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Let's work through each problem in the image step-by-step.

### **Question 17**
\[ 7.50 \times \left( \frac{4}{10} + 16\% \right) \times 8.27 = \, ? \]

1. Calculate \(\frac{4}{10} = 0.4\).
2. \(16\%\) as a decimal is \(0.16\).
3. Sum the values: \(0.4 + 0.16 = 0.56\).
4. Multiply: \(7.50 \times 0.56 \times 8.27\).

Calculating:

\[
7.50 \times 0.56 = 4.20
\]
\[
4.20 \times 8.27 = 34.374
\]

Answer: \(34.374\).

### **Question 18**
\[ 56.34^2 - 43.66^2 = \, ? \]

This is a difference of squares formula: \((a^2 - b^2 = (a-b)(a+b))\).

1. Calculate \(56.34 - 43.66 = 12.68\).
2. Calculate \(56.34 + 43.66 = 100\).
3. Multiply: \(12.68 \times 100 = 1268\).

Answer: \(1268\).

### **Question 19**
\[ 2 + \frac{1}{5} - \frac{2}{3} \times \frac{3}{7} = \, ? \]

1. Calculate the multiplication first: \(\frac{2}{3} \times \frac{3}{7} = \frac{6}{21} = \frac{2}{7}\).
2. Now we have \(2 + \frac{1}{5} - \frac{2}{7}\).
3. Find a common denominator for \(\frac{1}{5}\) and \(\frac{2}{7}\): \(35\).
\[
\frac{1}{5} = \frac{7}{35}, \quad \frac{2}{7} = \frac{10}{35}
\]
4. Calculate: \(2 + \frac{7}{35} - \frac{10}{35} = 2 - \frac{3}{35} = \frac{67}{35}\).

Answer: \(\frac{67}{35}\).

### **Question 20**
\[ 12^2 - 70 + 2 \times 13 = \, ? \]

1. Calculate \(12^2 = 144\).
2. Calculate \(2 \times 13 = 26\).
3. Substitute: \(144 - 70 + 26\).
4. Calculate: \(144 - 70 = 74\).
5. \(74 + 26 = 100\).

Answer: \(100\).

### **Question 21**
\[ 2024^2 - 2020 \times 2028 = \, ? \]

1. Use the identity \((a - b)(a + b) = a^2 - b^2\), where \(a = 2024\) and \(b = 2022\).
2. Calculate: \(2024^2 - 2020 \times 2028 = (2024 - 2020)(2024 + 2020)\).
3. \(2024 - 2020 = 4\).
4. \(2024 + 2020 = 4044\).
5. Multiply: \(4 \times 4044 = 16176\).

Answer: \(16176\).

Let me know which question you'd like to discuss further or if there are any adjustments you'd like. Here are five related problems:

1. Simplify \((\frac{3}{7} + \frac{2}{5}) \times 8.5\).
2. Calculate \(25.36^2 - 12.12^2\).
3. Evaluate \(2x^2 - 5x + 3\) for \(x = 4\).
4. Simplify \( \frac{3}{8} + \frac{2}{9} \).
5. Find \(24^2 - 13 \times 2 + 5\).

**Tip**: When solving algebraic problems, always prioritize parentheses and exponents before performing multiplication and addition.

Math problems from the uploaded image, including topics like arithmetic operations, exponentiation, fractions, and percentages.

This page provides step-by-step solutions to various math problems covering arithmetic, fractions, exponentiation, and percentages. Suitable for students in Grades 7-9, the problems focus on key algebraic concepts such as the difference of squares, percentage calculations, and fraction multiplication.

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