Question

1) 5/8х-1/4х-1/12х+1/6х; 2) 5/7у+1/4у+3/14у+1 целая 3/4; 3) 3 целых 3/5х+4 целых 10/21+ 1 целая 1/2х + 2 целых 1/3; 4) 5 целых 2/3у +8 целых 3/5у+3 целых 3/4 + 16 целых 5/8.

Answer 1

$1) \: \: \: \frac{5}{8} x - \frac{1}{4} x - \frac{1}{12} x + \frac{1}{6} x = \frac{15 - 6 - 2 + 4}{24} x = \frac{11}{24} x \\ 2) \: \: \: \frac{5}{7} y + \frac{1}{4} y + \frac{3}{14} y + 1 \frac{3}{4} = 1\frac{20 + 7 + 2}{28} y + 1 \frac{3}{4} = 1 \frac{29}{28} y + 1 \frac{3}{4} = 2 \frac{1}{28}y + 1 \frac{3}{4} \\ 3) \: \: \: 3 \frac{3}{5} x + 4 \frac{10}{21} + 1 \frac{1}{2} x + 2 \frac{1}{3} = 4 \frac{6 + 5}{10} x + 6 \frac{10 + 7}{21} = 4 \frac{11}{10} x + 6 \frac{17}{21} = 5 \frac{1}{10} x + 6 \frac{17}{21} \\ 4) \: \: \: 5 \frac{2}{3} y + 8 \frac{3}{5} y + 3 \frac{3}{4} + 16 \frac{5}{8} = 13 \frac{10 + 9}{15} y + 19 \frac{12 + 10}{16} = 13 \frac{19}{15} y + 19 \frac{22}{16} = 14 \frac{4}{15} y + 20 \frac{6}{16} = 14 \frac{4}{15} y + 20 \frac{3}{8}$
_______

Answer 2

Let's simplify each expression step by step:

1. 5/8x - 1/4x - 1/12x + 1/6x

Combining the terms with the same variable:

(5/8 - 1/4 - 1/12 + 1/6)x

To simplify this, we need to find a common denominator for the fractions. The least common multiple of 8, 4, 12, and 6 is 24.

(15/24 - 6/24 - 2/24 + 4/24)x

Combine the fractions:

(11/24)x

The simplified expression is 11/24x.

2. 5/7y + 1/4y + 3/14y + 1 3/4

Combining the terms with the same variable:

(5/7 + 1/4 + 3/14)y + 1 3/4

To simplify this, we need to find a common denominator for the fractions. The least common multiple of 7, 4, and 14 is 28.

(20/28 + 7/28 + 6/28)y + 1 3/4

Combine the fractions:

(33/28)y + 1 3/4

To add the whole number and the fraction, we need to convert the fraction into the same denominator. Multiply 4 by 28 to get 112:

(33/28)y + 1 84/112

Combine the whole number and the fraction:

(33/28)y + 1 3/4

The simplified expression is (33/28)y + 1 3/4.

3. 3 3/5x + 4 10/21 + 1 1/2x + 2 1/3

To add mixed numbers, we need to convert them into improper fractions.

3 3/5x = (3 * 5 + 3)/5x = 18/5x 4 10/21 = (4 * 21 + 10)/21 = 94/21 1 1/2x = (1 * 2 + 1)/2x = 3/2x 2 1/3 = (2 * 3 + 1)/3 = 7/3

Combining the terms:

18/5x + 94/21 + 3/2x + 7/3

To simplify this, we need to find a common denominator for the fractions. The least common multiple of 5, 21, 2, and 3 is 210.

(18/5 * 42/42)x + (94/21 * 10/10) + (3/2 * 105/105)x + (7/3 * 70/70)

Combine the fractions:

(756/210)x + (940/210) + (315/210)x + (490/210)

Simplify:

(756x + 315x + 940 + 490)/210

Combine like terms:

(1071x + 1430)/210

The simplified expression is (1071x + 1430)/210.

4. 5 2/3y + 8 3/5y + 3 3/4 + 16 5/8

To add mixed numbers, we need to convert them into improper fractions.

5 2/3y = (5 * 3 + 2)/3y = 17/3y 8 3/5y = (8 * 5 + 3)/5y =