Sasi Math (Revised for 1024)

Scroll:Ratios and proportions >> Compare ratios: word problems >> mcq (4079)

Written Instructions:

For each Multiple Choice Question (MCQ), four options are given. One of them is the correct answer. Make your choice (1,2,3 or 4). Write your answers in the brackets provided..

For each Short Answer Question(SAQ) and Long Answer Question(LAQ), write your answers in the blanks provided.

Leave your answers in the simplest form or correct to two decimal places.

Among the third graders at Weston high School, 14 play kickball during recess and 7 play four square. Among the fourth graders, 28 play kickball and 14 play four square. In which grade is there a lower ratio of kickball players to four-square players

1) neither; the ratios are equivalent
2) the third grade
3) the fourth grade

( )

While researching universities, Mahtab learns that a typical class at Summerfield Technical University has 20 men and 7 women, and a typical class at Grant County University has 18 men and 8 women. Which university has classes with a higher ratio of men to women

1) Grant County University
2) Summerfield Technical University
3) neither; the ratios are equivalent

( )

Of the 15-year-olds at a karate school, 5 have black belts and 9 have brown belts. Among the 16-year-olds, 4 have black belts and 10 have brown belts. Which age group has a lower ratio of black belts to brown belts

1) 15-year-olds
2) 16-year-olds
3) neither; the ratios are equivalent

( )

Among the third graders at Weston high School, 11 play kickball during recess and 6 play four square. Among the fourth graders, 22 play kickball and 12 play four square. In which grade is there a lower ratio of kickball players to four-square players

1) neither; the ratios are equivalent
2) the third grade
3) the fourth grade

( )

While researching universities, Mahtab learns that a typical class at Summerfield Technical University has 13 men and 6 women, and a typical class at Grant County University has 11 men and 7 women. Which university has classes with a higher ratio of men to women

1) neither; the ratios are equivalent
2) Grant County University
3) Summerfield Technical University

( )

Of the 15-year-olds at a karate school, 3 have black belts and 6 have brown belts. Among the 16-year-olds, 2 have black belts and 7 have brown belts. Which age group has a lower ratio of black belts to brown belts

1) 16-year-olds
2) 15-year-olds
3) neither; the ratios are equivalent

( )

Among the third graders at Weston high School, 12 play kickball during recess and 7 play four square. Among the fourth graders, 36 play kickball and 21 play four square. In which grade is there a lower ratio of kickball players to four-square players

1) the fourth grade
2) neither; the ratios are equivalent
3) the third grade

( )

While researching universities, Mahtab learns that a typical class at Summerfield Technical University has 17 men and 8 women, and a typical class at Grant County University has 15 men and 9 women. Which university has classes with a higher ratio of men to women

1) Grant County University
2) neither; the ratios are equivalent
3) Summerfield Technical University

( )

Of the 15-year-olds at a karate school, 5 have black belts and 7 have brown belts. Among the 16-year-olds, 4 have black belts and 8 have brown belts. Which age group has a lower ratio of black belts to brown belts

1) 16-year-olds
2) 15-year-olds
3) neither; the ratios are equivalent

( )

10)

Among the third graders at Weston high School, 16 play kickball during recess and 8 play four square. Among the fourth graders, 32 play kickball and 16 play four square. In which grade is there a lower ratio of kickball players to four-square players

1) the fourth grade
2) neither; the ratios are equivalent
3) the third grade

( )

1) neither; the ratios are equivalent
2) the fourth grade
3) the third grade

Answer: 1

SOLUTION 1 :

Solve:

In the third grade, the ratio of kickball players to four-square players is 14 to 7. In the fourth grade, the ratio is 28 to 14.

We want to figure out which ratio is higher:

$\frac{14}{7}$ or $\frac{28}{14}$

We can compare the ratios more easily if we express them as percentages.

First write the ratio $\frac{14}{7}$ as a decimal. Then convert the decimal to a percentage.

$\frac{14}{7}$ = 2.00 = 200 %

Do the same thing for $\frac{28}{14}$

$\frac{28}{14}$ = 2.00 = 200 %

Now compare the percentages.

200 % 200 %

200 % is equal to 200 %

Neither ratio is lower; the ratios are equivalent.

1) Grant County University
2) neither; the ratios are equivalent
3) Summerfield Technical University

Answer: 3

SOLUTION 1 :

Solve:

The ratio of men to women in a typical class at Summerfield Technical University is 20 to 7. At Grant County University, it is 18 to 8.

We want to figure out which ratio is higher:

$\frac{20}{7}$ or $\frac{18}{8}$

We can compare the ratios more easily if we express them as percentages.

First write the ratio $\frac{20}{7}$ as a decimal. Then convert the decimal to a percentage.

$\frac{20}{7}$ = 2.8571 = 285.71 %

Do the same thing for $\frac{18}{8}$

$\frac{18}{8}$ = 2.2500 = 225 %

Now compare the percentages.

285.71 % 225 %

225 % is smaller than 285.71 %

Summerfield Technical University has classes with a higher ratio of men to women.

1) 15-year-olds
2) 16-year-olds
3) neither; the ratios are equivalent

Answer: 2

SOLUTION 1 :

Solve:

Among 15-year-olds, the ratio of black belts to brown belts is 5 to 9. Among 16-year-olds, the ratio is 4 to 10.

We want to figure out which ratio is higher:

$\frac{5}{9}$ or $\frac{4}{10}$

We can compare the ratios more easily if we express them as percentages.

First write the ratio $\frac{5}{9}$ as a decimal. Then convert the decimal to a percentage.

$\frac{5}{9}$ = 0.56 = 56 %

Do the same thing for $\frac{4}{10}$

$\frac{4}{10}$ = 0.40 = 40 %

Now compare the percentages.

56 % 40 %

40 % is smaller than 56 %

The 16-year-olds have a lower ratio of black belts to brown belts.

1) neither; the ratios are equivalent
2) the fourth grade
3) the third grade

Answer: 1

SOLUTION 1 :

Solve:

In the third grade, the ratio of kickball players to four-square players is 11 to 6. In the fourth grade, the ratio is 22 to 12.

We want to figure out which ratio is higher:

$\frac{11}{6}$ or $\frac{22}{12}$

We can compare the ratios more easily if we express them as percentages.

First write the ratio $\frac{11}{6}$ as a decimal. Then convert the decimal to a percentage.

$\frac{11}{6}$ = 1.83 = 183 %

Do the same thing for $\frac{22}{12}$

$\frac{22}{12}$ = 1.83 = 183 %

Now compare the percentages.

183 % 183 %

183 % is equal to 183 %

Neither ratio is lower; the ratios are equivalent.

1) Summerfield Technical University
2) neither; the ratios are equivalent
3) Grant County University

Answer: 1

SOLUTION 1 :

Solve:

The ratio of men to women in a typical class at Summerfield Technical University is 13 to 6. At Grant County University, it is 11 to 7.

We want to figure out which ratio is higher:

$\frac{13}{6}$ or $\frac{11}{7}$

We can compare the ratios more easily if we express them as percentages.

First write the ratio $\frac{13}{6}$ as a decimal. Then convert the decimal to a percentage.

$\frac{13}{6}$ = 2.1667 = 216.67 %

Do the same thing for $\frac{11}{7}$

$\frac{11}{7}$ = 1.5714 = 157.14 %

Now compare the percentages.

216.67 % 157.14 %

157.14 % is smaller than 216.67 %

Summerfield Technical University has classes with a higher ratio of men to women.

1) neither; the ratios are equivalent
2) 15-year-olds
3) 16-year-olds

Answer: 3

SOLUTION 1 :

Solve:

Among 15-year-olds, the ratio of black belts to brown belts is 3 to 6. Among 16-year-olds, the ratio is 2 to 7.

We want to figure out which ratio is higher:

$\frac{3}{6}$ or $\frac{2}{7}$

We can compare the ratios more easily if we express them as percentages.

First write the ratio $\frac{3}{6}$ as a decimal. Then convert the decimal to a percentage.

$\frac{3}{6}$ = 0.50 = 50 %

Do the same thing for $\frac{2}{7}$

$\frac{2}{7}$ = 0.29 = 29 %

Now compare the percentages.

50 % 29 %

29 % is smaller than 50 %

The 16-year-olds have a lower ratio of black belts to brown belts.

1) the third grade
2) the fourth grade
3) neither; the ratios are equivalent

Answer: 3

SOLUTION 1 :

Solve:

In the third grade, the ratio of kickball players to four-square players is 12 to 7. In the fourth grade, the ratio is 36 to 21.

We want to figure out which ratio is higher:

$\frac{12}{7}$ or $\frac{36}{21}$

We can compare the ratios more easily if we express them as percentages.

First write the ratio $\frac{12}{7}$ as a decimal. Then convert the decimal to a percentage.

$\frac{12}{7}$ = 1.71 = 171 %

Do the same thing for $\frac{36}{21}$

$\frac{36}{21}$ = 1.71 = 171 %

Now compare the percentages.

171 % 171 %

171 % is equal to 171 %

Neither ratio is lower; the ratios are equivalent.

1) neither; the ratios are equivalent
2) Summerfield Technical University
3) Grant County University

Answer: 2

SOLUTION 1 :

Solve:

The ratio of men to women in a typical class at Summerfield Technical University is 17 to 8. At Grant County University, it is 15 to 9.

We want to figure out which ratio is higher:

$\frac{17}{8}$ or $\frac{15}{9}$

We can compare the ratios more easily if we express them as percentages.

First write the ratio $\frac{17}{8}$ as a decimal. Then convert the decimal to a percentage.

$\frac{17}{8}$ = 2.1250 = 212.5 %

Do the same thing for $\frac{15}{9}$

$\frac{15}{9}$ = 1.6667 = 166.67 %

Now compare the percentages.

212.5 % 166.67 %

166.67 % is smaller than 212.5 %

Summerfield Technical University has classes with a higher ratio of men to women.

1) neither; the ratios are equivalent
2) 15-year-olds
3) 16-year-olds

Answer: 3

SOLUTION 1 :

Solve:

Among 15-year-olds, the ratio of black belts to brown belts is 5 to 7. Among 16-year-olds, the ratio is 4 to 8.

We want to figure out which ratio is higher:

$\frac{5}{7}$ or $\frac{4}{8}$

We can compare the ratios more easily if we express them as percentages.

First write the ratio $\frac{5}{7}$ as a decimal. Then convert the decimal to a percentage.

$\frac{5}{7}$ = 0.71 = 71 %

Do the same thing for $\frac{4}{8}$

$\frac{4}{8}$ = 0.50 = 50 %

Now compare the percentages.

71 % 50 %

50 % is smaller than 71 %

The 16-year-olds have a lower ratio of black belts to brown belts.

10)

1) the third grade
2) neither; the ratios are equivalent
3) the fourth grade

Answer: 2

SOLUTION 1 :

Solve:

In the third grade, the ratio of kickball players to four-square players is 16 to 8. In the fourth grade, the ratio is 32 to 16.

We want to figure out which ratio is higher:

$\frac{16}{8}$ or $\frac{32}{16}$

We can compare the ratios more easily if we express them as percentages.

First write the ratio $\frac{16}{8}$ as a decimal. Then convert the decimal to a percentage.

$\frac{16}{8}$ = 2.00 = 200 %

Do the same thing for $\frac{32}{16}$

$\frac{32}{16}$ = 2.00 = 200 %

Now compare the percentages.

200 % 200 %

200 % is equal to 200 %

Neither ratio is lower; the ratios are equivalent.