Question

В виде бесконечной десятичной Перевод бесконечной периодической десятичной дроби в обыкновенн Выполни действия и запиши результаты в виде десятичной периодической дроби. 5/12 :2/7 4/6*4/12 12 7 20/3 -13/9

Answer 1

5/12 * 7/2 = 35/24 = 1.458(3)

4/6 * 4/12 = 16/72 = 0.(2)

?

20/3 - 13/9 = 60-13/9= 47/9 = 5.(2)

Answer 2

Converting Infinite Repeating Decimal to Fraction

To convert an infinite repeating decimal to a fraction, we can use algebraic manipulation. Let's go through the steps to convert the given infinite repeating decimal to a fraction.

The given infinite repeating decimal is: 5/12.

To convert this decimal to a fraction, we can represent it as follows:

Let x = 0.5555...

Multiplying both sides of the equation by 10, we get:

10x = 5.5555...

Subtracting the original equation from the second equation, we get:

10x - x = 5.5555... - 0.5555...

Simplifying the equation, we have:

9x = 5

Dividing both sides of the equation by 9, we get:

x = 5/9

Therefore, the infinite repeating decimal 0.5555... is equal to the fraction 5/9.

Performing Arithmetic Operations

Now, let's perform the arithmetic operations given and express the results as decimal fractions.

1. 5/12 : 2/7: To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. Therefore: (5/12) ÷ (2/7) = (5/12) * (7/2) = 35/24 = 1.4583...

2. 4/6 * 4/12: To multiply fractions, we multiply the numerators together and the denominators together. Therefore: (4/6) * (4/12) = (4 * 4) / (6 * 12) = 16/72 = 0.2222...

3. 12 + 7: Adding the numbers together, we get: 12 + 7 = 19

4. 20/3 - 13/9: To subtract fractions, we need to have a common denominator. The least common multiple of 3 and 9 is 9. Therefore: (20/3) - (13/9) = (20/3) * (3/3) - (13/9) * (1/1) = (60/9) - (13/9) = (60 - 13) / 9 = 47/9 = 5.2222...

Therefore, the results of the given arithmetic operations expressed as decimal fractions are: 1. 5/12 : 2/7 = 1.4583... 2. 4/6 * 4/12 = 0.2222... 3. 12 + 7 = 19 4. 20/3 - 13/9 = 5.2222...

Please let me know if there's anything else I can help you with!