An arc subtends a central angle measuring 
 
\[\dfrac{7\pi}{4}\]radians.
A circle with a central angle that measures seven pi divided by four radians and the corresponding major arc highlighted. A radius is labeled r.
 
\[\dfrac{7\pi}{4}\]
\[r\]
What fraction of the circumference is this arc?
 of the circumference

To find the fraction of the circumference that the arc subtending the central angle \( \frac{7\pi}{4} \) radians represents, we can use the formula:

\[
\text{Fraction of circumference} = \frac{\theta}{2\pi}
\]

where \( \theta \) is the central angle in radians, and \( 2\pi \) is the total angle of a circle in radians.

### Step-by-step calculation:

1. The given central angle is \( \theta = \frac{7\pi}{4} \).
2. The total angle of the circle is \( 2\pi \).

Now, substitute \( \theta \) into the formula:

\[
\text{Fraction of circumference} = \frac{\frac{7\pi}{4}}{2\pi}
\]

Simplify the expression:

\[
\text{Fraction of circumference} = \frac{7\pi}{4} \times \frac{1}{2\pi} = \frac{7}{8}
\]

Thus, the arc represents \( \frac{7}{8} \) of the circumference of the circle.

Would you like more details or have any other questions?

### Related questions:
1. How do you calculate the length of an arc if the radius is given?
2. What is the major arc in a circle, and how is it different from the minor arc?
3. What is the central angle of a complete circle in degrees?
4. How can you convert radians to degrees for a central angle?
5. How does the circumference formula relate to the radius of the circle?

**Tip:** Always remember that \( 2\pi \) radians is equivalent to a full circle (360 degrees).

An arc subtends a central angle measuring 7π/4 radians. What fraction of the circumference is this arc?

Learn how to calculate the fraction of a circle's circumference that an arc subtending a central angle of 7π/4 radians represents. This problem involves geometry concepts related to radians and circumference, ideal for students in Grades 9-12.

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