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Вопрос от Анонимного юзера 13 декабря 2023 06:30

Выполните действия 1)2 1/2×(2/15-3 5/6)-2 3/4 2)-1 1/7×(4/5+19/20)×(6 5/6+4 2/3) 3)(6 3/8 - 2 3/4)×(-4)+7/18×9 4)9 1/6:(4 1/3-8)+24×3/8

Ответ нейросети

13 декабря 2023 06:30

  1. To perform the calculations in the first expression, follow the order of operations:

2 1/2 × (2/15 - 3 5/6) - 2 3/4

First, convert mixed numbers to improper fractions:

2 1/2 = 5/2 3 5/6 = (6 × 3 + 5)/6 = 23/6 2 3/4 = (4 × 2 + 3)/4 = 11/4

Next, simplify the expression inside the parentheses:

(2/15 - 23/6) = (2 × 2 - 23 × 5)/(15 × 6) = (-103)/90 = -103/90

Now plug in the values and calculate:

5/2 × (-103/90) - 11/4

Expand the fractions:

(5 × (-103) - 2 × 90)/(2 × 90) - 11/4

Calculate the numerator:

(-515 - 180)/(2 × 90) - 11/4 = -695/180 - 11/4

Get a common denominator of 180:

-695/180 - 495/180 = (-695 - 495)/180 = -1190/180

Simplify the fraction:

-1190/180 = -119/18

So the result of the first expression is -119/18.

  1. Similarly, for the second expression:

-1 1/7 × (4/5 + 19/20) × (6 5/6 + 4 2/3)

Convert mixed numbers to improper fractions:

-1 1/7 = (-1 × 7 + 1)/7 = -8/7 6 5/6 = (6 × 6 + 5)/6 = 41/6 4 2/3 = (4 × 3 + 2)/3 = 14/3

Now simplify the expression:

-8/7 × (4/5 + 19/20) × (41/6 + 14/3)

Find the common denominator for fractions inside parentheses:

-8/7 × (16/20 + 19/20) × (41/6 + 28/6)

Combine the fractions:

-8/7 × (35/20) × (69/6)

Multiply the fractions:

(35 × 69)/(7 × 20 × 6)

Calculate the numerator:

2415/840

Simplify the fraction:

2415/840 = 161/56

So the result of the second expression is 161/56.

  1. Moving on to the third expression:

(6 3/8 - 2 3/4) × (-4) + 7/18 × 9

Convert mixed numbers to improper fractions:

6 3/8 = (8 × 6 + 3)/8 = 51/8 2 3/4 = (4 × 2 + 3)/4 = 11/4

Now simplify the expression:

(51/8 - 11/4) × (-4) + 7/18 × 9

Find a common denominator for fractions inside parentheses:

(51/8 - 22/8) × (-4) + 7/18 × 9

Combine the fractions:

29/8 × (-4) + 7/18 × 9

Multiply the fractions:

-116/8 + 63/18

Get a common denominator of 72:

(-116 × 9 + 63 × 4)/(8 × 9) = (-1044 + 252)/(72)

Calculate the numerator:

-792/72 = -11/1

So the result of the third expression is -11/1, which is equivalent to -11.

  1. Finally, the fourth expression:

9 1/6 : (4 1/3 - 8) + 24 × 3/8

Convert mixed numbers to improper fractions:

9 1/6 = (6 × 9 + 1)/6 = 55/6 4 1/3 = (3 × 4 + 1)/3 = 13/3 8 = 8/1

Now simplify the expression:

55/6 : (13/3 - 8) + 24 × 3/8

Perform the subtraction inside parentheses:

55/6 : (13/3 - 24/3) + 24 × 3/8

(55/6) : (-11/3) + 24 × 3/8

Now divide the fractions:

(55/6) / (-11/3) + 24 × 3/8

Multiply by the reciprocal of the divisor:

(55/6) × (-3/11) + 24 × 3/8

Combine the fractions:

(-55 × 3 + 6 × 3)/(6 × 11) + 72/8

Calculate the numerator:

(-165 + 18)/(6 × 11) + 72/8 = (-147)/(6 × 11) + 72/8

Get a common denominator of 88 for the fractions:

(-147)/(6 × 11) + 594/88

Calculate the numerator:

-147/66 + 594/88

Multiply the fractions:

(-147 × 8 + 594 × 6)/(66 × 88)

Calculate the numerator:

(-1176 + 3564)/(66 × 88) = 2388/(66 × 88)

Simplify the fraction:

2388/5808 = 397/968

So the result of the fourth expression is 397/968.

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Выполните действия 1)2 1/2×(2/15-3 5/6)-2 3/4 2)-1 1/7×(4/5+19/20)×(6 5/6+4 2/3) 3)(6 3/8 - 2 3/4)×(-4)+7/18×9 4)9 1/6:(4 1/3-8)+24×3/8
1) To perform the calculations in the first expression, follow the order of operations: 2 1/2 × (2/15 - 3 5/6) - 2 3/4 First, convert mixed numbers to improper fractions: 2 1/2 = 5/2 3 5/6 = (6 × 3 + 5)/6 = 23/6 2 3/4 = (4 × 2 + 3)/4 = 11/4 Next, simplify the expression inside the parentheses: (2/15 - 23/6) = (2 × 2 - 23 × 5)/(15 × 6) = (-103)/90 = -103/90 Now plug in the values and calculate: 5/2 × (-103/90) - 11/4 Expand the fractions: (5 × (-103) - 2 × 90)/(2 × 90) - 11/4 Calculate the numerator: (-515 - 180)/(2 × 90) - 11/4 = -695/180 - 11/4 Get a common denominator of 180: -695/180 - 495/180 = (-695 - 495)/180 = -1190/180 Simplify the fraction: -1190/180 = -119/18 So the result of the first expression is -119/18. 2) Similarly, for the second expression: -1 1/7 × (4/5 + 19/20) × (6 5/6 + 4 2/3) Convert mixed numbers to improper fractions: -1 1/7 = (-1 × 7 + 1)/7 = -8/7 6 5/6 = (6 × 6 + 5)/6 = 41/6 4 2/3 = (4 × 3 + 2)/3 = 14/3 Now simplify the expression: -8/7 × (4/5 + 19/20) × (41/6 + 14/3) Find the common denominator for fractions inside parentheses: -8/7 × (16/20 + 19/20) × (41/6 + 28/6) Combine the fractions: -8/7 × (35/20) × (69/6) Multiply the fractions: (35 × 69)/(7 × 20 × 6) Calculate the numerator: 2415/840 Simplify the fraction: 2415/840 = 161/56 So the result of the second expression is 161/56. 3) Moving on to the third expression: (6 3/8 - 2 3/4) × (-4) + 7/18 × 9 Convert mixed numbers to improper fractions: 6 3/8 = (8 × 6 + 3)/8 = 51/8 2 3/4 = (4 × 2 + 3)/4 = 11/4 Now simplify the expression: (51/8 - 11/4) × (-4) + 7/18 × 9 Find a common denominator for fractions inside parentheses: (51/8 - 22/8) × (-4) + 7/18 × 9 Combine the fractions: 29/8 × (-4) + 7/18 × 9 Multiply the fractions: -116/8 + 63/18 Get a common denominator of 72: (-116 × 9 + 63 × 4)/(8 × 9) = (-1044 + 252)/(72) Calculate the numerator: -792/72 = -11/1 So the result of the third expression is -11/1, which is equivalent to -11. 4) Finally, the fourth expression: 9 1/6 : (4 1/3 - 8) + 24 × 3/8 Convert mixed numbers to improper fractions: 9 1/6 = (6 × 9 + 1)/6 = 55/6 4 1/3 = (3 × 4 + 1)/3 = 13/3 8 = 8/1 Now simplify the expression: 55/6 : (13/3 - 8) + 24 × 3/8 Perform the subtraction inside parentheses: 55/6 : (13/3 - 24/3) + 24 × 3/8 (55/6) : (-11/3) + 24 × 3/8 Now divide the fractions: (55/6) / (-11/3) + 24 × 3/8 Multiply by the reciprocal of the divisor: (55/6) × (-3/11) + 24 × 3/8 Combine the fractions: (-55 × 3 + 6 × 3)/(6 × 11) + 72/8 Calculate the numerator: (-165 + 18)/(6 × 11) + 72/8 = (-147)/(6 × 11) + 72/8 Get a common denominator of 88 for the fractions: (-147)/(6 × 11) + 594/88 Calculate the numerator: -147/66 + 594/88 Multiply the fractions: (-147 × 8 + 594 × 6)/(66 × 88) Calculate the numerator: (-1176 + 3564)/(66 × 88) = 2388/(66 × 88) Simplify the fraction: 2388/5808 = 397/968 So the result of the fourth expression is 397/968.