Fractions and Measurement — Part 2
Semester 4B · Chapter 10 · Lesson 7 · MATH-4B-C10-L07
Before you begin: prerequisite check
Recall: Lesson 10.07 and 4A fraction operations. Attempt these questions independently first.
Find 1/5 of a quantity measuring 20 cm.
Show answer and reasoning
Each of 5 parts is 4 cm; 1 parts are 4 cm.
Find 5/8 of a quantity measuring 24 cm.
Show answer and reasoning
Each of 8 parts is 3 cm; 5 parts are 15 cm.
Find 1/2 of a quantity measuring 18 m.
Show answer and reasoning
Each of 2 parts is 9 m; 1 parts are 9 m.
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
More than one fraction can describe different stages of a measurement story. If one half of a 24-meter rope is removed, 12 meters remain. If one third of the remaining rope is removed, the second removal is four meters, not eight, because the reference whole is now 12 meters. Draw one bar for the original amount and a second bar for what remains. Complete each stage before changing units or applying the next fraction. Check your result by adding the quantities removed and left together.
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 2/5 of a quantity measuring 55 L.
Each of 5 parts is 11 L; 2 parts are 22 L.
Check 1: try it yourself
Find 1/5 of a quantity measuring 55 L.
Show answer and reasoning
Each of 5 parts is 11 L; 1 parts are 11 L.
Worked example 2
Find 2/4 of a quantity measuring 24 cm.
Each of 4 parts is 6 cm; 2 parts are 12 cm.
Check 2: try it yourself
Find 4/6 of a quantity measuring 66 cm.
Show answer and reasoning
Each of 6 parts is 11 cm; 4 parts are 44 cm.
Worked example 3
A quantity of 72 cm is reduced by 2/6 of the original amount. Then 1/2 of what remains is used. How much is left?
After first use, 72−24=48 cm. Second use is 48÷2=24 cm; final 24 cm.
Check 3: try it yourself
A quantity of 15 m is reduced by 1/3 of the original amount. Then 1/2 of what remains is used. How much is left?
Show answer and reasoning
After first use, 15−5=10 m. Second use is 10÷2=5 m; final 5 m.
Guided practice
Find 1/5 of a quantity measuring 20 m.
Show answer and reasoning
Each of 5 parts is 4 m; 1 parts are 4 m.
Find 3/6 of a quantity measuring 18 L.
Show answer and reasoning
Each of 6 parts is 3 L; 3 parts are 9 L.
A quantity of 36 L is reduced by 2/3 of the original amount. Then 1/4 of what remains is used. How much is left?
Show answer and reasoning
After first use, 36−24=12 L. Second use is 12÷4=3 L; final 9 L.
A quantity of 40 L is reduced by 3/4 of the original amount. Then 1/2 of what remains is used. How much is left?
Show answer and reasoning
After first use, 40−30=10 L. Second use is 10÷2=5 L; final 5 L.
A quantity of 56 m is reduced by 1/2 of the original amount. Then 1/4 of what remains is used. How much is left?
Show answer and reasoning
After first use, 56−28=28 m. Second use is 28÷4=7 m; final 21 m.
Independent practice
Find 2/5 of a quantity measuring 45 L.
Show answer and reasoning
Each of 5 parts is 9 L; 2 parts are 18 L.
Find 4/6 of a quantity measuring 36 m.
Show answer and reasoning
Each of 6 parts is 6 m; 4 parts are 24 m.
A quantity of 16 L is reduced by 1/2 of the original amount. Then 1/2 of what remains is used. How much is left?
Show answer and reasoning
After first use, 16−8=8 L. Second use is 8÷2=4 L; final 4 L.
A quantity of 56 L is reduced by 1/2 of the original amount. Then 1/4 of what remains is used. How much is left?
Show answer and reasoning
After first use, 56−28=28 L. Second use is 28÷4=7 L; final 21 L.
A quantity of 24 m is reduced by 2/3 of the original amount. Then 1/2 of what remains is used. How much is left?
Show answer and reasoning
After first use, 24−16=8 m. Second use is 8÷2=4 m; final 4 m.
Find 3/4 of a quantity measuring 40 m.
Show answer and reasoning
Each of 4 parts is 10 m; 3 parts are 30 m.
Find 4/5 of a quantity measuring 30 cm.
Show answer and reasoning
Each of 5 parts is 6 cm; 4 parts are 24 cm.
A quantity of 24 cm is reduced by 1/3 of the original amount. Then 1/4 of what remains is used. How much is left?
Show answer and reasoning
After first use, 24−8=16 cm. Second use is 16÷4=4 cm; final 12 cm.
Challenge and transfer
Use a diagram or verbal justification where appropriate. The goal is transfer rather than speed.
Find 6/8 of a quantity measuring 80 m. Explain or sketch the mathematical relationship.
Show answer and reasoning
Each of 8 parts is 10 m; 6 parts are 60 m. State which quantities or geometric properties justify the method.
A learner claims: “After removing 1/2 of 20 L, taking 1/2 of the remainder also removes 10 L.” Identify what is wrong or incomplete and give a mathematically correct explanation.
Show answer and reasoning
False: the remainder is 10 L, so half of the remainder is 5 L. Explain the relevant quantities or properties, not merely the final answer.
Exit check
Find 6/8 of a quantity measuring 88 m.
Show answer and reasoning
Each of 8 parts is 11 m; 6 parts are 66 m.
Find 3/6 of a quantity measuring 18 cm.
Show answer and reasoning
Each of 6 parts is 3 cm; 3 parts are 9 cm.
A quantity of 20 m is reduced by 3/5 of the original amount. Then 1/2 of what remains is used. How much is left?
Show answer and reasoning
After first use, 20−12=8 m. Second use is 8÷2=4 m; final 4 m.
Mastery check: Solve a new instance without hints, explain why the method works, and return later to confirm retention.