Customary Units of Length
Semester 4B · Chapter 10 · Lesson 2 · MATH-4B-C10-L02
Before you begin: prerequisite check
Recall: Multiplication/division with remainders. Attempt these questions independently first.
Convert 4 m 88 cm entirely to cm.
Show answer and reasoning
Each m is 100 cm. Multiply 4×100, then add 88: 488 cm.
Rename 8,030 m as whole km and leftover m.
Show answer and reasoning
Dividing by 1000 gives 8 whole km with 30 m remaining.
A measured quantity is 5 L 456 mL. Another quantity of 3 L 913 mL is taken away. How much remains in mL?
Show answer and reasoning
Convert both measurements to mL, then subtract: 5,456−3,913=1,543.
Key vocabulary
- metric unit
- meter, gram or liter family with decimal relationships
- customary unit
- inch, foot, pound or gallon family with its own conversion factor
- mixed units
- one measurement written using two units
- reference whole
- the full quantity of which a fraction is taken
Understand the concept
Customary lengths use relationships that are not all multiples of ten. Twelve inches make one foot, three feet make one yard, and 5,280 feet make one mile. A yard is 36 inches. To convert a larger unit into smaller ones, multiply by the number of smaller units in one larger unit. To reverse the process, divide. Draw a chain of labeled groups; it is safer than moving decimal points without considering units. A distance in feet can be compared with a distance in yards only after converting them to the same unit.
Fully worked examples and immediate checks
Read each example, predict how to begin, then follow its numerical explanation. The check below it is a fresh problem.
Worked example 1
Convert 3 mi to ft.
One mi = 5,280 ft; 3×5,280=15,840.
Check 1: try it yourself
Convert 7 mi to ft.
Show answer and reasoning
One mi = 5,280 ft; 7×5,280=36,960.
Worked example 2
Convert 10 ft to in.
One ft = 12 in; 10×12=120.
Check 2: try it yourself
A rope is 6 ft. Another is 70 in. Which is longer and by how much?
Show answer and reasoning
6 ft = 72 in; compare with 70.
Worked example 3
Convert 36,023 ft to mixed mi and ft.
Divide by 5,280: 6 groups and 4343 leftover.
Check 3: try it yourself
Convert 10 ft to mixed yd and ft.
Show answer and reasoning
Divide by 3: 3 groups and 1 leftover.
Guided practice
Convert 3 yd to ft.
Show answer and reasoning
One yd = 3 ft; 3×3=9.
Convert 6 yd to in.
Show answer and reasoning
One yd = 36 in; 6×36=216.
Convert 59,220 ft to mixed mi and ft.
Show answer and reasoning
Divide by 5,280: 11 groups and 1140 leftover.
A rope is 2 mi. Another is 10,558 ft. Which is longer and by how much?
Show answer and reasoning
2 mi = 10,560 ft; compare with 10,558.
A classmate claims 4 yd equals 120 ft. Explain the mistake.
Show answer and reasoning
The conversion factor is 3, so 4 yd equals 12 ft, not ten times that.
Independent practice
Convert 10 yd to in.
Show answer and reasoning
One yd = 36 in; 10×36=360.
Convert 12 yd to in.
Show answer and reasoning
One yd = 36 in; 12×36=432.
Convert 156 in to mixed yd and in.
Show answer and reasoning
Divide by 36: 4 groups and 12 leftover.
A rope is 9 yd. Another is 25 ft. Which is longer and by how much?
Show answer and reasoning
9 yd = 27 ft; compare with 25.
A classmate claims 10 mi equals 528,000 ft. Explain the mistake.
Show answer and reasoning
The conversion factor is 5280, so 10 mi equals 52,800 ft, not ten times that.
Convert 2 yd to ft.
Show answer and reasoning
One yd = 3 ft; 2×3=6.
Convert 8 ft to in.
Show answer and reasoning
One ft = 12 in; 8×12=96.
Convert 98 in to mixed ft and in.
Show answer and reasoning
Divide by 12: 8 groups and 2 leftover.
Challenge and transfer
Use a diagram or verbal justification where appropriate. The goal is transfer rather than speed.
Convert 5 ft to in. Explain or sketch the mathematical relationship.
Show answer and reasoning
One ft = 12 in; 5×12=60. State which quantities or geometric properties justify the method.
A learner claims: “3 yards equals 30 feet.” Identify what is wrong or incomplete and give a mathematically correct explanation.
Show answer and reasoning
False: 1 yard is 3 feet, so 3 yards is 9 feet. Explain the relevant quantities or properties, not merely the final answer.
Exit check
Convert 3 ft to in.
Show answer and reasoning
One ft = 12 in; 3×12=36.
Convert 9 yd to in.
Show answer and reasoning
One yd = 36 in; 9×36=324.
Convert 51,105 ft to mixed mi and ft.
Show answer and reasoning
Divide by 5,280: 9 groups and 3585 leftover.
Mastery check: Solve a new instance without hints, explain why the method works, and return later to confirm retention.