Question

Вычислите: 1) 14 1/4+75/7; 2) 4 11/18+87/12; 3) 7 5/24+2 3/16; 4) 7 5/16+41/6+33/8; 5) 4 4/7+61/4; 6) 2 3/4+32/5.

Answer 1

1) 199/14

2) 56/9

3) 3/4

4) 157/40

5) 65/8

6) 459/4

Answer 2

Sure, I'd be happy to help you with those calculations. Let's simplify each expression step by step:

1. 14 1/4 + 75/7 Convert 14 1/4 to an improper fraction: 14 1/4 = (14 * 4 + 1) / 4 = 57/4 Now, we can add the fractions: 57/4 + 75/7 To add fractions with different denominators, we need to find a common denominator, which in this case is 28 (4 * 7). Now, convert both fractions to have a common denominator: (57/4) * (7/7) = 399/28 (75/7) * (4/4) = 300/28 Now add the fractions: 399/28 + 300/28 = 699/28 Now, simplify the result if possible: 699/28 = 24 27/28

2. 4 11/18 + 87/12 Convert 4 11/18 to an improper fraction: 4 11/18 = (4 * 18 + 11) / 18 = 83/18 Now, add the fractions: 83/18 + 87/12 To add fractions with different denominators, we need to find a common denominator, which in this case is 36 (18 * 2). Now, convert both fractions to have a common denominator: (83/18) * (2/2) = 166/36 (87/12) * (3/3) = 261/36 Now add the fractions: 166/36 + 261/36 = 427/36 Now, simplify the result if possible: 427/36 = 11 31/36

3. 7 5/24 + 2 3/16 Convert 7 5/24 to an improper fraction: 7 5/24 = (7 * 24 + 5) / 24 = 173/24 Convert 2 3/16 to an improper fraction: 2 3/16 = (2 * 16 + 3) / 16 = 35/16 Now, add the fractions: 173/24 + 35/16 To add fractions with different denominators, we need to find a common denominator, which in this case is 48 (24 * 2). Now, convert both fractions to have a common denominator: (173/24) * (2/2) = 346/48 (35/16) * (3/3) = 105/48 Now add the fractions: 346/48 + 105/48 = 451/48 Now, simplify the result if possible: 451/48 = 9 19/48

4. 7 5/16 + 41/6 + 33/8 Convert 7 5/16 to an improper fraction: 7 5/16 = (7 * 16 + 5) / 16 = 117/16 Now, add all three fractions: 117/16 + 41/6 + 33/8 To add fractions with different denominators, we need to find a common denominator, which in this case is 48 (16 * 3 or 16 * 3). Now, convert all fractions to have a common denominator: (117/16) * (3/3) = 351/48 (41/6) * (8/8) = 328/48 (33/8) * (6/6) = 198/48 Now add the fractions: 351/48 + 328/48 + 198/48 = 877/48 Now, simplify the result if possible: 877/48 = 18 13/48

5. 4 4/7 + 61/4 Convert 4 4/7 to an improper fraction: 4 4/7 = (4 * 7 + 4) / 7 = 32/7 Now, add the fractions: 32/7 + 61/4 To add fractions with different denominators, we need to find a common denominator, which in this case is 28 (7 * 4). Now, convert both fractions to have a common denominator: (32/7) * (4/4) = 128/28 (61/4) * (7/7) = 427/28 Now add the fractions: 128/28 + 427/28 = 555/28 Now, simplify the result if possible: 555/28 = 19 17/28

6. 2 3/4 + 32/5 Convert 2 3/4 to an improper fraction: 2 3/4 = (2 * 4 + 3) / 4 = 11/4 Now, add the fractions: 11/4 + 32/5 To add fractions with different denominators, we need to find a common denominator, which in this case is 20 (4 * 5). Now, convert both fractions to have a common denominator: (11/4) * (5/5) = 55/20 (32/5) * (4/4) = 128/20 Now add the fractions: 55/20 + 128/20 = 183/20 Now, simplify the result if possible: 183/20 = 9 3/20

So, the final results are:

1. 14 1/4 + 75/7 = 24 27/28
2. 4 11/18 + 87/12 = 11 31/36
3. 7 5/24 + 2 3/16 = 9 19/48
4. 7 5/16 + 41/6 + 33/8 = 18 13/48
5. 4 4/7 + 61/4 = 19 17/28
6. 2 3/4 + 32/5 = 9 3/20