Fill in the blank to convert as indicated.13,200ft=13,200ft=_{}__ mi

25mi⁡25\operatorname{\mathrm{mi}}

7,920mi⁡7,920\operatorname{\mathrm{mi}}

9. Measurement

US Units of Length

9. Measurement

US Units of Length: 동영상 및 연습문제

주제 요약

US Units of Length focus on converting and operating with inches, feet, yards, and miles. Key equivalent measures are $12\text{ in}=1\text{ ft}$ , $3\text{ ft}=1\text{ yd}$ , $5280\text{ ft}=1\text{ mi}$ , and $1760\text{ yd}=1\text{ mi}$ . Conversions are done with a unit fraction, also called a conversion factor, using equivalent measures so units cancel correctly.

When changing from one unit to another, place the new unit in the numerator and the original unit in the denominator. Some conversions use one unit fraction, while others require a chain of unit fractions through an intermediate unit. Length can also be written as mixed units, such as feet and inches or yards and feet.

For operations with mixed units, add or subtract only like units first, then convert if needed. When subtracting, borrow by converting one larger unit to smaller units. When multiplying or dividing a measurement by a constant, apply the operation to each part of the mixed unit, then rewrite the result in simplest form.

개념

Conversions: US Length

영상 길이:

워크시트로 더 똑똑하게 공부하세요.

각 영상을 인쇄 가능한 워크시트로 따라 하세요

문제

Fill in the blank to convert as indicated.
$13 comma 200 f of t equals sub$ __ mi

$25 m i$

$\frac{1}{4} m i$

$2 and one half m i$

$7 comma 920$

문제

Fill in the blank to convert as indicated.
$2.5 equals$ __ yd

$1 comma 467 y d$

$8 comma 800 y d$

$13 comma 200 y d$

$4 comma 400 y d$

예시

Conversions: US Length Example 1

영상 길이:

예시

Conversions: US Length Example 2

영상 길이:

예시

Conversions: US Length Example 3

영상 길이:

예시

Conversions: US Length Example 4

영상 길이:

57s

예시

Conversions: US Length Example 5

영상 길이:

38s

개념

Operations: US Length

영상 길이:

문제

Perform the indicated operation.
5 yd 2 ft + 7 ft 1 ft

$12.3 yd$

$13 yd 2 ft$

$14 yd$

$13 yd$

문제

Perform the indicated operation.
$21 yd 2 ft times 5$

$107 yd 2 ft$

$108 yd 1 ft$

$105 yd 2 ft$

$103 yd 1 ft$

문제

Perform the indicated operation.
$24 ft 3 in minus 11 ft 8 in$

$12 ft 7 in$

$13 ft 5 in$

$12 ft 11 in$

$13 ft 7 in$

문제

Perform the indicated operation.
$168 mi division sign 6$

$28 mi$

$26 mi$

$34 mi$

$16 2 mi$

예시

Operations: US Length Example 6

영상 길이:

42s

학생들이 이 주제에 대해 묻는 질문은 다음과 같습니다:

To convert feet to inches, you use the fact that 1 foot equals 12 inches. You multiply the number of feet by the conversion factor expressed as a unit fraction with inches in the numerator and feet in the denominator. For example, to convert 14 feet to inches, multiply 14 by $\frac{12}{1}$ inches per foot, which gives $14 \times 12 = 168$ inches. This method ensures the feet units cancel out, leaving the answer in inches.

When adding mixed units such as feet and inches, first add the like units separately. For example, if you add 3 feet 5 inches and 9 feet 4 inches, add the inches: 5 + 4 = 9 inches, and add the feet: 3 + 9 = 12 feet. Since 9 inches is less than 12 inches (1 foot), no conversion is needed. The final sum is 12 feet 9 inches. Always add or subtract like units first, then convert if necessary.

When subtracting mixed units like yards and feet, and borrowing is needed, convert one larger unit into smaller units. For example, subtracting 2 yards 8 feet from 10 yards 5 feet requires borrowing 1 yard (which equals 3 feet) from the 10 yards, leaving 9 yards. Add the 3 feet to the 5 feet, making 8 feet. Now subtract: 8 feet minus 8 feet equals 0 feet, and 9 yards minus 2 yards equals 7 yards. The result is 7 yards. This method ensures proper subtraction across mixed units.

To multiply mixed units by a constant, multiply each unit separately by the constant, then convert if needed. For example, multiplying 7 feet 6 inches by 4 means multiplying 7 feet by 4 to get 28 feet, and 6 inches by 4 to get 24 inches. Since 24 inches is more than 12 inches, convert 24 inches to 2 feet (because $24 / 12 = 2$ feet). Add these 2 feet to 28 feet, resulting in 30 feet total. This approach keeps the units consistent and simplifies the final answer.

The key equivalent measures in the US units of length system are: $12 inches = 1 foot$ , $3 feet = 1 yard$ , $5280 feet = 1 mile$ , and $1760 yards = 1 mile$ . These equivalences are used as conversion factors to switch between units by multiplying with unit fractions that cancel out the original units and introduce the new units.