplication and division from left to right: 7/9 ÷ 9 + 5/9 * 1/9 - 1/3 * 1/9

   7/9 ÷ 9 = 7/9 * 1/9 (to divide by a number, we can multiply by its reciprocal) = 7/81

   5/9 * 1/9 = 5/81

   1/3 * 1/9 = 1/27

The expression becomes: 7/81 + 5/81 - 1/27

3. Now, we need to find a common denominator to add/subtract the fractions. The common denominator for 81 and 27 is 81.

   Convert all fractions to have a denominator of 81:

   7/81 + 5/81 - 3/81

4. Now, we can add/subtract the fractions with the common denominator:

   (7 + 5 - 3) / 81 = 9 / 81

5. Finally, we can simplify the fraction:

   9 / 81 = 1 / 9

So, the rational result of the expression is 1/9.