Questions: a) (35,814: 7,05+2,12) * 0,15 / (1,6+187,5: (16,25^2 * 3,75-3,75^3)) б) (0,73^3-0,73 * 0,27^2): 0,023+2,4 / (18,544: 3,05-1,83) * 0,16

Transcript text: a) $\frac{(35,814: 7,05+2,12) \cdot 0,15}{1,6+187,5:\left(16,25^{2} \cdot 3,75-3,75^{3}\right)}$ б) $\frac{\left(0,73^{3}-0,73 \cdot 0,27^{2}\right): 0,023+2,4}{(18,544: 3,05-1,83) \cdot 0,16}$.

Solution

Solution Steps

To solve these expressions, we need to follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)). We will evaluate each part of the expression step by step, simplifying the numerator and the denominator separately before performing the final division.

Part a

Simplify the expression inside the parentheses in the numerator.
Multiply the result by 0.15.
Simplify the expression inside the parentheses in the denominator.
Divide the result of the numerator by the result of the denominator.

Part б

Simplify the expression inside the parentheses in the numerator.
Divide the result by 0.023 and add 2.4.
Simplify the expression inside the parentheses in the denominator.
Multiply the result by 0.16.
Divide the result of the numerator by the result of the denominator.

Step 1: Simplify the Numerator of Part a

The numerator of part a is given by: \[ \left(\frac{35,814}{7.05} + 2.12\right) \times 0.15 \] Calculating the division and addition inside the parentheses: \[ \frac{35,814}{7.05} + 2.12 = 5,082.12 + 2.12 = 5,084.24 \] Multiplying by 0.15: \[ 5,084.24 \times 0.15 = 762.318 \]

Step 2: Simplify the Denominator of Part a

The denominator of part a is: \[ 1.6 + \frac{187.5}{\left(16.25^2 \times 3.75 - 3.75^3\right)} \] Calculating the expression inside the parentheses: \[ 16.25^2 \times 3.75 - 3.75^3 = 989.0625 \times 3.75 - 52.734375 = 3,708.984375 - 52.734375 = 3,656.25 \] Now, calculate the division and addition: \[ \frac{187.5}{3,656.25} = 0.0513 \] \[ 1.6 + 0.0513 = 1.6513 \]

Step 3: Calculate the Result of Part a

Divide the simplified numerator by the simplified denominator: \[ \frac{762.318}{1.6513} = 461.5 \]

Step 4: Simplify the Numerator of Part б

The numerator of part б is: \[ \left(\left(0.73^3 - 0.73 \times 0.27^2\right) \div 0.023\right) + 2.4 \] Calculating the expression inside the parentheses: \[ 0.73^3 - 0.73 \times 0.27^2 = 0.389017 - 0.053073 = 0.335944 \] Now, calculate the division and addition: \[ \frac{0.335944}{0.023} = 14.6061 \] \[ 14.6061 + 2.4 = 17.0061 \]

Step 5: Simplify the Denominator of Part б

The denominator of part б is: \[ \left(\frac{18.544}{3.05} - 1.83\right) \times 0.16 \] Calculating the division and subtraction: \[ \frac{18.544}{3.05} = 6.0793 \] \[ 6.0793 - 1.83 = 4.2493 \] Now, multiply by 0.16: \[ 4.2493 \times 0.16 = 0.6799 \]

Step 6: Calculate the Result of Part б

Divide the simplified numerator by the simplified denominator: \[ \frac{17.0061}{0.6799} = 25.01 \]