Fractions and Measurement — Part 1
Semester 4B · Chapter 10 · Lesson 6 · MATH-4B-C10-L06
Before you begin: prerequisite check
Recall: 4A fraction-of-whole skills; measurement conversions. Attempt these questions independently first.
Convert 3 h 38 min to minutes.
Show answer and reasoning
3×60+38=218 minutes.
Convert 749 seconds to minutes and seconds.
Show answer and reasoning
Each 60 seconds is one minute; 749=60×12+29.
How many days are in 7 weeks and 4 days?
Show answer and reasoning
7×7+4=53.
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
Taking a fraction of a measurement is taking equal parts of a specific whole. For three quarters of 20 centimeters, divide the 20-centimeter bar into four equal 5-centimeter segments, then select three: 15 centimeters. The fraction does not change the unit; the result is still a length. A diagram works only if all pieces refer to the same whole and have equal measure. Before calculating, name that whole explicitly. Then divide by the denominator and multiply by the numerator.
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
Find 1/5 of a quantity measuring 35 L.
Each of 5 parts is 7 L; 1 parts are 7 L.
Check 1: try it yourself
Find 1/3 of a quantity measuring 15 L.
Show answer and reasoning
Each of 3 parts is 5 L; 1 parts are 5 L.
Worked example 2
Find 1/6 of a quantity measuring 60 cm.
Each of 6 parts is 10 cm; 1 parts are 10 cm.
Check 2: try it yourself
Find 6/8 of a quantity measuring 48 cm.
Show answer and reasoning
Each of 8 parts is 6 cm; 6 parts are 36 cm.
Worked example 3
Find 1/2 of a quantity measuring 8 cm.
Each of 2 parts is 4 cm; 1 parts are 4 cm.
Check 3: try it yourself
Find 1/2 of a quantity measuring 6 L.
Show answer and reasoning
Each of 2 parts is 3 L; 1 parts are 3 L.
Guided practice
Find 4/8 of a quantity measuring 64 m.
Show answer and reasoning
Each of 8 parts is 8 m; 4 parts are 32 m.
Find 2/4 of a quantity measuring 16 cm.
Show answer and reasoning
Each of 4 parts is 4 cm; 2 parts are 8 cm.
Find 1/4 of a quantity measuring 20 m.
Show answer and reasoning
Each of 4 parts is 5 m; 1 parts are 5 m.
Find 1/2 of a quantity measuring 8 L.
Show answer and reasoning
Each of 2 parts is 4 L; 1 parts are 4 L.
Explain why 1/2 of 6 cm still has units of cm.
Show answer and reasoning
You divide the original 6 cm into 2 equal cm-valued portions and select 1.
Independent practice
Find 3/6 of a quantity measuring 48 m.
Show answer and reasoning
Each of 6 parts is 8 m; 3 parts are 24 m.
Find 1/6 of a quantity measuring 48 L.
Show answer and reasoning
Each of 6 parts is 8 L; 1 parts are 8 L.
Find 2/4 of a quantity measuring 32 cm.
Show answer and reasoning
Each of 4 parts is 8 cm; 2 parts are 16 cm.
Find 1/6 of a quantity measuring 66 m.
Show answer and reasoning
Each of 6 parts is 11 m; 1 parts are 11 m.
Explain why 4/5 of 35 cm still has units of cm.
Show answer and reasoning
You divide the original 35 cm into 5 equal cm-valued portions and select 4.
Find 2/3 of a quantity measuring 24 cm.
Show answer and reasoning
Each of 3 parts is 8 cm; 2 parts are 16 cm.
Find 1/8 of a quantity measuring 64 cm.
Show answer and reasoning
Each of 8 parts is 8 cm; 1 parts are 8 cm.
Explain why 1/6 of 18 m still has units of m.
Show answer and reasoning
You divide the original 18 m into 6 equal m-valued portions and select 1.
Challenge and transfer
Use a diagram or verbal justification where appropriate. The goal is transfer rather than speed.
Find 1/3 of a quantity measuring 9 L. Explain or sketch the mathematical relationship.
Show answer and reasoning
Each of 3 parts is 3 L; 1 parts are 3 L. State which quantities or geometric properties justify the method.
A learner claims: “One-fourth of 20 centimeters is a quarter of one centimeter.” Identify what is wrong or incomplete and give a mathematically correct explanation.
Show answer and reasoning
False: the entire 20 cm is the whole; 20 ÷ 4 = 5 cm. Explain the relevant quantities or properties, not merely the final answer.
Exit check
Find 2/4 of a quantity measuring 12 cm.
Show answer and reasoning
Each of 4 parts is 3 cm; 2 parts are 6 cm.
Find 5/6 of a quantity measuring 72 L.
Show answer and reasoning
Each of 6 parts is 12 L; 5 parts are 60 L.
Find 3/5 of a quantity measuring 30 L.
Show answer and reasoning
Each of 5 parts is 6 L; 3 parts are 18 L.
Mastery check: Solve a new instance without hints, explain why the method works, and return later to confirm retention.