To solve the expression \( 42: 23 - (24 - 32 - 62) + 25 \times 3 \), let's break it down step by step.

1. **Simplify within the parentheses**:  
   \[
   24 - 32 - 62 = 24 - 32 - 62 = -70
   \]

2. **Substitute back into the expression**:  
   \[
   42 : 23 - (-70) + 25 \times 3
   \]

3. **Simplify the subtraction with a negative number**:
   \[
   42 : 23 + 70 + 25 \times 3
   \]

4. **Perform multiplication**:
   \[
   25 \times 3 = 75
   \]

5. **Substitute back into the expression**:
   \[
   42 : 23 + 70 + 75
   \]

6. **Perform the division**:
   \[
   42 : 23 \approx 1.8261
   \]

7. **Substitute back into the expression**:
   \[
   1.8261 + 70 + 75
   \]

8. **Add up the numbers**:
   \[
   1.8261 + 70 + 75 = 146.8261
   \]

The value of the expression \( 42 : 23 - (24 - 32 - 62) + 25 \times 3 \) is approximately **146.8261**.

Would you like more details or have any questions?

Here are some related questions you might find interesting:

1. How do you handle expressions with multiple levels of parentheses?
2. What is the order of operations in mathematics?
3. How do you convert a fraction to a decimal?
4. How does negative multiplication work in expressions?
5. What are some common mistakes made when calculating expressions?

**Tip**: Always perform operations inside parentheses first, then handle exponents and roots, followed by multiplication and division (from left to right), and finally addition and subtraction (from left to right). This is known as the order of operations.

Learn how to solve the arithmetic expression 42 divided by 23 minus the quantity 24 minus 32 minus 62 plus 25 times 3 step-by-step. This problem involves arithmetic operations and demonstrates the application of the order of operations. Suitable for students in Grades 6-8.

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