Question

1)(2/7+ 3 2/3)*4 2/3 2)(4 1/5-2 3/4)*2 2/193)(5 5/7+3 5/21*2 1/104)(7 5/12-3 1/6)*2 2/27​

Answer 1

Ответ:

1)166/63 2)58/19 3)438/35 4)238/27

Пошаговое объяснение:

Answer 2

Let's solve each of these expressions step by step:

1. (2/7 + 3 2/3) * 4 2/3

First, let's add the fractions inside the parentheses: 2/7 + 3 2/3 = 2/7 + 11/3

Now, find a common denominator, which is 21:

(2/7) * (3/3) + (11/3) * (7/7) = 6/21 + 77/21

Combine the fractions: 6/21 + 77/21 = 83/21

Now, multiply by 4 2/3:

(83/21) * 4 2/3

To multiply a mixed number by a fraction, convert the mixed number to an improper fraction:

4 2/3 = (3 * 4 + 2)/3 = 14/3

Now, multiply:

(83/21) * (14/3)

Multiply the numerators together and the denominators together:

(83 * 14)/(21 * 3) = 1162/63

So, the result is 1162/63.

2. (4 1/5 - 2 3/4) * 2 2/19

First, let's subtract the fractions inside the parentheses:

4 1/5 - 2 3/4 = (4 - 2) + (1/5 - 3/4) = 2 + (-7/20)

Now, add 2 and -7/20:

2 - 7/20 = (40/20) - (7/20) = 33/20

Now, multiply by 2 2/19:

(33/20) * 2 2/19

To multiply a mixed number by a fraction, convert the mixed number to an improper fraction:

2 2/19 = (19 * 2 + 2)/19 = 40/19

Now, multiply:

(33/20) * (40/19)

Multiply the numerators together and the denominators together:

(33 * 40)/(20 * 19) = 1320/380

Simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 20:

(1320/20) / (380/20) = 66/19

So, the result is 66/19.

3. (5 5/7 + 3 5/21 * 2 1/10)

First, let's multiply the fractions inside the parentheses:

3 5/21 * 2 1/10 = (3 * 2) + (5/21 * 1/10) = 6 + 5/210

Now, add 6 and 5/210:

6 + 5/210 = 6 + 1/42

Now, add this to 5 5/7:

5 5/7 + 1/42

To add a mixed number to a fraction, convert the mixed number to an improper fraction:

5 5/7 = (7 * 5 + 5)/7 = 40/7

Now, add:

(40/7) + (1/42)

To add fractions, you need a common denominator, which is 42:

(40/7) * (6/6) + (1/42)

Now, add:

(240/42) + (1/42) = 241/42

So, the result is 241/42.

4. (7 5/12 - 3 1/6) * 2 2/27

First, let's subtract the fractions inside the parentheses:

7 5/12 - 3 1/6 = (7 - 3) + (5/12 - 1/6) = 4 + (5/12 - 2/12)

Now, subtract the fractions:

4 + (3/12) = 4 + 1/4

Now, add this to 2 2/27:

2 2/27 + 1/4

To add a mixed number to a fraction, convert the mixed number to an improper fraction:

2 2/27 = (27 * 2 + 2)/27 = 56/27

Now, add:

(56/27) + (1/4)

To add fractions, you need a common denominator, which is 27 * 4 = 108:

(56/27) * (4/4) + (1/4) * (27/27)

Now, add:

(224/108) + (27/108) = 251/108

So, the result is 251/108.