Question

8/9*(2 1/4)² - 3/7:3 3/7+5/6 :3 1/3 по действиям

Answer 1

Скачай приложение photomath а вообще как я думаю решение такое : 1. (2 1/4)2 = 1/4 2.8/9*1/4= 2/9 3. 3/7:3 3/7 = 3 4. 5/6:3 1/3= 5/54 5. 3+ 5/54= 167/54 6. 2/9 - 167/54= 155/54
ОТВЕТ : 155/54

Answer 2

To simplify the given expression, let's perform the operations step by step:

Step 1: Simplify the square of the mixed number (2 1/4)². (2 1/4)² = (9/4)² = 81/16

Step 2: Simplify the fraction 8/9 multiplied by (2 1/4)². 8/9 * (2 1/4)² = 8/9 * 81/16

Step 3: Multiply the numerators and denominators separately: Numerator: 8 * 81 = 648 Denominator: 9 * 16 = 144

So, 8/9 * (2 1/4)² = 648/144

Step 4: Simplify the fraction 648/144 (by dividing both numerator and denominator by their greatest common divisor, which is 72): 648/144 = 9/2

Step 5: Now, let's simplify the next fraction 3/7 : 3 3/7. To divide by a mixed number, we need to convert it to an improper fraction first: 3 3/7 = (7 * 3 + 3)/7 = 24/7

Now, perform the division: 3/7 : 24/7 Invert the second fraction and multiply: 3/7 * 7/24

Step 6: Simplify the multiplication: Numerator: 3 * 1 = 3 Denominator: 7 * 24 = 168

So, 3/7 : 3 3/7 = 3/168

Step 7: Next, let's simplify the fraction 5/6 : 3 1/3. Similarly, convert the mixed number to an improper fraction: 3 1/3 = (3 * 3 + 1)/3 = 10/3

Now, perform the division: 5/6 : 10/3 Invert the second fraction and multiply: 5/6 * 3/10

Step 8: Simplify the multiplication: Numerator: 5 * 1 = 5 Denominator: 6 * 10 = 60

So, 5/6 : 3 1/3 = 5/60

Step 9: Finally, let's combine the results of the two divisions: 9/2 - 3/168 + 5/60

To combine these fractions, they need to have a common denominator. The least common multiple (LCM) of 2, 168, and 60 is 840.

Step 10: Convert all the fractions to have a denominator of 840: (9/2) * (420/420) - (3/168) * (55/55) + (5/60) * (14/14) (9/2) * (420/420) - (3/168) * (25/25) + (5/60) * (14/14) (9/2) * (420/420) - (3/168) * (25/25) + (5/60) * (14/14)

Step 11: Simplify further: (1890/840) - (75/840) + (70/840)

Step 12: Combine the fractions: 1890/840 - 75/840 + 70/840

Step 13: Perform the subtraction: (1890 - 75 + 70)/840

Step 14: Simplify the numerator: (1885)/840

Step 15: The final result is a fraction: 1885/840

If required, you can further simplify the fraction or convert it to a mixed number.