Explore · MATH-5B-C15-L04-OPEN
Express 1/2 as a percent and state how many of 4 equal cells would be shaded.
Great Inheritance Mathematics Term B · Original independent course
Expressing Fractions as Percentages
Watch for: Assuming every numerator denominator can scale to hundred by integers.. Explain what the quantities mean before calculating.
Opening task
Prerequisite check
Before instruction · MATH-5B-C15-L04-PREREQ
What percent is one quarter of a whole?
Show worked answer (after attempting)
Answer: 25%
1/4 = 25/100 = 25%.
Understand the idea
Convert appropriate fractions to percentages by equivalent hundredths or division, including non-integer percentages when intended. The essential earlier idea is: Chapter 15 L01–03 and fraction equivalence.. The model below will always use the actual quantities from the worked problem. Check assuming every numerator denominator can scale to hundred by integers when you explain your answer.
Three worked examples
Worked example 1 · MATH-5B-C15-L04-Q01
Express 3/8 as a percent and state how many of 8 equal cells would be shaded.
Solution: 37.5%; shaded cells = 3
3/8 × 100% = (3 × 100 ÷ 8)% = 37.5%. A grid of 8 equal cells would shade 3.
Worked example 2 · MATH-5B-C15-L04-Q02
A whole has 7 highlighted parts out of 20. Convert this fraction to a percent.
Solution: 35%
7/20 × 100% = (7 × 100 ÷ 20)% = 35%. A grid of 20 equal cells would shade 7.
Worked example 3 · MATH-5B-C15-L04-Q03
Explain how 1/4 corresponds to 25% of a whole modeled using 4 equal parts.
Solution: 25%
1/4 × 100% = (1 × 100 ÷ 4)% = 25%. A grid of 4 equal cells would shade 1.
Check understanding
1 · MATH-5B-C15-L04-Q04
Express 1/2 as a percent and state how many of 4 equal cells would be shaded.
Show worked answer (after attempting)
Answer: 50%; shaded cells = 2
1/2 × 100% = (1 × 100 ÷ 2)% = 50%. A grid of 4 equal cells would shade 2.
2 · MATH-5B-C15-L04-Q05
A whole has 4 highlighted parts out of 10. Convert this fraction to a percent.
Show worked answer (after attempting)
Answer: 40%
2/5 × 100% = (2 × 100 ÷ 5)% = 40%. A grid of 10 equal cells would shade 4.
3 · MATH-5B-C15-L04-Q06
Explain how 1/2 corresponds to 50% of a whole modeled using 4 equal parts.
Show worked answer (after attempting)
Answer: 50%
1/2 × 100% = (1 × 100 ÷ 2)% = 50%. A grid of 4 equal cells would shade 2.
Guided practice
1 · MATH-5B-C15-L04-Q07
Express 5/8 as a percent and state how many of 24 equal cells would be shaded.
Show worked answer (after attempting)
Answer: 62.5%; shaded cells = 15
5/8 × 100% = (5 × 100 ÷ 8)% = 62.5%. A grid of 24 equal cells would shade 15.
2 · MATH-5B-C15-L04-Q08
A whole has 27 highlighted parts out of 60. Convert this fraction to a percent.
Show worked answer (after attempting)
Answer: 45%
9/20 × 100% = (9 × 100 ÷ 20)% = 45%. A grid of 60 equal cells would shade 27.
3 · MATH-5B-C15-L04-Q09
Explain how 3/4 corresponds to 75% of a whole modeled using 12 equal parts.
Show worked answer (after attempting)
Answer: 75%
3/4 × 100% = (3 × 100 ÷ 4)% = 75%. A grid of 12 equal cells would shade 9.
4 · MATH-5B-C15-L04-Q10
Express 3/4 as a percent and state how many of 16 equal cells would be shaded.
Show worked answer (after attempting)
Answer: 75%; shaded cells = 12
3/4 × 100% = (3 × 100 ÷ 4)% = 75%. A grid of 16 equal cells would shade 12.
Independent practice
1 · MATH-5B-C15-L04-Q11
A whole has 4 highlighted parts out of 8. Convert this fraction to a percent.
Show worked answer (after attempting)
Answer: 50%
1/2 × 100% = (1 × 100 ÷ 2)% = 50%. A grid of 8 equal cells would shade 4.
2 · MATH-5B-C15-L04-Q12
Explain how 1/4 corresponds to 25% of a whole modeled using 16 equal parts.
Show worked answer (after attempting)
Answer: 25%
1/4 × 100% = (1 × 100 ÷ 4)% = 25%. A grid of 16 equal cells would shade 4.
3 · MATH-5B-C15-L04-Q13
Express 7/8 as a percent and state how many of 40 equal cells would be shaded.
Show worked answer (after attempting)
Answer: 87.5%; shaded cells = 35
7/8 × 100% = (7 × 100 ÷ 8)% = 87.5%. A grid of 40 equal cells would shade 35.
4 · MATH-5B-C15-L04-Q14
A whole has 55 highlighted parts out of 100. Convert this fraction to a percent.
Show worked answer (after attempting)
Answer: 55%
11/20 × 100% = (11 × 100 ÷ 20)% = 55%. A grid of 100 equal cells would shade 55.
5 · MATH-5B-C15-L04-Q15
Explain how 1/2 corresponds to 50% of a whole modeled using 10 equal parts.
Show worked answer (after attempting)
Answer: 50%
1/2 × 100% = (1 × 100 ÷ 2)% = 50%. A grid of 10 equal cells would shade 5.
6 · MATH-5B-C15-L04-Q16
Express 3/8 as a percent and state how many of 48 equal cells would be shaded.
Show worked answer (after attempting)
Answer: 37.5%; shaded cells = 18
3/8 × 100% = (3 × 100 ÷ 8)% = 37.5%. A grid of 48 equal cells would shade 18.
7 · MATH-5B-C15-L04-Q17
A whole has 18 highlighted parts out of 30. Convert this fraction to a percent.
Show worked answer (after attempting)
Answer: 60%
3/5 × 100% = (3 × 100 ÷ 5)% = 60%. A grid of 30 equal cells would shade 18.
8 · MATH-5B-C15-L04-Q18
Explain how 3/4 corresponds to 75% of a whole modeled using 24 equal parts.
Show worked answer (after attempting)
Answer: 75%
3/4 × 100% = (3 × 100 ÷ 4)% = 75%. A grid of 24 equal cells would shade 18.
Challenge and error analysis
1 · MATH-5B-C15-L04-ERR1
The assigned question is: “A whole has 27 highlighted parts out of 36. Convert this fraction to a percent.” A learner wrote: “I treated the fraction from 27 as a proportion of ten parts instead of a whole of 100 percent; I gave 75.1%.” 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: 75%
The attempted reasoning or reported result does not satisfy the specified operation, units or geometric conditions. Correct mathematical result: 75%. Recompute from the given data: 3/4 × 100% = (3 × 100 ÷ 4)% = 75%. A grid of 36 equal cells would shade 27.
2 · MATH-5B-C15-L04-ERR2
The assigned question is: “Explain how 3/4 corresponds to 75% of a whole modeled using 36 equal parts.” A learner wrote: “I treated the fraction from 3 as a proportion of ten parts instead of a whole of 100 percent; I gave 76%.” 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: 75%
The attempted reasoning or reported result does not satisfy the specified operation, units or geometric conditions. Correct mathematical result: 75%. Recompute from the given data: 3/4 × 100% = (3 × 100 ÷ 4)% = 75%. A grid of 36 equal cells would shade 27.
Exit check
Exit · MATH-5B-C15-L04-Q19
Express 1/2 as a percent and state how many of 14 equal cells would be shaded.
Show worked answer (after attempting)
Answer: 50%; shaded cells = 7
1/2 × 100% = (1 × 100 ÷ 2)% = 50%. A grid of 14 equal cells would shade 7.