Question 1

A ratio is the result of comparing two quantities to determine how much larger one is than the other.

Accepted Answer

A ratio compares two quantities to show their relative sizes, not necessarily how much larger one is than the other. It can express how many times one number contains another or the proportion between them, without implying a comparison of magnitude in terms of "larger" or "smaller."

Question 2

A ratio is the result of comparing two quantities to determine how many times as large one is compared with the other. Using this information, answer the questions below. If enough information is not provided to determine the answer, respond "impossible to determine."
At Riverdale Middle School, 1/8 of the students are in the band. Two out of every three students in the band are girls.
A) The number of boys in the band is _____ times the number of girls in the band.
B) What fraction of the students who play in the band are boys?
C) What fraction of the students at Riverdale are boys who play in the band?
D) The number of girls in the band is _____ times the number of students in the school.
E) What is the ratio of girls who do not play in the band to the boys who do not play in the band?

Accepted Answer

(A diagram may be helpful for parts C, D, and E.)
A) 1/2 B) 1/3 C) 1/24 D) 1/12 (or 2/24) E) impossible to determine

Question 3

A ratio is the result of comparing two quantities to determine how many times as large one is compared with the other. Using this information, answer the questions below. If enough information is not provided to determine the answer, respond "impossible to determine."
Five of every six students interviewed favored a change in library hours.
A) Among those interviewed, what is the ratio of those who favor a change to those who do not favor a change?
B) Among those interviewed, there are _____ times as many students who favor a change as there are students who do not favor a change.
C) Among those interviewed, there are _____ times as many students who do not favor a change as there are students who do favor a change.
D) What fraction of the students interviewed favor a change in the library hours?

Accepted Answer

A) 5:1 B) 5 C) 1/5 D) 5/6

Question 4

A ratio is the result of comparing two quantities to determine how many times as large one is compared with the other. Using this information, answer the questions below. If enough information is not provided to determine the answer, respond "impossible to determine."
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According to a U.S. News/CNN poll, 3 out of 10 people went away on vacation in August.
A) What is the ratio of those who went away on vacation in August to those who didn't?
B) What percent of people did not go away on vacation in August?
C) The number of people who did not go on vacation is _____ times the number who did.

Accepted Answer

The answer of A ratio is the result of comparing...

Question 5

A ratio is the result of comparing two quantities to determine how many times as large one is compared with the other. Using this information, answer the questions below. If enough information is not provided to determine the answer, respond "impossible to determine."
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Maxine polled her entire class concerning the date for the next test. Twelve people preferred that the test be given on Wednesday. Twenty-eight voted to have the test on Friday.
A) What fraction of the class wanted the test on Wednesday?
B) What is the ratio of those who prefer Wednesday to Friday?
C) Those who want the test on Friday are how many times as many as those who prefer the test on Wednesday?

Accepted Answer

The answer of A ratio is the result of comparing...

Question 6

For the situation below, answer the questions and fill in the blanks. If you cannot answer a question, explain why. If the question asks for an explanation, give one. If the question instructs you to draw a relevant diagram, be sure to label it. If enough information is not provided to determine the answer, respond "impossible to determine."
Ms. Collins's class has 15 girls and 18 boys. Twenty-five of the children have pets. Twenty of the children have dogs.
A) The ratio of boys to girls is _____.
B) The girls make up what fractional part of the class?
C) The number of boys is _____ times the number of girls.
D) The number of girls is _____ times the number of boys.
E) The ratio of the number of children who have pets to the number of children who do not have pets is _____.
F) The number of children who have dogs is what fractional part of the number of children who have pets?
G) Of the children who have pets, the number of children who do not have dogs is what fractional part of the number of children who have dogs? Draw a relevant diagram and label it.
H) The number of girls who have dogs is _____.
I) If eight of the children have cats, is this inconsistent with the information already given? Explain.

Accepted Answer

The answer of For the situation below, answer the questions...

Question 7

Two landscapers mowed the lawn of a wealthy family. When they finished, landscaper A had mowed only 3/7 as much as the more experienced landscaper B mowed.  
A) Mark on the drawing of the lawn to show how the mowing might have been done.
B) A's part is _____ times as much as B's part.
C) A's part is what part of the lawn?
D) What is the ratio of A's part to B's part?
E) If they are paid $150 for mowing the lawn, what would be a fair split of the $150?

Accepted Answer

The answer of Two landscapers mowed the lawn of a...

Question 8

If town A had 12,000 more people than it currently does, its population would be $1 \frac { 2 } { 3 }$ 
times as big as town B is now. Town B has 45,000 people currently. What is the current population of town A?

Accepted Answer

The answer of If town A had 12,000 more people...

Question 9

Alan and Bob started mowing a rectangular lawn. After mowing 3/4 of the whole lawn, they got tired and stopped. When they stopped, Alan had mowed 2/7 as much as Bob had mowed.
A) Mark the diagram of the lawn below to show how much of the lawn each boy mowed. Label the parts with each boy's initial to indicate clearly the parts mowed by each boy.
B) The area of lawn that Bob mowed is _____ times as large as the area that Alan mowed.
C) Alan mowed _____ of the total lawn area.
D) The ratio of the area of lawn Bob mowed to the area Alan mowed is _____.
E) Together, they were paid $18 for the work they did. How much money did each boy get if they were paid proportionally to the amount they worked?

Accepted Answer

The answer of Alan and Bob started mowing a rectangular...

Question 10

Tim worked 30 hours last week, which was 5/2 times as many hours as Robert worked.
A) How many hours did Robert work?
B) Who worked more hours?
C) Which type of comparison does the question in part B address, additive or multiplicative?

Accepted Answer

The answer of Tim worked 30 hours last week, which...

Question 11

Below is a diagram of a candy bar that is being shared between two people.  
A) Cut the bar into two parts, so that part A is 3/4 of part
B) Part B is _____ times as large as part
C) Part B is how much of the bar?
D) What is the ratio of part B to part A?

Accepted Answer

The answer of Below is a diagram of a candy...

Question 12

A) Cut the rectangle into two regions, A and B, so that A is 3/2 as large as B.
B) What fraction of the whole rectangle is A?

Accepted Answer

The answer of A) Cut the rectangle into two regions,...

Question 13

Four-fifths of an amount is $20. How many dollars is the full amount?

Accepted Answer

The answer of Four-fifths of an amount is $20. How...

Question 14

Pat and Ron split a cake. Pat's share is 2/3 as large as Ron's share.  
A) Sketch fairly accurately on the "cake" to show Pat's and Ron's shares. Label them P and R.
B) Ron's share is _____ times as large as Pat's share.
C) Pat's share is what fractional part of the whole cake?
D) What is the ratio of Ron's share to Pat's share?

Accepted Answer

The answer of Pat and Ron split a cake. Pat's...

Question 15

John baked a cake for his son's birthday party. At the party, 2/7 as much was left over as was eaten. (A diagram may be helpful.)
A) The remaining portion is what fractional part of the whole cake?
B) What is the ratio of the amount of cake eaten to the whole cake?

Accepted Answer

The answer of John baked a cake for his son's...

Question 16

Two painters paint a wall from opposite ends. When they finish, painter P has painted only 2/3 as much as the more experienced painter Q.

A) Mark on the drawing of the wall to show how the painting might have been done.
B) Painter Q's part is _____ times as much as painter P's part.
C) Painter Q's part is what part of the wall?
D) What is the ratio of painter P's part to painter Q's part?
E) If they are paid $100 for painting the wall, what would be a fair split of the $100?

Accepted Answer

The answer of Two painters paint a wall from opposite...

Question 17

Consider the region below as a pizza that is being shared by two people.  
A) Divide the pizza into two parts so that part A is 3/5 of part
B) Part A is how much of the pizza?
C) What is the ratio of part B to part A?

Accepted Answer

The answer of Consider the region below as a pizza...

Question 18

Nerita and Olivia type at the same speed. One day, Olivia starts later, and when she has typed 100 words, Nerita has typed 600 words. When Olivia has typed 500 words, how many words has Nerita typed?

Accepted Answer

The answer of Nerita and Olivia type at the same...

Question 19

Pete can type 80 words in the same time that Ralph can type 50 words. If they type at those rates for an extended period of time, when Ralph has typed 4000 words, how many words has Pete typed?

Accepted Answer

The answer of Pete can type 80 words in the...

Quiz 8: Multiplicative Comparisons and Multiplicative Reasoning

A ratio is the result of comparing two quantities to determine how much larger one is than the other.

If town A had 12,000 more people than it currently does, its population would be $1 \frac { 2 } { 3 }$ times as big as town B is now. Town B has 45,000 people currently. What is the current population of town A?

Tim worked 30 hours last week, which was 5/2 times as many hours as Robert worked. A) How many hours did Robert work? B) Who worked more hours? C) Which type of comparison does the question in part B address, additive or multiplicative?

Below is a diagram of a candy bar that is being shared between two people. A) Cut the bar into two parts, so that part A is 3/4 of part B) Part B is _____ times as large as part C) Part B is how much of the bar? D) What is the ratio of part B to part A?

A) Cut the rectangle into two regions, A and B, so that A is 3/2 as large as B. B) What fraction of the whole rectangle is A? $A) Cut the rectangle into two regions, A and B, so that A is 3/2 as large as B. B) What fraction of the whole rectangle is A?$

Four-fifths of an amount is $20. How many dollars is the full amount?

John baked a cake for his son's birthday party. At the party, 2/7 as much was left over as was eaten. (A diagram may be helpful.) A) The remaining portion is what fractional part of the whole cake? B) What is the ratio of the amount of cake eaten to the whole cake?

Consider the region below as a pizza that is being shared by two people. A) Divide the pizza into two parts so that part A is 3/5 of part B) Part A is how much of the pizza? C) What is the ratio of part B to part A?

Nerita and Olivia type at the same speed. One day, Olivia starts later, and when she has typed 100 words, Nerita has typed 600 words. When Olivia has typed 500 words, how many words has Nerita typed?

Pete can type 80 words in the same time that Ralph can type 50 words. If they type at those rates for an extended period of time, when Ralph has typed 4000 words, how many words has Pete typed?

Quiz 8: Multiplicative Comparisons and Multiplicative Reasoning

A ratio is the result of comparing two quantities to determine how much larger one is than the other.

If town A had 12,000 more people than it currently does, its population would be 1231 \frac { 2 } { 3 }132​ times as big as town B is now. Town B has 45,000 people currently. What is the current population of town A?

Tim worked 30 hours last week, which was 5/2 times as many hours as Robert worked. A) How many hours did Robert work? B) Who worked more hours? C) Which type of comparison does the question in part B address, additive or multiplicative?

Below is a diagram of a candy bar that is being shared between two people. A) Cut the bar into two parts, so that part A is 3/4 of part B) Part B is _____ times as large as part C) Part B is how much of the bar? D) What is the ratio of part B to part A?

A) Cut the rectangle into two regions, A and B, so that A is 3/2 as large as B. B) What fraction of the whole rectangle is A?

Four-fifths of an amount is $20. How many dollars is the full amount?

John baked a cake for his son's birthday party. At the party, 2/7 as much was left over as was eaten. (A diagram may be helpful.) A) The remaining portion is what fractional part of the whole cake? B) What is the ratio of the amount of cake eaten to the whole cake?

Consider the region below as a pizza that is being shared by two people. A) Divide the pizza into two parts so that part A is 3/5 of part B) Part A is how much of the pizza? C) What is the ratio of part B to part A?

Nerita and Olivia type at the same speed. One day, Olivia starts later, and when she has typed 100 words, Nerita has typed 600 words. When Olivia has typed 500 words, how many words has Nerita typed?

Pete can type 80 words in the same time that Ralph can type 50 words. If they type at those rates for an extended period of time, when Ralph has typed 4000 words, how many words has Pete typed?

If town A had 12,000 more people than it currently does, its population would be $1 \frac { 2 } { 3 }$ times as big as town B is now. Town B has 45,000 people currently. What is the current population of town A?

A) Cut the rectangle into two regions, A and B, so that A is 3/2 as large as B. B) What fraction of the whole rectangle is A? $A) Cut the rectangle into two regions, A and B, so that A is 3/2 as large as B. B) What fraction of the whole rectangle is A?$