Measurement and Conversion
Examples
1. Change 75 inches to feet.
75 in. = (75 ÷ 12) ft. = 6 ¼ ft. There are fewer feet than inches because feet are larger units.
2. Change 3 pounds 14 ounces to ounces.
3 lb. = (3 × 16) oz. = 48 oz. Add the ounces. 48 oz. + 14 oz. = 62 oz.
There are more ounces than pounds because ounces are smaller units.
3. 35 qt. = gal. qt.
35 ÷ 4 = 8r3 35 qt. = 8 gal 3 qt.
Practice
1. A math book weighs 2 lb. 6 oz. How much do 6 of these books weigh?
2 lb. 6 oz. = 2×16 + 6 = 38 oz. 38 ×6 = 228 oz. 228 ÷ 6 = 14r4
Ans.: 14 lb. 4 oz. or 14 ¼ lb.
2. A piece of rope 10 ft. 8 in. long is cut into 4 equal pieces. How long is each piece?
2 ⅔ ft. = 2 ft 8 in.
3. A piece of wire 6 yd. 2 ft. long is cut into 5 equal pieces. Which measure is NOT equivalent to the length of each piece?
a. 1 yd. 1 ft.
b. 4 ft.
c. 1 ⅓ yd.
d. 64 in.
- An auto mechanic converts a metric part to 0.473 inch. The part comes only in fractional sizes given to the nearest 64th of an inch. What is the closest size?
.473 = 3/64 => x = 30 => closest size is 30/64
- Lumber is often measured in board feet. A board foot of lumber is a piece one foot square and one inch thick. To calculate board feet, multiply the thickness in inches by the width in feet by the length in feet. Count any thickness under one inch as one inch. The floor of a small building requires 245 boards, each 2 inches thick by 12 inches wide by 12 feet long. How many board feet should be ordered?
(245 × 2 × 12 × 12) / 12 = 5880
- Ordering carpeting can be very complicated because it usually comes in 12-foot widths. If a customer had a 14-foot by 20-foot room to carpet, the decorator might design the following plan to minimize waste:
In this plan, Area I is 20 by 12 feet, Area II is 2 by 12 feet, and Area III is 2 by 8 feet. The only waste is a 2- by 4-foot section from Area III. The total amount- needed is 24 by 12 feet.
There is a way to have no waste at all, but this would involve a large number of seams to patch the small pieces together, as shown below:
Design a way of carpeting each of the following room sizes using 12-foot widths of carpet. Waste as little as possible, but use no more than three seams.
- 18 feet by 30 feet
- 13 feet by 19 feet
- When riveting a piece of metal to an airplane, a mechanic must follow certain guidelines for the spacing of the rivets. For example, 1/4-inch rivets should be 1¼ inches apart. In addition, the first and last rivets should be 3/4 inch from the edge of the piece.
As an example, to determine the number of rivets needed for a 4 ½ -foot section, first subtract 1 ½ -inches from 54 inches to account for the distance from each edge. This leaves 52 ½ inches of length to be riveted. Next, divide this by 1¼ (the spacing between rivets) to get 42 spaces. Finally, add 1 to account for the fact that there is a rivet at each end of the interval. This means that 43 rivets are needed.
Determine the number of 1/4-inch rivets needed for a piece of metal 5 feet 9 inches long
5’9” = 60” + 9” = 69”
69” – 1.5” = 67.5”
67.5 ÷ 1.25 + 1 = 55
- A doctor orders 75 cc of juice for a certain patient's breakfast. If 120 cc is about 1/2 cup, how many cups of juice should the cook be told to measure?
75/x = 120/1/2 => x = 75/240 = .3125
- If the flow into a reservoir is 15 cubic feet per second, how long (in hours, minutes, seconds) will it take .to fill a 1,000,000-gallon reservoir? (Hint: 1 cubic foot= 7.48 gallons)
1,000,000 ÷ 7.48 ÷ 15 = 8912.66” => 8912.66” ÷ (60 × 60) = 2.476 hrs
8912.66” – 3600 × 2 = 1712.66” => 1712.66 ÷ 60 = 28.54 mins
1712.66 – 28 × 60 = 32.66 => 2hrs 28 mins 33”
10. A customer orders some brochures with 8 1/2- by 11-inch pages. The pages are printed on 17 ½ - by 22 ½ -inch sheets and then cut. How many of the larger sheets are needed for 8000 pages?
8000 ÷ (2 × 2) = 2000
- How many grams of NaCl (salt) would you add to a liter of water to make up a normal saline solution (0.85%, or 0.85 grams per 100 milliliters)? (1 liter = 1000 milliliters)
0.85 : 100 = x: 1000 =>x = 8.5
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