Question

[6,75-4,5×1 2/3]×[-1 1/3]³ d) [-5/12-13/20]²×[-1 13/32] c) [-11/18+[-2 2/9]×(-0,2)]³×(-1,2)​

Answer 1

Ответ:

Пошаговое объяснение:

Answer 2

To solve these expressions, we'll break them down step by step and simplify each part as needed. Let's start with the first expression:

a) [6,75-4,5×1 2/3]×[-1 1/3]³

Step 1: Calculate the expression inside the square brackets: 6.75 - (4.5 × 1 2/3)

To multiply 1 2/3 by 4.5, convert 1 2/3 to an improper fraction: 1 2/3 = (3 × 1 + 2) / 3 = 5/3

Now, calculate: 6.75 - (4.5 × 5/3)

To multiply, multiply the numerators and denominators separately: 6.75 - (22.5 / 3)

Step 2: Subtract the fractions: 6.75 - (7.5)

Step 3: Calculate the expression inside the parentheses: 6.75 - 7.5 = -0.75

Now, we have the expression:

-0.75 × [-1 1/3]³

Step 4: Calculate [-1 1/3]³: -1 1/3 = -(4/3)

Now, calculate the cube: (-4/3)³ = (-64/27)

Step 5: Multiply -0.75 by (-64/27): -0.75 × (-64/27) = 16/9

So, the value of expression (a) is 16/9.

Now, let's move on to the second expression:

b) [-5/12-13/20]²×[-1 13/32]

Step 1: Calculate the expression inside the square brackets: (-5/12) - (13/20)

To find a common denominator, the least common multiple of 12 and 20 is 60: (-25/60) - (39/60)

Step 2: Subtract the fractions: (-25/60) - (39/60) = -64/60

Now, we have the expression:

(-64/60)²×[-1 13/32]

Step 3: Simplify (-64/60)²: (-64/60)² = (16/15)² = 256/225

Step 4: Calculate [-1 13/32]: -1 13/32 = -(32/32 + 13/32) = -45/32

Now, calculate the product: (256/225) × (-45/32)

Step 5: Multiply the fractions: (256/225) × (-45/32) = -5760/7200 = -8/10 = -4/5

So, the value of expression (b) is -4/5.

Finally, let's solve the third expression:

c) [-11/18+[-2 2/9]×(-0,2)]³×(-1,2)

Step 1: Calculate the expression inside the square brackets: -11/18 + [-2 2/9] × (-0.2)

Step 2: Calculate [-2 2/9]: -2 2/9 = -(18/9 + 2/9) = -20/9

Now, calculate the product: -11/18 + (-20/9) × (-0.2)

Step 3: Multiply the fractions: (-20/9) × (-0.2) = 4/9

Step 4: Add -11/18 and 4/9: (-11/18) + (4/9) = -22/36 + 16/36 = -6/36 = -1/6

Now, we have the expression:

(-1/6)³ × (-1.2)

Step 5: Calculate (-1/6)³: (-1/6)³ = -1/216

Step 6: Multiply by (-1.2): (-1/216) × (-1.2) = 0.005

So, the value of expression (c) is 0.005.