Question

А) 3 1/9 + 2 1/3; б) 5 4/7 + 2 1/2; в) 2 7/12 + 11 7/16; г) 8 7/15 - 3 1/30; д) 5 3/8 - 4 1/3; е) 9 3/4 - 3 7/8; ж) 16 1/4 - (8 2/5 + 3 3/10); з) (3 2/3 + 1 2/7) + (2 1/3 + 1 5/7)

Answer 1

А)5 4/9

Б)7 11/14

В)14 1/48

Г)5 13/30

Д)1 1/24

Е)5 7/8

Ж)4 11/20

З)9 1/3

Answer 2

To solve these arithmetic expressions involving mixed numbers, we'll start by converting the mixed numbers to improper fractions and then perform the operations.

a) 3 1/9 + 2 1/3: Convert to improper fractions: 3 1/9 = (3 * 9 + 1) / 9 = 28 / 9 2 1/3 = (2 * 3 + 1) / 3 = 7 / 3

Add the fractions: 28/9 + 7/3

To add fractions, we need a common denominator. The least common multiple of 9 and 3 is 9.

Convert 7/3 to have a denominator of 9: 7/3 = (7 * 3) / (3 * 3) = 21 / 9

Now, add the fractions: 28/9 + 21/9 = (28 + 21) / 9 = 49 / 9

The result as a mixed number: 49 / 9 = 5 4/9

b) 5 4/7 + 2 1/2: Convert to improper fractions: 5 4/7 = (5 * 7 + 4) / 7 = 39 / 7 2 1/2 = (2 * 2 + 1) / 2 = 5 / 2

Add the fractions: 39/7 + 5/2

To add fractions, we need a common denominator. The least common multiple of 7 and 2 is 14.

Convert 39/7 to have a denominator of 14: 39/7 = (39 * 2) / (7 * 2) = 78 / 14

Convert 5/2 to have a denominator of 14: 5/2 = (5 * 7) / (2 * 7) = 35 / 14

Now, add the fractions: 78/14 + 35/14 = (78 + 35) / 14 = 113 / 14

The result as a mixed number: 113 / 14 = 8 1/14 ≈ 8 1/7

c) 2 7/12 + 11 7/16: Convert to improper fractions: 2 7/12 = (2 * 12 + 7) / 12 = 31 / 12 11 7/16 = (11 * 16 + 7) / 16 = 183 / 16

Add the fractions: 31/12 + 183/16

To add fractions, we need a common denominator. The least common multiple of 12 and 16 is 48.

Convert 31/12 to have a denominator of 48: 31/12 = (31 * 4) / (12 * 4) = 124 / 48

Convert 183/16 to have a denominator of 48: 183/16 = (183 * 3) / (16 * 3) = 549 / 48

Now, add the fractions: 124/48 + 549/48 = (124 + 549) / 48 = 673 / 48

The result as a mixed number: 673 / 48 ≈ 14 1/48

d) 8 7/15 - 3 1/30: Convert to improper fractions: 8 7/15 = (8 * 15 + 7) / 15 = 127 / 15 3 1/30 = (3 * 30 + 1) / 30 = 91 / 30

Subtract the fractions: 127/15 - 91/30

To subtract fractions, we need a common denominator. The least common multiple of 15 and 30 is 30.

Convert 127/15 to have a denominator of 30: 127/15 = (127 * 2) / (15 * 2) = 254 / 30

Now, subtract the fractions: 254/30 - 91/30 = (254 - 91) / 30 = 163 / 30

The result as a mixed number: 163 / 30 ≈ 5 13/30

e) 5 3/8 - 4 1/3: Convert to improper fractions: 5 3/8 = (5 * 8 + 3) / 8 = 43 / 8 4 1/3 = (4 * 3 + 1) / 3 = 13 / 3

Subtract the fractions: 43/8 - 13/3

To subtract fractions, we need a common denominator. The least common multiple of 8 and 3 is 24.

Convert 43/8 to have a denominator of 24: 43/8 = (43 * 3) / (8 * 3) = 129 / 24

Convert 13/3 to have a denominator of 24: 13/3 = (13 * 8) / (3 * 8) = 104 / 24

Now, subtract the fractions: 129/24 - 104/24 = (129 - 104) / 24 = 25 / 24

The result as a mixed number: 25 / 24 ≈ 1 1/24

f) 9 3/4 - 3 7/8: Convert to improper fractions: 9 3/4 = (9 * 4 + 3) / 4 = 39 / 4 3 7/8 = (3 * 8 + 7) / 8 = 31 / 8

Subtract the fractions: 39/4 - 31/8

To subtract fractions, we need a common denominator. The least common multiple of 4 and 8 is 8.

Convert 39/4 to have a denominator of 8: 39/4 = (39 * 2) / (4 * 2) = 78 / 8

Now, subtract the fractions: 78/8 - 31/8 = (78 - 31) / 8 = 47 / 8

The result as a mixed number: 47 / 8 = 5 7/8

g) 16 1/4 - (8 2/5 + 3 3/10): Convert all mixed numbers to improper fractions: 16 1/4 = (16 * 4 + 1) / 4 = 65 / 4 8 2/5 = (8 * 5 + 2) / 5 = 42 / 5 3 3/10 = (3 * 10 + 3) / 10 = 33 / 10

Now, perform the operations within the parentheses: 8 2/5 + 3 3/10 = 42/5 + 33/10

To add fractions, we need a common denominator. The least common multiple of 5 and 10 is 10.

Convert 42/5 to have a denominator of 10: 42/5 = (42 * 2) / (5 * 2) = 84 / 10

Now, add the fractions: 84/10 + 33/10 = (