https://file.aiquickdraw.com/mathbot/file/17253763094872xe1vumi.jpg

Let's go through the math problems on the uploaded image one by one. I will describe each problem, solve it, and provide an explanation for the solution.

### Top Page Questions:

1. **Question 1**:
   - Problem: A circle is divided into sections with angles given in degrees. The problem asks to identify the fraction of the circle represented by a shaded section with an angle of 90 degrees.
   - Solution: A full circle is 360 degrees. The fraction for 90 degrees is \(\frac{90}{360} = \frac{1}{4}\).

2. **Question 2**:
   - Problem: Another circle with shaded sections is presented. The shaded angle is 120 degrees.
   - Solution: The fraction of the circle that is shaded is \(\frac{120}{360} = \frac{1}{3}\).

3. **Question 3**:
   - Problem: This circle has a shaded area of 45 degrees.
   - Solution: The fraction of the circle that is shaded is \(\frac{45}{360} = \frac{1}{8}\).

4. **Question 4**:
   - Problem: A pie chart shows sectors with different colors, and the angle of the shaded region is 135 degrees.
   - Solution: The fraction of the circle that is shaded is \(\frac{135}{360} = \frac{3}{8}\).

5. **Question 5**:
   - Problem: The problem involves a circle divided into different sectors with given angles. It asks to find the fraction of the circle represented by a 180-degree shaded section.
   - Solution: The fraction of the circle that is shaded is \(\frac{180}{360} = \frac{1}{2}\).

### Bottom Page Questions:

6. **Question 6**:
   - Problem: This circle has a shaded area of 30 degrees.
   - Solution: The fraction of the circle that is shaded is \(\frac{30}{360} = \frac{1}{12}\).

7. **Question 7**:
   - Problem: A circle with a 270-degree shaded section.
   - Solution: The fraction of the circle that is shaded is \(\frac{270}{360} = \frac{3}{4}\).

8. **Question 8**:
   - Problem: Another circle shows a shaded region of 60 degrees.
   - Solution: The fraction of the circle that is shaded is \(\frac{60}{360} = \frac{1}{6}\).

9. **Question 9**:
   - Problem: A shaded region is 15 degrees.
   - Solution: The fraction of the circle that is shaded is \(\frac{15}{360} = \frac{1}{24}\).

10. **Question 10**:
    - Problem: The shaded section is 225 degrees.
    - Solution: The fraction of the circle that is shaded is \(\frac{225}{360} = \frac{5}{8}\).

11. **Question 11**:
    - Problem: The problem shows a 300-degree shaded sector.
    - Solution: The fraction of the circle that is shaded is \(\frac{300}{360} = \frac{5}{6}\).

12. **Question 12**:
    - Problem: A shaded section is 75 degrees.
    - Solution: The fraction of the circle that is shaded is \(\frac{75}{360} = \frac{5}{24}\).

### Summary:
The above answers convert each given angle into a fraction of a full circle (360 degrees). This involves dividing the given angle by 360 and simplifying the resulting fraction.

Would you like more details on any particular problem, or do you have any questions?

### Follow-Up Questions:
1. What is the formula to convert degrees into a fraction of a circle?
2. How do you simplify fractions?
3. What are the properties of a circle in geometry?
4. Can you explain the concept of radians and how they relate to degrees?
5. How would you calculate the area of a sector given the central angle and radius?

### Tip:
Always ensure that fractions are simplified to their lowest terms to make comparisons easier and to fully understand proportions in problems involving geometry and other mathematical contexts.

Solve various circle geometry problems by converting sector angles into fractions of a circle. This tutorial covers essential concepts, including how to calculate and simplify fractions based on sector angles. Suitable for students in Grades 6-8.

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