Question

Вычислите 1) 5/7 ×(21/20 - 7/30) + 16/21 : 8/7 2) 4/45 : (12/25 - 4/15 ) + 15/16 × 4/15 3) 2 : 2 целых 2/3 + 1 целая 4/5 × 3 целые 1/3 - 2 целых 5/6 4) 3 : 3 целых 3/4 + 2 целых 2/5 × 2 целых 1/2 - 3 целых 5/6

Answer 1

Спрашивай, если что непонятно.

Answer 2

1. 5/7 × (21/20 - 7/30) + 16/21 : 8/7

To simplify the expression, let's calculate each part separately and then combine the results.

First, let's simplify the expression inside the parentheses: 21/20 - 7/30 = (213)/(203) - (72)/(302) = 63/60 - 14/60 = 49/60

Now let's calculate the first part of the expression: 5/7 × (49/60) = (549)/(760) = 245/420

Next, let's simplify the division: 16/21 : 8/7 = (167)/(218) = 112/168 = 14/21

Finally, let's add the two results: 245/420 + 14/21 = (2453)/(4203) + (1420)/(2120) = 735/1260 + 280/1260 = 1015/1260

The result is 1015/1260, which can be simplified by dividing both numerator and denominator by their greatest common divisor (GCD), which is 5: 1015/1260 = (1015/5)/(1260/5) = 203/252

Therefore, the final result is 203/252.

2. 4/45 : (12/25 - 4/15) + 15/16 × 4/15

Let's simplify the expression step by step.

First, let's simplify the expression inside the parentheses: 12/25 - 4/15 = (123)/(253) - (45)/(155) = 36/75 - 20/75 = 16/75

Now let's calculate the division: 4/45 : (16/75) = (475)/(4516) = 300/720 = 5/12

Next, let's calculate the multiplication: 15/16 × 4/15 = (154)/(1615) = 60/240 = 1/4

Finally, let's add the two results: 5/12 + 1/4 = (52)/(122) + (13)/(43) = 10/24 + 3/12 = 10/24 + 6/24 = 16/24

The result is 16/24, which can be simplified by dividing both numerator and denominator by their greatest common divisor (GCD), which is 8: 16/24 = (16/8)/(24/8) = 2/3

Therefore, the final result is 2/3.

3. 2 : 2 целых 2/3 + 1 целая 4/5 × 3 целые 1/3 - 2 целых 5/6

To calculate this expression, let's convert the mixed numbers into improper fractions first.

2 целых 2/3 = (2 * 3 + 2) / 3 = 8/3 1 целая 4/5 = (1 * 5 + 4) / 5 = 9/5 3 целые 1/3 = (3 * 3 + 1) / 3 = 10/3 2 целых 5/6 = (2 * 6 + 5) / 6 = 17/6

Now let's substitute these values into the expression