Question

Вычислите наиболее удобным способом,применяя свойства умножения 1.(1\5*3\4)*2/3 2.2\9(3\10*7\8) 3.15\19*(19\25*7\9)*5\7 Помогите пожалуйста и напишите побольше объяснении

Answer 1

(1\5*3\4)*2/3=1/5*(3/4*2/3)=1/5*1/2=1/10

2\9(3\10*7\8)=(2/9*3/10)*7/8=1/15*7/8=7/120

15\19*(19\25*7\9)*5\7= (15/19*19*25)*(7/9*5/7)=3/5*5/9=1/3

Answer 2

Calculation 1: (1/5 * 3/4) * 2/3

To solve this calculation, we can follow the order of operations, which is parentheses, multiplication, and then division.

1. First, let's simplify the expression within the parentheses: 1/5 * 3/4. To multiply fractions, we multiply the numerators together and the denominators together. So, (1/5 * 3/4) becomes (1 * 3) / (5 * 4) = 3/20.

2. Now, let's multiply the result by 2/3: (3/20) * 2/3. Again, we multiply the numerators together and the denominators together. So, (3/20 * 2/3) becomes (3 * 2) / (20 * 3) = 6/60.

3. Finally, we can simplify the fraction 6/60 by dividing both the numerator and denominator by their greatest common divisor, which is 6. So, 6/60 simplifies to 1/10.

Therefore, the result of the calculation (1/5 * 3/4) * 2/3 is 1/10.

Calculation 2: 2/9 * (3/10 * 7/8)

To solve this calculation, we can again follow the order of operations.

1. First, let's simplify the expression within the parentheses: 3/10 * 7/8. To multiply fractions, we multiply the numerators together and the denominators together. So, (3/10 * 7/8) becomes (3 * 7) / (10 * 8) = 21/80.

2. Now, let's multiply the result by 2/9: 2/9 * (21/80). Again, we multiply the numerators together and the denominators together. So, (2/9 * 21/80) becomes (2 * 21) / (9 * 80) = 42/720.

3. Finally, we can simplify the fraction 42/720 by dividing both the numerator and denominator by their greatest common divisor, which is 6. So, 42/720 simplifies to 7/120.

Therefore, the result of the calculation 2/9 * (3/10 * 7/8) is 7/120.

Calculation 3: 15/19 * (19/25 * 7/9) * 5/7

To solve this calculation, we can once again follow the order of operations.

1. First, let's simplify the expression within the parentheses: 19/25 * 7/9. To multiply fractions, we multiply the numerators together and the denominators together. So, (19/25 * 7/9) becomes (19 * 7) / (25 * 9) = 133/225.

2. Now, let's multiply the result by 15/19: 15/19 * (133/225). Again, we multiply the numerators together and the denominators together. So, (15/19 * 133/225) becomes (15 * 133) / (19 * 225) = 1995/4275.

3. Finally, let's multiply the result by 5/7: (1995/4275) * 5/7. Again, we multiply the numerators together and the denominators together. So, (1995/4275 * 5/7) becomes (1995 * 5) / (4275 * 7) = 9975/29925.

Therefore, the result of the calculation 15/19 * (19/25 * 7/9) * 5/7 is 9975/29925.

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