Question

1) (2 3/7+1 1/2):5/7; 2) (5 2/5+9 1/6):9 32/45; 3) (10-2 2/3):4 8/9

Answer 1

(2 3/7 + 1 1/2) : 5/7 = (17/7 + 3/2) : 5/7 = (34+21)/14 : 5/7 = 55/14 * 7/5 = 11/2 = 5 1/2

(5 2/5 + 9 1/6) : 9 32/45 = (27/5 + 55/6) : 437/45 = (162+275)/30 : 437/45 = 437/30 * 45/437 = 9/6 = 3/2 = 1 1/2

(10 - 2 2/3) : 4 8/9 = 7 1/3 : 4 8/9 = 22/3 : 44/9 = 22/3 * 9/44 = 3/2 = 1 1/2

Answer 2

To solve the expression (1)+(2+3/7+1+1/2):5/7; (2)+(5+2/5+9+1/6):9+32/45; (3)+(10-2+2/3):4+8/9, we need to follow the order of operations (also known as PEMDAS or BODMAS) to perform the calculations correctly.

Let's break down each expression one by one:

Expression 1: (1)+(2+3/7+1+1/2):5/7 1. Start by simplifying the expression inside the parentheses: (2+3/7+1+1/2). To add fractions, we need a common denominator. The common denominator for 7 and 2 is 14. So, (2+3/7+1+1/2) = 2 + (6/14 + 2/14) + (14/14 + 7/14) = 2 + 8/14 + 21/14. 2. Combine the fractions: 8/14 + 21/14 = 29/14. 3. Now, simplify the entire expression: (1) + (29/14) : 5/7. To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. (29/14) : (5/7) = (29/14) * (7/5) = 203/70. 4. Finally, add 1 to the result: 1 + 203/70. To add fractions, we need a common denominator. The common denominator for 70 and 1 is 70. (1 + 203/70) = 70/70 + 203/70 = 273/70.

Expression 2: (2)+(5+2/5+9+1/6):9+32/45 1. Start by simplifying the expression inside the parentheses: (5+2/5+9+1/6). To add fractions, we need a common denominator. The common denominator for 5 and 6 is 30. So, (5+2/5+9+1/6) = 5 + (12/30 + 6/30) + (270/30 + 5/30) = 5 + 18/30 + 275/30. 2. Combine the fractions: 18/30 + 275/30 = 293/30. 3. Now, simplify the entire expression: (2) + (293/30) : (9 + 32/45). To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. (293/30) : (9 + 32/45) = (293/30) * (45/9 + 32/45). To add fractions, we need a common denominator. The common denominator for 9 and 45 is 45. (293/30) * (45/9 + 32/45) = (293/30) * (5/1 + 32/45) = (293/30) * (225/45 + 32/45) = (293/30) * (257/45). To multiply fractions, we multiply the numerators and denominators. (293/30) * (257/45) = 75201/1350. 4. Finally, add 2 to the result: 2 + 75201/1350. To add fractions, we need a common denominator. The common denominator for 1350 and 1 is 1350. (2 + 75201/1350) = 2700/1350 + 75201/1350 = 77901/1350.

Expression 3: (3)+(10-2+2/3):4+8/9 1. Start by simplifying the expression inside the parentheses: (10-2+2/3). To subtract fractions, we need a common denominator. The common denominator for 3 and 9 is 9. So, (10-2+2/3) = 10 - 2 + (6/9) = 10 - 2 + 2/3. 2. Combine the fractions: 2/3. 3. Now, simplify the entire expression: (3) + (10 - 2 + 2/3) : (4 + 8/9). To add fractions, we need a common denominator. The common denominator for 3 and 9 is 9. (10 - 2 + 2/3) : (4 + 8/9) = (8 + 2/3) : (4 + 8/9) = (8 + 6/9) : (4 + 8/9) = (14/3) : (36/9). To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. (14/3) : (36/9) = (14/3) * (9/36) = 126/108. 4. Finally, add 3 to the result: 3 + 126/108. To add fractions, we need a common denominator. The common denominator for 108 and 1 is 108. (3 + 126/108) = 324/108 + 126/108 = 450/108.

Therefore, the final answer to the given expression is: 273/70; 77901/1350; 450/108.

Please note that fractions can be simplified further if needed.