Chapter 13 Exam

A display contains 5 blue objects and 7 red objects. Which ratio describes blue to total objects?

The assigned question is: “A display contains 5 blue objects and 7 red objects. Which ratio describes blue to total objects?” A learner wrote: “I put the categories in reverse order for the recorded amounts beginning with 5, and wrote 6:12.” Identify a concrete invalid step or assumption. Work out the correct result and explain why it is valid.

An assistant scales 4:9 to 12:12. Explain why that is not a valid uniform scaling.

The assigned question is: “An assistant scales 4:9 to 12:12. Explain why that is not a valid uniform scaling.” A learner wrote: “I changed only one term of the named ratio starting with 4, giving Correct scale is 13:27.” Identify a concrete invalid step or assumption. Work out the correct result and explain why it is valid.

A ratio sign shows A:B = 6:7, but a worker proposes A=24, B=30. Check if it matches.

The assigned question is: “A ratio sign shows A:B = 6:7, but a worker proposes A=24, B=30. Check if it matches.” A learner wrote: “I matched the two ratio quantities using different part sizes for the pair beginning with 6, and obtained Yes; the original statement is correct..” Identify a concrete invalid step or assumption. Work out the correct result and explain why it is valid.

Three groups have ratio 8:9:9. If B holds 27 tokens, how many does C hold?

The assigned question is: “Three groups have ratio 8:9:9. If B holds 27 tokens, how many does C hold?” A learner wrote: “I combined the three-way ratio by changing one occurrence of the middle term independently, giving 28.” Identify a concrete invalid step or assumption. Work out the correct result and explain why it is valid.

An event proposes splitting 54 prizes into 22 and 32 while keeping ratio 7:11. Does that preserve the ratio?

The assigned question is: “An event proposes splitting 54 prizes into 22 and 32 while keeping ratio 7:11. Does that preserve the ratio?” A learner wrote: “I divided the stated total beginning with 54 by one ratio term instead of the sum of the parts, and got Yes; the original statement is correct..” Identify a concrete invalid step or assumption. Work out the correct result and explain why it is valid.