Explore · MATH-5B-C13-L03-OPEN
The ratio cats:dogs is 2:3. If there are 10 cats, how many dogs?
Singapore Math 5B · Original independent course
Finding a Quantity
Watch for: Using total number of parts as the known part count.. Explain what the quantities mean before calculating.
Opening task
Prerequisite check
Before instruction · MATH-5B-C13-L03-PREREQ
In the ratio first:second = 1:2, if the first is 4, find the second.
Show worked answer (after attempting)
Answer: 8
Each part is 4; two parts is 8.
Understand the idea
Find an unknown part or total given a ratio and one known part or total. The essential earlier idea is: Equivalent ratios, 5A multi-step division.. The model below will always use the actual quantities from the worked problem. Check using total number of parts as the known part count when you explain your answer.
Three worked examples
Worked example 1 · MATH-5B-C13-L03-Q01
The ratio cats:dogs is 2:3. If there are 8 cats, how many dogs?
Solution: 12
Each A-part is 8 ÷ 2 = 4. Then B has 3 parts, giving 12.
Worked example 2 · MATH-5B-C13-L03-Q02
Red to blue tiles are 3:4, and the red count is 15. Find the blue count.
Solution: 20
Each A-part is 15 ÷ 3 = 5. Then B has 4 parts, giving 20.
Worked example 3 · MATH-5B-C13-L03-Q03
There are 12 B-counters for a ratio A:B = 5:2. Find A.
Solution: 30
Each B-part is 12 ÷ 2 = 6. A has 5 equal parts, giving 30.
Check understanding
1 · MATH-5B-C13-L03-Q04
The ratio cats:dogs is 2:3. If there are 10 cats, how many dogs?
Show worked answer (after attempting)
Answer: 15
Each A-part is 10 ÷ 2 = 5. Then B has 3 parts, giving 15.
2 · MATH-5B-C13-L03-Q05
Red to blue tiles are 3:4, and the red count is 18. Find the blue count.
Show worked answer (after attempting)
Answer: 24
Each A-part is 18 ÷ 3 = 6. Then B has 4 parts, giving 24.
3 · MATH-5B-C13-L03-Q06
There are 14 B-counters for a ratio A:B = 5:2. Find A.
Show worked answer (after attempting)
Answer: 35
Each B-part is 14 ÷ 2 = 7. A has 5 equal parts, giving 35.
Guided practice
1 · MATH-5B-C13-L03-Q07
The ratio cats:dogs is 2:3. If there are 12 cats, how many dogs?
Show worked answer (after attempting)
Answer: 18
Each A-part is 12 ÷ 2 = 6. Then B has 3 parts, giving 18.
2 · MATH-5B-C13-L03-Q08
Red to blue tiles are 3:4, and the red count is 21. Find the blue count.
Show worked answer (after attempting)
Answer: 28
Each A-part is 21 ÷ 3 = 7. Then B has 4 parts, giving 28.
3 · MATH-5B-C13-L03-Q09
There are 16 B-counters for a ratio A:B = 5:2. Find A.
Show worked answer (after attempting)
Answer: 40
Each B-part is 16 ÷ 2 = 8. A has 5 equal parts, giving 40.
4 · MATH-5B-C13-L03-Q10
The ratio cats:dogs is 2:3. If there are 14 cats, how many dogs?
Show worked answer (after attempting)
Answer: 21
Each A-part is 14 ÷ 2 = 7. Then B has 3 parts, giving 21.
Independent practice
1 · MATH-5B-C13-L03-Q11
Red to blue tiles are 3:4, and the red count is 24. Find the blue count.
Show worked answer (after attempting)
Answer: 32
Each A-part is 24 ÷ 3 = 8. Then B has 4 parts, giving 32.
2 · MATH-5B-C13-L03-Q12
There are 18 B-counters for a ratio A:B = 5:2. Find A.
Show worked answer (after attempting)
Answer: 45
Each B-part is 18 ÷ 2 = 9. A has 5 equal parts, giving 45.
3 · MATH-5B-C13-L03-Q13
The ratio cats:dogs is 2:3. If there are 16 cats, how many dogs?
Show worked answer (after attempting)
Answer: 24
Each A-part is 16 ÷ 2 = 8. Then B has 3 parts, giving 24.
4 · MATH-5B-C13-L03-Q14
Red to blue tiles are 3:4, and the red count is 27. Find the blue count.
Show worked answer (after attempting)
Answer: 36
Each A-part is 27 ÷ 3 = 9. Then B has 4 parts, giving 36.
5 · MATH-5B-C13-L03-Q15
There are 20 B-counters for a ratio A:B = 5:2. Find A.
Show worked answer (after attempting)
Answer: 50
Each B-part is 20 ÷ 2 = 10. A has 5 equal parts, giving 50.
6 · MATH-5B-C13-L03-Q16
The ratio cats:dogs is 2:3. If there are 18 cats, how many dogs?
Show worked answer (after attempting)
Answer: 27
Each A-part is 18 ÷ 2 = 9. Then B has 3 parts, giving 27.
7 · MATH-5B-C13-L03-Q17
Red to blue tiles are 3:4, and the red count is 30. Find the blue count.
Show worked answer (after attempting)
Answer: 40
Each A-part is 30 ÷ 3 = 10. Then B has 4 parts, giving 40.
8 · MATH-5B-C13-L03-Q18
There are 22 B-counters for a ratio A:B = 5:2. Find A.
Show worked answer (after attempting)
Answer: 55
Each B-part is 22 ÷ 2 = 11. A has 5 equal parts, giving 55.
Challenge and error analysis
1 · MATH-5B-C13-L03-ERR1
The assigned question is: “Red to blue tiles are 3:4, and the red count is 39. Find the blue count.” A learner wrote: “39 ÷ 3 = 13.1. I used this intermediate value to finish the assigned problem.” 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: 52
The attempted reasoning or reported result does not satisfy the specified operation, units or geometric conditions. Correct mathematical result: 52. Recompute from the given data: Each A-part is 39 ÷ 3 = 13. Then B has 4 parts, giving 52.
2 · MATH-5B-C13-L03-ERR2
The assigned question is: “There are 28 B-counters for a ratio A:B = 5:2. Find A.” A learner wrote: “28 ÷ 2 = 15. I used this intermediate value to finish the assigned problem.” 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: 70
The attempted reasoning or reported result does not satisfy the specified operation, units or geometric conditions. Correct mathematical result: 70. Recompute from the given data: Each B-part is 28 ÷ 2 = 14. A has 5 equal parts, giving 70.
Exit check
Exit · MATH-5B-C13-L03-Q19
The ratio cats:dogs is 2:3. If there are 20 cats, how many dogs?
Show worked answer (after attempting)
Answer: 30
Each A-part is 20 ÷ 2 = 10. Then B has 3 parts, giving 30.