https://file.aiquickdraw.com/mathbot/file/1726205571424u88nqm00.jpg

Let's go through each part of the question in detail:

### Part (a):
\[
\frac{3^2 + 2.8}{16 - 11}
\]
1. First, calculate the exponent \(3^2 = 9\).
2. Add \(9 + 2.8 = 11.8\).
3. Now, simplify the denominator \(16 - 11 = 5\).
4. The expression becomes \(\frac{11.8}{5} = 2.36\).

Thus, the value of (a) is \(2.36\).

### Part (b):
\[
32 \cdot \left(\frac{1}{2} + 6\right) - (4 - 1)
\]
1. First, simplify the expression inside the parentheses: \(\frac{1}{2} + 6 = 6.5\).
2. Multiply: \(32 \cdot 6.5 = 208\).
3. Now, simplify the subtraction: \(4 - 1 = 3\).
4. Subtract: \(208 - 3 = 205\).

Thus, the value of (b) is \(205\).

### Part (c):
\[
4 \left((8 - 10 \cdot 3) + 2^3 - 5\right)
\]
1. Begin with the multiplication: \(10 \cdot 3 = 30\).
2. Simplify inside the parentheses: \(8 - 30 = -22\).
3. Now, calculate the exponent: \(2^3 = 8\).
4. Simplify the entire expression: \((-22 + 8 - 5) = -19\).
5. Multiply by 4: \(4 \cdot (-19) = -76\).

Thus, the value of (c) is \(-76\).

### Summary:
- (a) = 2.36
- (b) = 205
- (c) = -76

Would you like further explanations or details on any of the steps?

Here are 5 relative questions for you to practice:
1. Simplify \(\frac{4^2 + 3.5}{20 - 6}\).
2. Solve \(25 \cdot \left(\frac{3}{5} + 8\right) - (6 - 2)\).
3. What is \(5 \left((15 - 5 \cdot 2) + 3^2 - 6\right)\)?
4. Evaluate \(\frac{5^2 + 1.4}{18 - 13}\).
5. Solve \(28 \cdot \left(\frac{2}{3} + 5\right) - (7 - 4)\).

**Tip**: Always follow the order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) to ensure correct results.

Calculate the value of each of the following expressions:
(a) (3^2 + 2.8) / (16 - 11)
(b) 32 * (1/2 + 6) - (4 - 1)
(c) 4 * ((8 - 10 * 3) + 2^3 - 5)

Learn how to calculate the value of expressions involving exponents, fractions, and multiple operations. This detailed solution demonstrates the use of PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction) and arithmetic rules. Suitable for Grades 7-9 students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation