Question

1)(2,6:(-13)+1,2):(-0,1); 2)7/8:(-2 1/4):5/6:(2 1/2):(-6/25); 3) (4 3/7)•1 4/31+(-6 2/3):3 1/3;​

Answer 1

1)

$\displaystyle \tt (2,6\div(-13)+1,2)\div(-0,1)=(-0,2+1,2)\div(-0,1)=1\div(-0,1)=-10$

2)

$\displaystyle \tt \frac{7}{8}\div(-2\frac{1}{4})\div\frac{5}{6}\div(2\frac{1}{2})\div(-\frac{6}{25})=\frac{7}{8}\div(-\frac{9}{4})\div\frac{5}{6}\div\frac{5}{2}\div(-\frac{6}{25})=\\\\\\ =\frac{7}{8}\cdot\frac{4}{9}\cdot\frac{6}{5}\cdot\frac{2}{5}\cdot\frac{25}{6}=\frac{7}{2}\cdot\frac{1}{9}\cdot\frac{2}{5}\cdot5=7\cdot\frac{1}{9}=\frac{7}{9}$

3)

$\displaystyle \tt (4\frac{3}{7})\cdot1\frac{4}{31}+(-6\frac{2}{3})\div3\frac{1}{3}=\frac{31}{7}\cdot\frac{35}{31}+(-\frac{20}{3})\div\frac{10}{3}=\frac{5}{1}+(-\frac{20}{3})\cdot\frac{3}{10}=\\\\\\=5+(-\frac{2}{1})==5-2=3$

Answer 2

To solve the given expressions, let's break them down step by step:

1. (2,6:(-13)+1,2):(-0,1)

Step 1: Calculate inside the parentheses first: (2,6:(-13) + 1,2) = (2,6:-12 + 1,2)

Step 2: Perform the division: (2,6:-12 + 1,2) = (-2.5 + 1.2)

Step 3: Perform the final division: (-2.5 + 1.2) / (-0.1) = -12

Answer: -12

2. 7/8:(-2 1/4):5/6:(2 1/2):(-6/25)

Step 1: Perform the division from left to right: 7/8 ÷ (-2 1/4) = 7/8 ÷ (-9/4) = -7/8 * 4/9 = -7/18

Step 2: Continue with the next division: -7/18 ÷ 5/6 = -7/18 * 6/5 = -7/15

Step 3: Continue with the next division: -7/15 ÷ (2 1/2) = -7/15 ÷ (5/2) = -7/15 * 2/5 = -14/75

Step 4: Continue with the last division: -14/75 ÷ (-6/25) = -14/75 ÷ (-6/25) = 14/75 * 25/6 = 7/54

Answer: 7/54

3. (4 3/7)•1 4/31+(-6 2/3):3 1/3

Step 1: Calculate the product inside the parentheses: (4 3/7) • 1 4/31 = 4 3/7 • 35/31

Step 2: Convert both mixed numbers into improper fractions: 4 3/7 = (4 * 7 + 3)/7 = 31/7 1 4/31 = (1 * 31 + 4)/31 = 35/31

So the expression becomes: (31/7) • (35/31) + (-6 2/3):3 1/3

Step 3: Perform the multiplication: (31/7) • (35/31) = 31 * 35 / 7 * 31 = 35

Step 4: Perform the addition: 35 + (-6 2/3) = 35 - (20/3) = (105 - 20) / 3 = 85 / 3

Step 5: Perform the final division: 85 / 3 ÷ 3 1/3 = 85 / 3 ÷ (10/3) = 85 / 3 * 3/10 = 85 / 10 = 8.5

Answer: 8.5

So, the solutions to the given expressions are:

1. -12
2. 7/54
3. 8.5