Question

1) 0,(4)+2/3= 2) 6,(24)-5/33= 3) 2,(8)+1 2/3= 4) 3,(216) +87/111=

Answer 1

Ответ:

Пошаговое объяснение:

1) 0,(4)+2/3=4/9 +2/3=4/9 +6/9=10/9=1 1/9=1,(1)

2) 6,(24)-5/33=6 24/99 -15/99=6 9/99=6 1/11=6,(09)

3) 2,(8)+1 2/3=2 8/9 +1 6/9=3 14/9=4 5/9=4,(5)

4) 3,(216) +87/111=3 216/999 +783/999=3 999/999=4

Answer 2

Let's solve each of the given expressions step by step:

1. 0,(4) + 2/3:

To add the repeating decimal 0,(4) to a fraction, we need to convert the repeating decimal into a fraction.

Let x = 0,(4). Multiply both sides of this equation by 10 to eliminate the repeating part:

10x = 4,(4).

Subtracting the left side of the equation from the right side eliminates the repeating part:

10x - x = 4,(4) - 0,(4), 9x = 4.

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

x = 4/9.

Now we can add 4/9 to 2/3:

2/3 + 4/9.

To add fractions with different denominators, we need to find a common denominator. In this case, the least common multiple of 3 and 9 is 9. We can convert both fractions to have a denominator of 9:

2/3 = 6/9.

Now we can add the fractions:

6/9 + 4/9 = (6 + 4)/9 = 10/9.

Therefore, 0,(4) + 2/3 = 10/9.

2. 6,(24) - 5/33:

Similar to the previous question, we need to convert the repeating decimal 6,(24) into a fraction.

Let y = 6,(24). Multiply both sides by 100 to eliminate the repeating part:

100y = 624,(24).

Subtracting the left side of the equation from the right side eliminates the repeating part:

100y - y = 624,(24) - 6,(24), 99y = 618.

Dividing both sides of the equation by 99, we get:

y = 618/99 = 206/33.

Now we can subtract 5/33 from 206/33:

206/33 - 5/33 = (206 - 5)/33 = 201/33.

Therefore, 6,(24) - 5/33 = 201/33.

3. 2,(8) + 1 2/3:

First, let's convert the repeating decimal 2,(8) into a fraction.

Let z = 2,(8). Multiply both sides by 10 to eliminate the repeating part:

10z = 28,(8).

Subtracting the left side of the equation from the right side eliminates the repeating part:

10z - z = 28,(8) - 2,(8), 9z = 26.

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

z = 26/9.

Now we can add 26/9 to 1 2/3:

1 2/3 + 26/9.

To add a whole number and a fraction, we need to convert the whole number into an improper fraction:

1 2/3 = (1 * 3 + 2)/3 = 5/3.

Now we can add the fractions:

5/3 + 26/9.

To find a common denominator, we multiply the denominators: 3 * 9 = 27.

Converting both fractions to have a denominator of 27:

5/3 = 45/27, 26/9 = 78/27.

Now we can add the fractions:

45/27 + 78/27 = (45 + 78)/27 = 123/27.

We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 3:

123/27 = (3 * 41)/(3 * 9) = 41/9.

Therefore, 2,(8) + 1 2/3 = 41/9.

4. 3,(216) + 87/111:

Let w = 3,(216). Multiply both sides by 1000 to eliminate the repeating part:

1000w = 3216,(216).

Subtracting the left side of the equation from the right side eliminates the repeating part:

1000w - w = 3216,(216) - 3,(216), 999w = 3213.

Dividing both sides of the equation by 999, we get:

w = 3213/999 = 107/111.

Now we can add 107/111 to 87/111:

107/111 + 87/111 = (107 + 87)/111 = 194/111.

Therefore, 3,(216) + 87/111 = 194/111.

To summarize:

1. 0,(4) + 2/3 = 10/9.
2. 6,(24) - 5/33 = 201/33.
3. 2,(8) + 1 2/3 = 41/9.
4. 3,(216) + 87/111 = 194/111.