Question

Пожалуйста помогите решить 7/9 * (1 1/6 - 1 : 1 1/19 -1/15) + 4 2/5 : 24 = заранее спасибо!!!!!

Answer 1

1)1:1 1/19 = 1/1 * 19/20 = 19/20

2)1 1/6 - 19/20 = 1 10 - 57/60 = 70 - 57/60 = 13/60

3)13/60 - 1/15 = 13 - 4/60 = 9/60

4)7/9 * 9/60 = 7/60

5)4 2/5 : 24 = 22/5 * 1/24 = 11/60

6)11/60 + 7/60 = 18/60

Answer 2

To solve the expression 7/9 * (1 + 1/6 - 1 : 1 1/19 - 1/15) + 4 2/5 : 24, we need to follow the order of operations (PEMDAS/BODMAS). This means we need to perform the operations inside parentheses first, then any multiplication or division from left to right, and finally any addition or subtraction from left to right.

Let's break down the expression step by step:

1. Inside the parentheses, we have 1 + 1/6 - 1 : 1 1/19 - 1/15. We need to simplify this part first.

- The division symbol ":" represents the division operation. - The fraction 1 1/19 can be converted to an improper fraction as (19 + 1)/19 = 20/19. - The fraction 1/15 cannot be simplified further.

So, the expression inside the parentheses becomes: 1 + 1/6 - 1 : 20/19 - 1/15.

2. Now, let's simplify the division operation inside the parentheses.

- To divide by a fraction, we can multiply by its reciprocal. So, 1 : 20/19 is equivalent to 1 * 19/20 = 19/20.

The expression inside the parentheses becomes: 1 + 1/6 - 19/20 - 1/15.

3. Next, let's simplify the addition and subtraction operations inside the parentheses.

- To add or subtract fractions, we need a common denominator. The least common multiple (LCM) of 6, 20, and 15 is 60. - Converting all the fractions to have a denominator of 60:

- 1 can be written as 60/60. - 1/6 can be written as 10/60. - 19/20 remains the same. - 1/15 can be written as 4/60.

The expression inside the parentheses becomes: 60/60 + 10/60 - 19/20 - 4/60.

4. Now, let's simplify the addition and subtraction operations inside the parentheses.

- Adding the fractions: 60/60 + 10/60 - 19/20 - 4/60 = (60 + 10 - 19)/60 - 4/60 = 51/60 - 4/60 = 47/60.

The expression inside the parentheses simplifies to: 47/60.

5. Now, let's substitute the simplified expression back into the original expression.

7/9 * 47/60 + 4 2/5 : 24.

6. Let's simplify the multiplication and division operations from left to right.

- Multiplying fractions: 7/9 * 47/60 = (7 * 47)/(9 * 60) = 329/540.

- Dividing mixed numbers: 4 2/5 : 24 = (22/5) : 24 = (22/5) * (1/24) = 22/120 = 11/60.

The expression becomes: 329/540 + 11/60.

7. Finally, let's add the fractions.

- Adding fractions: 329/540 + 11/60 = (329 * 60 + 11 * 540)/(540 * 60) = (19740 + 5940)/(32400) = 25680/32400 = 107/135.

Therefore, the solution to the expression 7/9 * (1 + 1/6 - 1 : 1 1/19 - 1/15) + 4 2/5 : 24 is 107/135.

Please note that the solution is provided based on the given expression. If there are any errors or misunderstandings in the expression, the solution may differ.