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Chapter 1: Problem 28

For Exercises \(27-29,\) draw a clock face with hands to show these times. $$3: 40$$

Short Answer

Expert verified
Hour hand slightly past 3, minute hand on 8.

Step by step solution

01

Draw the Clock Face

Begin by drawing a circle to represent the clock face. Mark the numbers 1 through 12 evenly spaced around the circle, starting with 12 at the top, 3 on the right, 6 at the bottom, and 9 on the left. Then fill in the remaining numbers in their respective positions.
02

Position the Hour Hand

To position the hour hand accurately: 40 minutes past 3 means the hour hand is not exactly on 3, but slightly past it. Calculate fraction of hour: 40 minutes is \( \frac{40}{60} = \frac{2}{3} \) of the way to the next hour. Place the hour hand two-thirds of the way between 3 and 4.
03

Position the Minute Hand

The minute hand points at the 8, since each number on the clock represents 5 minutes and 8 times 5 equals 40 minutes. Draw the minute hand pointing at the 8.
04

Finalize and Label

Ensure both hands are clearly visible and double-check the positions: the hour hand slightly past 3 towards 4, and the minute hand exactly on 8. Label each hand if necessary for clarity.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Reading Clock Time
Reading time on an analog clock involves understanding the positions of the hour and minute hands. The hour hand is shorter and moves from one number to the next as each hour passes. The minute hand is longer and moves through all the numbers as each hour progresses. To read the time, identify the number the hour hand is closest to and the exact number where the minute hand points.
Hour Hand Positioning
For hour hand positioning, remember that it moves gradually between numbers as the hour progresses. For example, at 3:40, the hour hand won't be on the 3 but will have moved a bit past it. To find the exact position, calculate the fraction of the hour passed. Since 40 minutes is \(\frac{40}{60}\), or \(\frac{2}{3}\), the hour hand should be two-thirds of the way between the 3 and 4.
Minute Hand Positioning
Each number on the clock corresponds to a 5-minute interval, which means the minute hand counts five-minute steps around the clock. At 3:40, you need to place the minute hand on the 8 because 8 times 5 equals 40. Always place the minute hand exactly on the number that matches the multiplication of 5 to get your minutes correct.
Drawing Clock Face
To draw a clock face effectively, start with a circle. Mark 12 at the top, 6 at the bottom, 3 on the right, and 9 on the left. Fill in with the remaining numbers in their respective positions in a clockwise manner. Make sure to draw the hands of the clock accurately: the shorter hour hand based on the fraction past the hour, and the longer minute hand pointing exactly to its specific position. Label both hands for clarity if needed.

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