Clock Math
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ACT Math › Clock Math
Find the distance between the hour and minute hand of a clock at 2:00 with a hand length of 
Explanation
To find the distance, first you need to find circumference. Thus,
Then, multiply the fraction of the clock they cover. Thus,
How many degrees are in each hour-long section of an analog clock with 8 equally spaced numbers on the face?
Explanation
If creating a picture helps, draw a circle and place 8 at the top where 12 normally is. Then put 2, 4, and 6 at the positions of 3, 6, and 9 on a normal 12-hour analog clock. 1, 3, 5, and 7 go halfway in between each even number.
Now, because each section is equally spaced, and because there are 8 sections we simply divide the total number of degrees in a circle (
Find the distance between the hour and minute hand of a clock at 2:00 with a hand length of
Explanation
To find the distance, first you need to find circumference. Thus,
Then, multiply the fraction of the clock they cover. Thus,
How many degrees are in each hour-long section of an analog clock with 8 equally spaced numbers on the face?
Explanation
If creating a picture helps, draw a circle and place 8 at the top where 12 normally is. Then put 2, 4, and 6 at the positions of 3, 6, and 9 on a normal 12-hour analog clock. 1, 3, 5, and 7 go halfway in between each even number.
Now, because each section is equally spaced, and because there are 8 sections we simply divide the total number of degrees in a circle (
What is the measure, in degrees, of the acute angle formed by the hands of a 12-hour clock that reads exactly 3:10?
35°
55°
60°
65°
72°
Explanation
The entire clock measures 360°. As the clock is divided into 12 sections, the distance between each number is equivalent to 30° (360/12). The distance between the 2 and the 3 on the clock is 30°. One has to account, however, for the 10 minutes that have passed. 10 minutes is 1/6 of an hour so the hour hand has also moved 1/6 of the distance between the 3 and the 4, which adds 5° (1/6 of 30°). The total measure of the angle, therefore, is 35°.
What is the measure, in degrees, of the acute angle formed by the hands of a 12-hour clock that reads exactly 3:10?
35°
55°
60°
65°
72°
Explanation
The entire clock measures 360°. As the clock is divided into 12 sections, the distance between each number is equivalent to 30° (360/12). The distance between the 2 and the 3 on the clock is 30°. One has to account, however, for the 10 minutes that have passed. 10 minutes is 1/6 of an hour so the hour hand has also moved 1/6 of the distance between the 3 and the 4, which adds 5° (1/6 of 30°). The total measure of the angle, therefore, is 35°.
What is the angle between the clock hands when the clock reads 6:30?
Explanation
Remember there are 
When the clock reads 6:30 the minute hand is on the 6, and the hour hand is halfway between the 6 and 7.
Thus the number of degrees between the hands is
What is the angle between the clock hands when the clock reads 6:30?
Explanation
Remember there are
When the clock reads 6:30 the minute hand is on the 6, and the hour hand is halfway between the 6 and 7.
Thus the number of degrees between the hands is
It is 4 o’clock. What is the measure of the angle formed between the hour hand and the minute hand?
Explanation
At four o’clock the minute hand is on the 12 and the hour hand is on the 4. The angle formed is 4/12 of the total number of degrees in a circle, 360.
4/12 * 360 = 120 degrees
It is 4 o’clock. What is the measure of the angle formed between the hour hand and the minute hand?
Explanation
At four o’clock the minute hand is on the 12 and the hour hand is on the 4. The angle formed is 4/12 of the total number of degrees in a circle, 360.
4/12 * 360 = 120 degrees