Calculate the Representative Fraction (RF).

Question

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Here's how to construct the plain scale:

A plain scale is used to represent two consecutive units (e.g., yards and feet, or meters and decimeters).

Calculate the Representative Fraction (RF).
The scale is given as 1 foot (actual length) = 1.5 inches (drawing length).
We need to express both in the same units to find the RF.
We know that 1 foot = 12 inches.
$\text{RF} = \frac{\text{Drawing length}}{\text{Actual length}} = \frac{1.5 \text{ inches}}{1 \text{ foot}} = \frac{1.5 \text{ inches}}{12 \text{ inches}} = \frac{1.5}{12} = \frac{15}{120} = \frac{1}{8}$
The Representative Fraction is $\boxed{\frac{1}{8}}$ .
Determine the Length of the Scale (LOS).
The scale needs to be long enough to measure up to 4 feet and read yards and feet.
Since 1 yard = 3 feet, 4 feet is 1 yard and 1 foot. To have clear yard divisions, it's practical to make the total length of the scale represent a whole number of yards that covers 4 feet. The smallest such whole number is 2 yards (which is 6 feet).
$\text{LOS} = \text{RF} \times \text{Maximum actual length to be represented}$ $\text{LOS} = \frac{1}{8} \times 2 \text{ yards}$
Convert 2 yards to inches: 2 yards = 2 $\times$ 3 feet = 6 feet = 6 $\times$ 12 inches = 72 inches.
$\text{LOS} = \frac{1}{8} \times 72 \text{ inches} = 9 \text{ inches}$
The total length of the scale to be drawn is $\boxed{9 \text{ inches}}$ .
Construct the Scale.
- Draw a straight line 9 inches long.
- Draw another line parallel to it, about 0.5 inches above, to form a narrow rectangle. Close the ends.
Divide into Primary Divisions (Yards).
- The 9-inch line represents 2 yards. Divide this line into 2 equal parts. Each part will be 4.5 inches long and represent 1 yard.
- Mark the point at 4.5 inches from the left as '0'. Mark the point at 9 inches (the right end) as '1 YARD'. (The question asks to read yards, so we can label the rightmost mark as 1 YARD, and the 0 mark as the start of the yards section).
- Label the rightmost division 'YARDS'.
Divide the Leftmost Primary Division into Secondary Divisions (Feet).
- The segment from '0' to the left end (4.5 inches long) represents 1 yard.
- Since 1 yard = 3 feet, divide this 4.5-inch segment into 3 equal parts. Each part will be 1.5 inches long and represent 1 foot.
- Mark these divisions to the left of '0' as '1', '2', and '3'. The '3' mark will be at the extreme left end.
- Label this section 'FEET'.

Final Touches.

Add the title "PLAIN SCALE" and state the RF = 1:8.
The scale is now constructed to read yards and feet, and can measure up to 4 feet (e.g., by taking 1 YARD from the right section and 1 FOOT from the left section, which totals 3 feet + 1 foot = 4 feet).

Here is a conceptual diagram of the constructed scale:

<----------------------------------------------------------------------------------------------------->
|      1 ft      |      1 ft      |      1 ft      |                 1 yard                 |
|                |                |                |                                        |
<----------------------------------------------------------------------------------------------------->
  3      2      1      0                       1 YARD
  (FEET)                                       (YARDS)

RF = 1:8

Calculate the Representative Fraction (RF).

Answer

Step-by-step solution

Calculate the Representative Fraction (RF).

Determine the Length of the Scale (LOS).

Construct the Scale.

Divide into Primary Divisions (Yards).

Divide the Leftmost Primary Division into Secondary Divisions (Feet).

Final Touches.

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