Question

Запишите десятичные дроби в виде обыкновенных дробей. Выполните действия (3 5/9 - 1 2/15)*5/9+((1/20+0,24)*8 1/3-1 1/6)*2 помогите плиз =()

Answer 1

(3 5/9 - 1 2/15) * 5/9 + ((1/20 + 0,24) * 8 1/3 - 1 1/6) * 2 = 3 137/162

1) 1/20 + 0,24 = 1/20 + 24/100 = 5/100 + 24/100 = 29/100
2) 29/100 * 8 1/3 = 29/100 * 25/3 = (29*1)/(4*3) = 29/12 = 2 5/12
3) 2 5/12 - 1 1/6 = 2 5/12 - 1 2/12 = 1 3/12 = 1 1/4
4) 1 1/4 * 2 = 5/4 * 2 = 5/2 = 2 1/2
5) 3 5/9 - 1 2/15 = 3 25/45 - 1 6/45 = 2 19/45
6) 2 19/45 * 5/9 = 109/45 * 5/9 = (109*1)/(9*9) = 109/81 = 1 28/81
7) 1 28/81 + 2 1/2 = 1 56/162 + 2 81/162 = 3 137/162

Answer 2

Converting Decimal Fractions to Ordinary Fractions

To convert decimal fractions to ordinary fractions, we need to express the decimal fractions as a fraction with a denominator of 10, 100, 1000, etc., depending on the number of decimal places.

For example, to convert the decimal fraction 0.24 to an ordinary fraction, we can write it as 24/100. Similarly, the decimal fraction 0.5712 can be written as 5712/10000.

Now, let's solve the given expression step by step.

Solving the Expression

The given expression is:

(3 5/9 - 1 2/15) * 5/9 + ((1/20 + 0.24) * 8 + 1/3 - 1 + 1/6) * 2

Let's break it down and solve it step by step.

Step 1: Simplify the mixed numbers and convert them to improper fractions.

- 3 5/9 can be written as (3 * 9 + 5)/9 = 32/9. - 1 2/15 can be written as (1 * 15 + 2)/15 = 17/15.

So, the expression becomes:

(32/9 - 17/15) * 5/9 + ((1/20 + 0.24) * 8 + 1/3 - 1 + 1/6) * 2

Step 2: Perform the operations within the parentheses.

- (1/20 + 0.24) can be written as (1/20 + 24/100) = (1/20 + 24/100) = (5/100 + 24/100) = 29/100. - ((1/20 + 0.24) * 8 + 1/3 - 1 + 1/6) can be simplified as (29/100 * 8 + 1/3 - 1 + 1/6) = (232/100 + 1/3 - 1 + 1/6).

So, the expression becomes:

(32/9 - 17/15) * 5/9 + (232/100 + 1/3 - 1 + 1/6) * 2

Step 3: Perform the operations within the parentheses.

- (32/9 - 17/15) can be simplified as (480/135 - 153/135) = 327/135. - (232/100 + 1/3 - 1 + 1/6) can be simplified as (232/100 + 40/120 - 120/120 + 20/120) = 172/100.

So, the expression becomes:

(327/135) * 5/9 + (172/100) * 2

Step 4: Perform the multiplications and additions.

- (327/135) * 5/9 can be simplified as (327/135) * (5/9) = (327 * 5)/(135 * 9) = 1635/1215. - (172/100) * 2 can be simplified as (172/100) * 2 = (172 * 2)/100 = 344/100.

So, the expression becomes:

1635/1215 + 344/100

Step 5: Find a common denominator and add the fractions.

To add fractions, we need to find a common denominator. In this case, the common denominator is 1215 * 100 = 121500.

- 1635/1215 can be written as (1635 * 100)/(1215 * 100) = 163500/121500. - 344/100 can be written as (344 * 1215)/(100 * 1215) = 41760/121500.

So, the expression becomes:

(163500/121500) + (41760/121500)

Step 6: Add the fractions.

To add fractions, we add the numerators and keep the common denominator.

- (163500 + 41760)/121500 = 205260/121500

The final result of the expression is 205260/121500.

I hope this helps! Let me know if you have any further questions.