Question

1) (1/6+(7/8+2/27)÷5/9)+3/11*2 1/5 2) 2:1/4+((1 1/2+2 2/3):3 3/4-2/3):8 8/93) 8/15+((11/18-1/15):1 2/5-1/5)*8/25:1/50по действиям помагитеее

Answer 1

1) 1- 7/8+2/27=189/216+16/216=205/216

2- 205/216:5/9=205*9/216*5=41/24

3- 1/6+41/24=4/24+41/24=45/24=15/8

4- 3/11*2 1/5=3*11/11*5=3/5

5- 15/8+3/5=75/40+24/40=99/40=2 19/40

2) 1- 2:1/4=2*4/1*1=8

2- 1 1/2+2 2/3=3/2+8/3=9/6+16/6=25/6

3- 25/6:3 3/4=25*4/6*15=10/9

4- 10/9-2/3=10/9-6/9=4/9

5- 4/9:8 8/9=4*9/9*80=1/20

3) 1- 11/18-1/15=55/90-6/90=49/90

2- 49/90:1 2/5=49*5/90*7=7/18

3- 7/18-1/5=35/90-18/90=17/90

4- 17/90*8/25:1/50=17*8*50/90*25*1=17*8/5*9=136/45

5- 8/15+136/45=24/45+136/45=160/45=32/9=3 5/9

Answer 2

To solve the given expressions, follow the order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right). Let's break down each expression step by step:

1. (1/6 + (7/8 + 2/27) ÷ 5/9) + 3/11 * 2 1/5

Step 1: Solve the innermost parentheses: (7/8 + 2/27) = (189/216 + 16/216) = 205/216

Step 2: Divide the result by 5/9: (205/216) ÷ (5/9) = (205/216) * (9/5) = (205/216) * (9/5) = 205/120

Step 3: Add 1/6 to the result: (1/6) + (205/120) = (20/120) + (205/120) = (20 + 205)/120 = 225/120 = 15/8

Step 4: Multiply 3/11 by 2 1/5: (3/11) * 2 1/5 = (3/11) * (11/5 + 2/5) = (3/11) * (13/5) = 39/55

Step 5: Finally, add the results from Step 3 and Step 4: (15/8) + (39/55) = (225/120) + (312/120) = (225 + 312)/120 = 537/120

Now, simplify the result: 537/120 = 4 17/120

So, the final answer is 4 17/120.

2. 2:1/4 + ((1 1/2 + 2 2/3):3 3/4 - 2/3):8 8/9

Step 1: Convert mixed numbers to improper fractions: 1 1/2 = (21 + 1)/2 = 3/2 2 2/3 = (32 + 2)/3 = 8/3 3 3/4 = (43 + 3)/4 = 15/4 8 8/9 = (98 + 8)/9 = 80/9

Step 2: Solve the innermost parentheses: (3/2 + 8/3) = (9/6 + 16/6) = 25/6

Step 3: Divide the result by 15/4: (25/6) ÷ (15/4) = (25/6) * (4/15) = 100/90 = 10/9

Step 4: Subtract 2/3 from the result: (10/9) - (2/3) = (10/9) - (6/9) = 4/9

Step 5: Divide 2 by 1/4: 2 ÷ (1/4) = 2 * (4/1) = 8

Step 6: Solve the final division: 8 ÷ (8 8/9) = 8 * (9/80) = 72/80 = 9/10

Step 7: Finally, add the results from Step 4 and Step 6: (4/9) + (9/10) = (40/90) + (81/90) = (40 + 81)/90 = 121/90

Now, simplify the result: 121/90 = 1 31/90

So, the final answer is 1 31/90.

3. 8/15 + ((11/18 - 1/15):1 2/5 - 1/5) * 8/25 : 1/50

Step 1: Convert mixed numbers to improper fractions: 1 2/5 = (5*1 + 2)/5 = 7/5

Step 2: Subtract 1/5 from 11/18: (11/18) - (1/5) = (55/90) - (18/90) = 37/90

Step 3: Divide the result by 7/5: (37/90) ÷ (7/5) = (37/90) * (5/7) = 185/630

Step 4: Multiply the result by 8/25: (185/630) * (8/25) = 1480/15750

Step 5: Divide the result by 1/50: (1480/15750) ÷ (1/50) = (1480/15750) * (50/1) = 1480/315

Step 6: Finally, add 8/15 to the result: (8/15) + (1480/315) = (336/630) + (1480/315) = (336 + 1480)/315 = 1816/315

Now, simplify the result: 1816/315 = 5 41/315

So, the final answer is 5 41/315.