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.

Of the 15-year-olds at a karate school, 2 have black belts and 8 have brown belts. Among the 16-year-olds, 1 have black belts and 9 have brown belts. Which age group has a lower ratio of black belts to brown belts

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

( )

While researching universities, Mahtab learns that a typical class at Summerfield Technical University has 18 men and 5 women, and a typical class at Grant County University has 16 men and 6 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

( )

Among the third graders at Weston high School, 19 play kickball during recess and 8 play four square. Among the fourth graders, 57 play kickball and 24 play four square. In which grade is there a lower ratio of kickball players to four-square players

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

( )

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

( )

While researching universities, Mahtab learns that a typical class at Summerfield Technical University has 12 men and 5 women, and a typical class at Grant County University has 10 men and 6 women. Which university has classes with a higher ratio of men to women

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

( )

Among the third graders at Weston high School, 14 play kickball during recess and 7 play four square. Among the fourth graders, 42 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

( )

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

( )

While researching universities, Mahtab learns that a typical class at Summerfield Technical University has 14 men and 7 women, and a typical class at Grant County University has 12 men and 8 women. Which university has classes with a higher ratio of men to women

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

( )

Among the third graders at Weston high School, 14 play kickball during recess and 5 play four square. Among the fourth graders, 42 play kickball and 15 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 fourth grade
3) the third grade

( )

10)

Of the 15-year-olds at a karate school, 4 have black belts and 7 have brown belts. Among the 16-year-olds, 3 have black belts and 8 have brown belts. Which age group has a lower ratio of black belts to brown belts

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

( )

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 2 to 8. Among 16-year-olds, the ratio is 1 to 9.

We want to figure out which ratio is higher:

$\frac{2}{8}$ or $\frac{1}{9}$

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

First write the ratio $\frac{2}{8}$ as a decimal. Then convert the decimal to a percentage.

$\frac{2}{8}$ = 0.25 = 25 %

Do the same thing for $\frac{1}{9}$

$\frac{1}{9}$ = 0.11 = 11 %

Now compare the percentages.

25 % 11 %

11 % is smaller than 25 %

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

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 18 to 5. At Grant County University, it is 16 to 6.

We want to figure out which ratio is higher:

$\frac{18}{5}$ or $\frac{16}{6}$

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

First write the ratio $\frac{18}{5}$ as a decimal. Then convert the decimal to a percentage.

$\frac{18}{5}$ = 3.6000 = 360 %

Do the same thing for $\frac{16}{6}$

$\frac{16}{6}$ = 2.6667 = 266.67 %

Now compare the percentages.

360 % 266.67 %

266.67 % is smaller than 360 %

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

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 19 to 8. In the fourth grade, the ratio is 57 to 24.

We want to figure out which ratio is higher:

$\frac{19}{8}$ or $\frac{57}{24}$

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

First write the ratio $\frac{19}{8}$ as a decimal. Then convert the decimal to a percentage.

$\frac{19}{8}$ = 2.38 = 238 %

Do the same thing for $\frac{57}{24}$

$\frac{57}{24}$ = 2.38 = 238 %

Now compare the percentages.

238 % 238 %

238 % is equal to 238 %

Neither ratio is lower; the ratios are equivalent.

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

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 12 to 5. At Grant County University, it is 10 to 6.

We want to figure out which ratio is higher:

$\frac{12}{5}$ or $\frac{10}{6}$

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

First write the ratio $\frac{12}{5}$ as a decimal. Then convert the decimal to a percentage.

$\frac{12}{5}$ = 2.4000 = 240 %

Do the same thing for $\frac{10}{6}$

$\frac{10}{6}$ = 1.6667 = 166.67 %

Now compare the percentages.

240 % 166.67 %

166.67 % is smaller than 240 %

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

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 14 to 7. In the fourth grade, the ratio is 42 to 21.

We want to figure out which ratio is higher:

$\frac{14}{7}$ or $\frac{42}{21}$

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 $\frac{42}{21}$

$\frac{42}{21}$ = 2.00 = 200 %

Now compare the percentages.

200 % 200 %

200 % is equal to 200 %

Neither ratio is lower; the ratios are equivalent.

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

Answer: 3

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

Answer: 2

SOLUTION 1 :

Solve:

The ratio of men to women in a typical class at Summerfield Technical University is 14 to 7. At Grant County University, it is 12 to 8.

We want to figure out which ratio is higher:

$\frac{14}{7}$ or $\frac{12}{8}$

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.

$\frac{14}{7}$ = 2.0000 = 200 %

Do the same thing for $\frac{12}{8}$

$\frac{12}{8}$ = 1.5000 = 150 %

Now compare the percentages.

200 % 150 %

150 % is smaller than 200 %

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

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

Answer: 1

SOLUTION 1 :

Solve:

In the third grade, the ratio of kickball players to four-square players is 14 to 5. In the fourth grade, the ratio is 42 to 15.

We want to figure out which ratio is higher:

$\frac{14}{5}$ or $\frac{42}{15}$

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

First write the ratio $\frac{14}{5}$ as a decimal. Then convert the decimal to a percentage.

$\frac{14}{5}$ = 2.80 = 280 %

Do the same thing for $\frac{42}{15}$

$\frac{42}{15}$ = 2.80 = 280 %

Now compare the percentages.

280 % 280 %

280 % is equal to 280 %

Neither ratio is lower; the ratios are equivalent.

10)

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

Answer: 1

SOLUTION 1 :

Solve:

Among 15-year-olds, the ratio of black belts to brown belts is 4 to 7. Among 16-year-olds, the ratio is 3 to 8.

We want to figure out which ratio is higher:

$\frac{4}{7}$ or $\frac{3}{8}$

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

First write the ratio $\frac{4}{7}$ as a decimal. Then convert the decimal to a percentage.

$\frac{4}{7}$ = 0.57 = 57 %

Do the same thing for $\frac{3}{8}$

$\frac{3}{8}$ = 0.38 = 38 %

Now compare the percentages.

57 % 38 %

38 % is smaller than 57 %

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