Explore · MATH-5B-C15-L02-OPEN
A ribbon is 4 m long, and 30% of it is colored. Express the colored proportion as a simplest fraction.
Singapore Math 5B · Original independent course
Expressing Percentages as Fractions
Watch for: Leaving 25/100 irreducible or using the wrong whole.. Explain what the quantities mean before calculating.
Opening task
Prerequisite check
Before instruction · MATH-5B-C15-L02-PREREQ
Express 20% as a fraction in simplest form.
Show worked answer (after attempting)
Answer: 1/5
20/100 simplifies to 1/5.
Understand the idea
Convert percentages to fractions in simplest terms and explain what 100% represents. The essential earlier idea is: Fraction equivalence and Chapter 15 L01.. The model below will always use the actual quantities from the worked problem. Check leaving 25/100 irreducible or using the wrong whole when you explain your answer.
Three worked examples
Worked example 1 · MATH-5B-C15-L02-Q01
A ribbon is 3 m long, and 25% of it is colored. Express the colored proportion as a simplest fraction.
Solution: 1/4
Start with 25/100. Reduce numerator and denominator by their common factor to get 1/4.
Worked example 2 · MATH-5B-C15-L02-Q02
A sign says 40% of 100 seats are filled. Write the fraction of seats.
Solution: 2/5
Start with 40/100. Reduce numerator and denominator by their common factor to get 2/5.
Worked example 3 · MATH-5B-C15-L02-Q03
Explain why 50% equals 1/2 as a simplified fraction for a 100-counter whole.
Solution: 1/2
Start with 50/100. Reduce numerator and denominator by their common factor to get 1/2.
Check understanding
1 · MATH-5B-C15-L02-Q04
A ribbon is 4 m long, and 30% of it is colored. Express the colored proportion as a simplest fraction.
Show worked answer (after attempting)
Answer: 3/10
Start with 30/100. Reduce numerator and denominator by their common factor to get 3/10.
2 · MATH-5B-C15-L02-Q05
A sign says 45% of 200 seats are filled. Write the fraction of seats.
Show worked answer (after attempting)
Answer: 9/20
Start with 45/100. Reduce numerator and denominator by their common factor to get 9/20.
3 · MATH-5B-C15-L02-Q06
Explain why 55% equals 11/20 as a simplified fraction for a 200-counter whole.
Show worked answer (after attempting)
Answer: 11/20
Start with 55/100. Reduce numerator and denominator by their common factor to get 11/20.
Guided practice
1 · MATH-5B-C15-L02-Q07
A ribbon is 5 m long, and 35% of it is colored. Express the colored proportion as a simplest fraction.
Show worked answer (after attempting)
Answer: 7/20
Start with 35/100. Reduce numerator and denominator by their common factor to get 7/20.
2 · MATH-5B-C15-L02-Q08
A sign says 50% of 300 seats are filled. Write the fraction of seats.
Show worked answer (after attempting)
Answer: 1/2
Start with 50/100. Reduce numerator and denominator by their common factor to get 1/2.
3 · MATH-5B-C15-L02-Q09
Explain why 60% equals 3/5 as a simplified fraction for a 300-counter whole.
Show worked answer (after attempting)
Answer: 3/5
Start with 60/100. Reduce numerator and denominator by their common factor to get 3/5.
4 · MATH-5B-C15-L02-Q10
A ribbon is 6 m long, and 40% of it is colored. Express the colored proportion as a simplest fraction.
Show worked answer (after attempting)
Answer: 2/5
Start with 40/100. Reduce numerator and denominator by their common factor to get 2/5.
Independent practice
1 · MATH-5B-C15-L02-Q11
A sign says 55% of 400 seats are filled. Write the fraction of seats.
Show worked answer (after attempting)
Answer: 11/20
Start with 55/100. Reduce numerator and denominator by their common factor to get 11/20.
2 · MATH-5B-C15-L02-Q12
Explain why 65% equals 13/20 as a simplified fraction for a 400-counter whole.
Show worked answer (after attempting)
Answer: 13/20
Start with 65/100. Reduce numerator and denominator by their common factor to get 13/20.
3 · MATH-5B-C15-L02-Q13
A ribbon is 7 m long, and 45% of it is colored. Express the colored proportion as a simplest fraction.
Show worked answer (after attempting)
Answer: 9/20
Start with 45/100. Reduce numerator and denominator by their common factor to get 9/20.
4 · MATH-5B-C15-L02-Q14
A sign says 60% of 500 seats are filled. Write the fraction of seats.
Show worked answer (after attempting)
Answer: 3/5
Start with 60/100. Reduce numerator and denominator by their common factor to get 3/5.
5 · MATH-5B-C15-L02-Q15
Explain why 70% equals 7/10 as a simplified fraction for a 500-counter whole.
Show worked answer (after attempting)
Answer: 7/10
Start with 70/100. Reduce numerator and denominator by their common factor to get 7/10.
6 · MATH-5B-C15-L02-Q16
A ribbon is 8 m long, and 50% of it is colored. Express the colored proportion as a simplest fraction.
Show worked answer (after attempting)
Answer: 1/2
Start with 50/100. Reduce numerator and denominator by their common factor to get 1/2.
7 · MATH-5B-C15-L02-Q17
A sign says 65% of 600 seats are filled. Write the fraction of seats.
Show worked answer (after attempting)
Answer: 13/20
Start with 65/100. Reduce numerator and denominator by their common factor to get 13/20.
8 · MATH-5B-C15-L02-Q18
Explain why 75% equals 3/4 as a simplified fraction for a 600-counter whole.
Show worked answer (after attempting)
Answer: 3/4
Start with 75/100. Reduce numerator and denominator by their common factor to get 3/4.
Challenge and error analysis
1 · MATH-5B-C15-L02-ERR1
The assigned question is: “A sign says 80% of 900 seats are filled. Write the fraction of seats.” A learner wrote: “I reduced only the numerator of the percent fraction involving 80, and wrote 4.1/5.” 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: 4/5
The attempted reasoning or reported result does not satisfy the specified operation, units or geometric conditions. Correct mathematical result: 4/5. Recompute from the given data: Start with 80/100. Reduce numerator and denominator by their common factor to get 4/5.
2 · MATH-5B-C15-L02-ERR2
The assigned question is: “Explain why 90% equals 9/10 as a simplified fraction for a 900-counter whole.” A learner wrote: “I reduced only the numerator of the percent fraction involving 90, and wrote 10/10.” 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: 9/10
The attempted reasoning or reported result does not satisfy the specified operation, units or geometric conditions. Correct mathematical result: 9/10. Recompute from the given data: Start with 90/100. Reduce numerator and denominator by their common factor to get 9/10.
Exit check
Exit · MATH-5B-C15-L02-Q19
A ribbon is 9 m long, and 55% of it is colored. Express the colored proportion as a simplest fraction.
Show worked answer (after attempting)
Answer: 11/20
Start with 55/100. Reduce numerator and denominator by their common factor to get 11/20.