Convert $40^{\circ} 20^{\prime}$ into radian measure.

Step 1: Convert minutes to degrees

First, we need to convert the given angle from degrees and minutes into a single decimal degree value. Since there are 60 minutes in 1 degree, we divide the minutes by 60 to convert them into degrees.

Step 2: Express the angle in decimal degrees

Now, we add the converted minutes (in degrees) to the whole degree part of the angle. This gives us the total angle expressed entirely in degrees as a single fraction.

Step 3: Convert degrees to radians

To convert degrees to radians, we use the conversion factor that 1 degree is equal to $\frac{\pi}{180}$ radians. This is derived from the fact that $180^{\circ} = \pi$ radians.

Step 4: Calculate the radian measure

Finally, we multiply the angle in degrees by the conversion factor $\frac{\pi}{180}$ to get the equivalent angle in radians. We simplify the resulting fraction.

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