Explore · MATH-5B-C15-L01-OPEN
What fraction of a fixed whole is 36%?
Great Inheritance Mathematics Term B · Original independent course
Meaning of Percentage
Watch for: Treating 35% as 35 individual objects regardless of whole.. Explain what the quantities mean before calculating.
Opening task
Prerequisite check
Before instruction · MATH-5B-C15-L01-PREREQ
What percent is 50 out of 100 equal parts?
Show worked answer (after attempting)
Answer: 50%
50/100 is fifty percent.
Understand the idea
Interpret percentage as parts per hundred and show a percentage of an explicitly identified whole. The essential earlier idea is: Chapter 13 ratio, fractions and decimals.. The model below will always use the actual quantities from the worked problem. Check treating 35% as 35 individual objects regardless of whole when you explain your answer.
Three worked examples
Worked example 1 · MATH-5B-C15-L01-Q01
What fraction of a fixed whole is 35%?
Solution: 7/20
Percent literally means per hundred. 35% = 35/100 = 7/20. The whole has exactly 100 equal units.
Worked example 2 · MATH-5B-C15-L01-Q02
A 100-seat room has 60 seats reserved. What percentage is reserved?
Solution: 60%
Percent literally means per hundred. 60% = 60/100 = 3/5. The whole has exactly 100 equal units.
Worked example 3 · MATH-5B-C15-L01-Q03
Explain 12% as parts per hundred; express as fraction.
Solution: 3/25
Percent literally means per hundred. 12% = 12/100 = 3/25. The whole has exactly 100 equal units.
Check understanding
1 · MATH-5B-C15-L01-Q04
What fraction of a fixed whole is 36%?
Show worked answer (after attempting)
Answer: 9/25
Percent literally means per hundred. 36% = 36/100 = 9/25. The whole has exactly 100 equal units.
2 · MATH-5B-C15-L01-Q05
A 100-seat room has 61 seats reserved. What percentage is reserved?
Show worked answer (after attempting)
Answer: 61%
Percent literally means per hundred. 61% = 61/100 = 61/100. The whole has exactly 100 equal units.
3 · MATH-5B-C15-L01-Q06
Explain 13% as parts per hundred; express as fraction.
Show worked answer (after attempting)
Answer: 13/100
Percent literally means per hundred. 13% = 13/100 = 13/100. The whole has exactly 100 equal units.
Guided practice
1 · MATH-5B-C15-L01-Q07
What fraction of a fixed whole is 37%?
Show worked answer (after attempting)
Answer: 37/100
Percent literally means per hundred. 37% = 37/100 = 37/100. The whole has exactly 100 equal units.
2 · MATH-5B-C15-L01-Q08
A 100-seat room has 62 seats reserved. What percentage is reserved?
Show worked answer (after attempting)
Answer: 62%
Percent literally means per hundred. 62% = 62/100 = 31/50. The whole has exactly 100 equal units.
3 · MATH-5B-C15-L01-Q09
Explain 14% as parts per hundred; express as fraction.
Show worked answer (after attempting)
Answer: 7/50
Percent literally means per hundred. 14% = 14/100 = 7/50. The whole has exactly 100 equal units.
4 · MATH-5B-C15-L01-Q10
What fraction of a fixed whole is 38%?
Show worked answer (after attempting)
Answer: 19/50
Percent literally means per hundred. 38% = 38/100 = 19/50. The whole has exactly 100 equal units.
Independent practice
1 · MATH-5B-C15-L01-Q11
A 100-seat room has 63 seats reserved. What percentage is reserved?
Show worked answer (after attempting)
Answer: 63%
Percent literally means per hundred. 63% = 63/100 = 63/100. The whole has exactly 100 equal units.
2 · MATH-5B-C15-L01-Q12
Explain 15% as parts per hundred; express as fraction.
Show worked answer (after attempting)
Answer: 3/20
Percent literally means per hundred. 15% = 15/100 = 3/20. The whole has exactly 100 equal units.
3 · MATH-5B-C15-L01-Q13
What fraction of a fixed whole is 39%?
Show worked answer (after attempting)
Answer: 39/100
Percent literally means per hundred. 39% = 39/100 = 39/100. The whole has exactly 100 equal units.
4 · MATH-5B-C15-L01-Q14
A 100-seat room has 64 seats reserved. What percentage is reserved?
Show worked answer (after attempting)
Answer: 64%
Percent literally means per hundred. 64% = 64/100 = 16/25. The whole has exactly 100 equal units.
5 · MATH-5B-C15-L01-Q15
Explain 16% as parts per hundred; express as fraction.
Show worked answer (after attempting)
Answer: 4/25
Percent literally means per hundred. 16% = 16/100 = 4/25. The whole has exactly 100 equal units.
6 · MATH-5B-C15-L01-Q16
What fraction of a fixed whole is 40%?
Show worked answer (after attempting)
Answer: 2/5
Percent literally means per hundred. 40% = 40/100 = 2/5. The whole has exactly 100 equal units.
7 · MATH-5B-C15-L01-Q17
A 100-seat room has 65 seats reserved. What percentage is reserved?
Show worked answer (after attempting)
Answer: 65%
Percent literally means per hundred. 65% = 65/100 = 13/20. The whole has exactly 100 equal units.
8 · MATH-5B-C15-L01-Q18
Explain 17% as parts per hundred; express as fraction.
Show worked answer (after attempting)
Answer: 17/100
Percent literally means per hundred. 17% = 17/100 = 17/100. The whole has exactly 100 equal units.
Challenge and error analysis
1 · MATH-5B-C15-L01-ERR1
The assigned question is: “A 100-seat room has 68 seats reserved. What percentage is reserved?” A learner wrote: “I used tenths as the percent base instead of hundredths for the portion involving 100, giving 68.1%.” Identify a concrete invalid step or assumption. Work out the correct result and explain why it is valid.
Show worked answer (after attempting)
Answer: Correct result: 68%
The attempted reasoning or reported result does not satisfy the specified operation, units or geometric conditions. Correct mathematical result: 68%. Recompute from the given data: Percent literally means per hundred. 68% = 68/100 = 17/25. The whole has exactly 100 equal units.
2 · MATH-5B-C15-L01-ERR2
The assigned question is: “Explain 20% as parts per hundred; express as fraction.” A learner wrote: “I used tenths as the percent base instead of hundredths for the portion involving 20, giving 2/5.” Identify a concrete invalid step or assumption. Work out the correct result and explain why it is valid.
Show worked answer (after attempting)
Answer: Correct result: 1/5
The attempted reasoning or reported result does not satisfy the specified operation, units or geometric conditions. Correct mathematical result: 1/5. Recompute from the given data: Percent literally means per hundred. 20% = 20/100 = 1/5. The whole has exactly 100 equal units.
Exit check
Exit · MATH-5B-C15-L01-Q19
What fraction of a fixed whole is 41%?
Show worked answer (after attempting)
Answer: 41/100
Percent literally means per hundred. 41% = 41/100 = 41/100. The whole has exactly 100 equal units.