5.1.1 Length Measurements

[ The foot measurement is thought to be derived from the length of a man’s foot with shoes! (If your bare foot is a foot long, you have pretty big feet). It was first defined in law by Edward I of England in 1305. Most likely, the relationship among feet, yards, and miles were made to fit existing units. These units are also defined in terms of the metric system, so for example, 1 yard is equal to 0.9144 meters. ] The common units used for measurement of length in the U.S. are inches (abbreviated in), feet (abbreviated ft), yards (abbreviated yd), and miles (abbreviated mi). Unlike the SI, there is not an easy or constant relationship among these units. In short, there are 12 inches in one foot, 3 feet in one yard, and 1760 yards, or 5280 ft, in one mile. Whoa! That’s a lot of feet.

[ Perimeter and area will be discussed in greater detail in Unit 10. ] We measure items such as height, perimeter, and area using these common units. Perimeter is the total distance around an object. Area measures the size of the surface of an object.

Let’s suppose at your physical this year, your height was measured as 67 inches. How tall are you in feet and inches?

First, we see how many times 12 can divide into 67, because there are 12 inches in 1 foot: 67 division 12 equals five cap r seven. We found that there are 5 feet in 67 inches, with 7 inches left over. So, you are 5 feet 7 inches tall. This is often written 5’7” in shorthand notation.

Here’s another example. If you have a photograph that measures 8 inches by 10 inches, what is the perimeter, in feet and inches?

The top and bottom of the photo have the same measurement, 8 inches. Similarly, the left side and right side share a measurement of 10 inches. Therefore, the perimeter, or the length of the border of the picture, is eight inches prefix plus of 10 inches prefix plus of eight inches prefix plus of 10 inches equals 36 inches. Since 36 division 12 equals three, this means that 36 inches is the same as 3 feet. Thus, the perimeter of the picture is 3 feet.

Activity symbol Activity: Length

For each of the following scenarios, use the appropriate operation and unit to determine the answer.

(a) A three-year-old girl measures 34 inches in height. Over her lifetime, she grows another 34 inches. Fully grown, how tall is she in feet and inches?

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Discussion

Try drawing pictures to help visualize each situation—you don’t need to be an artist!

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Answer

(a) 34 inches prefix multiplication of two equals 68 inches

(The calculation could also be carried out using addition: 34 inches prefix plus of 34 inches equals 68 inches.)

Because 68 division 12 equals five cap r eight, this means 68 inches is the same as 5 feet and 8 inches. Thus, the woman is 5’8”, which is rather tall for a woman.

(b) A rectangular garden measures 12 feet by 18 feet. What is the perimeter of the garden in feet? In yards?

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Discussion

Make sure you know what each word means. For example, “perimeter” is a measurement of the border, or edges, of a structure.

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Answer

(b) Because the garden is rectangular, this means that the opposite sides have the same length.

To determine the perimeter, we could just add up the sides of the garden: 18 feet prefix plus of 12 feet prefix plus of 18 feet prefix plus of 12 feet equals 60 feet.

Alternatively, we could double each side: two multiplication 18 feet prefix plus of two multiplication 12 feet equals 36 feet prefix plus of 24 feet equals 60 feet

. Since there are 3 feet in 1 yard, the number of yards is 60 division three equals 20. Thus, the perimeter of the garden is 20 yards.

(c) During a road trip with your friends you drive 187 miles through Pennsylvania and then 225 miles in Kentucky. How many miles did you drive in total? How many feet is this?

Answer

(c) The total distance driven is 187 miles prefix plus of 225 miles equals 412 miles .

To determine the number of feet, we need to remember that each mile contains 5,280 feet. Thus, the total distance can also be expressed as 412 multiplication 5280 equals two comma 175 comma 360 feet.

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(d) A football field measures 120 yards in length. How many yards long are four football fields if they are arranged end-to-end?

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Answer

(d) Four football fields each measuring 120 yards, will total four multiplication 120 yards equals 480 yards.

5.1 Using Units of Measurement

5.1.2 Weight Measurements