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}}

How do you write and use unit fractions for converting US units of length?

Unit fractions, or conversion factors, are ratios of equivalent measures used to convert between units. To write a unit fraction, place the new unit in the numerator and the original unit in the denominator. For example, to convert feet to inches, use 12inches1foot. Multiply the original measurement by this fraction so the original units cancel, leaving the new units. This method ensures accurate and consistent conversions between US units of length.

9. Measurement

US Units of Length

9. Measurement

US Units of Length: 동영상 및 연습문제

비디오 강의 워크시트

주제 요약

US Units of Length focuses on the common length units inches, feet, yards, and miles, and how to convert between them using unit fraction or conversion factor ideas. Important equivalent measures include 12 inches in 1 foot, 3 feet in 1 yard, 5280 feet in 1 mile, and 1760 yards in 1 mile. To convert correctly, place the new unit in the numerator and the original unit in the denominator so units cancel. If a direct conversion is not available, convert step by step through an intermediate unit.

Mixed units such as feet and inches or yards and feet can also be rewritten as a single unit or as mixed units. Converting from a smaller unit to mixed units means finding how many whole larger units fit and what amount remains. When adding or subtracting measurements, combine only like units first, then convert if needed. When multiplying or dividing a measurement by a constant, operate on each unit and then regroup so the result is written in standard form.

개념

Conversions: US Length

영상 길이:

워크시트로 더 똑똑하게 공부하세요.

각 영상을 인쇄 가능한 워크시트로 따라 하세요

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:

예시

Operations: US Length Example 6

영상 길이:

42s

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

$1 comma 467 y d$

$8 comma 800 y d$

$13 comma 200 y d$

$4 comma 400 y d$

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.
$168 mi division sign 6$

$28 mi$

$26 mi$

$34 mi$

$16 2 mi$

학생들이 이 주제에 대해 묻는 질문은 다음과 같습니다:

To convert feet to inches, use the fact that $12 inches = 1 foot$ . Write this as a unit fraction (conversion factor) with inches in the numerator and feet in the denominator: $\frac{12}{inches} \frac{1}{foot}$ . Multiply the number of feet by this fraction to cancel feet and convert to inches. For example, to convert 14 feet to inches: $14 feet \times \frac{12}{inches} \frac{1}{foot} = 168 inches$ . This method ensures units cancel correctly and the conversion is accurate.

When adding mixed units such as feet and inches, first add the like units separately. For example, add all inches together and all feet together. If the total inches exceed 12 (since 12 inches = 1 foot), convert the excess inches into feet. For instance, adding 3 feet 5 inches and 9 feet 4 inches: add inches (5 + 4 = 9 inches) and feet (3 + 9 = 12 feet). Since 9 inches is less than 12, no conversion is needed, so the sum is 12 feet 9 inches. This approach keeps units consistent and simplifies the final answer.

When subtracting mixed units like yards and feet, and borrowing is needed, convert the larger unit to the smaller unit before borrowing. For example, subtract 2 yards 8 feet from 10 yards 5 feet. Since 5 feet is less than 8 feet, borrow 1 yard from 10 yards, leaving 9 yards. Convert the borrowed yard to feet: $1 yard = 3 feet$ , so add 3 feet to 5 feet, making 8 feet. Now subtract feet: 8 - 8 = 0 feet, and yards: 9 - 2 = 7 yards. The result is 7 yards. This method ensures accurate subtraction across different units.

To multiply mixed units by a constant, multiply each unit separately by the constant, then simplify. For example, multiply 7 feet 6 inches by 4. Multiply feet: $7 × 4 = 28 feet$ . Multiply inches: $6 × 4 = 24 inches$ . Since 24 inches is more than 12 inches (1 foot), convert 24 inches to feet: $\frac{24}{inches} = 2 feet$ . Add these 2 feet to 28 feet for a total of 30 feet. The final answer is 30 feet. This process ensures the result is expressed in proper units.

The US system of length uses several key equivalent measures: $12 inches = 1 foot$ , $3 feet = 1 yard$ , $5280 feet = 1 mile$ , and $1760 yards = 1 mile$ . These equivalences allow conversions between units by using unit fractions (conversion factors) to cancel units properly during calculations.

Unit fractions, or conversion factors, are ratios of equivalent measures used to convert between units. To write a unit fraction, place the new unit in the numerator and the original unit in the denominator. For example, to convert feet to inches, use $\frac{12}{inches} \frac{1}{foot}$ . Multiply the original measurement by this fraction so the original units cancel, leaving the new units. This method ensures accurate and consistent conversions between US units of length.