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, 13 play kickball during recess and 8 play four square. Among the fourth graders, 39 play kickball and 24 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

( )

Of the 15-year-olds at a karate school, 4 have black belts and 8 have brown belts. Among the 16-year-olds, 3 have black belts and 9 have brown belts. Which age group has a lower ratio of black belts to brown belts

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

( )

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

( )

Among the third graders at Weston high School, 17 play kickball during recess and 7 play four square. Among the fourth graders, 34 play kickball and 14 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) 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 20 men and 8 women, and a typical class at Grant County University has 18 men and 9 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

( )

Among the third graders at Weston high School, 20 play kickball during recess and 6 play four square. Among the fourth graders, 60 play kickball and 18 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

( )

Of the 15-year-olds at a karate school, 5 have black belts and 6 have brown belts. Among the 16-year-olds, 4 have black belts and 7 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 15 men and 5 women, and a typical class at Grant County University has 13 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

( )

10)

Among the third graders at Weston high School, 15 play kickball during recess and 7 play four square. Among the fourth graders, 30 play kickball and 14 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

( )

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 13 to 8. In the fourth grade, the ratio is 39 to 24.

We want to figure out which ratio is higher:

$\frac{13}{8}$ or $\frac{39}{24}$

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

First write the ratio $\frac{13}{8}$ as a decimal. Then convert the decimal to a percentage.

$\frac{13}{8}$ = 1.63 = 163 %

Do the same thing for $\frac{39}{24}$

$\frac{39}{24}$ = 1.63 = 163 %

Now compare the percentages.

163 % 163 %

163 % is equal to 163 %

Neither ratio is lower; the ratios are equivalent.

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 8. Among 16-year-olds, the ratio is 3 to 9.

We want to figure out which ratio is higher:

$\frac{4}{8}$ or $\frac{3}{9}$

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

First write the ratio $\frac{4}{8}$ as a decimal. Then convert the decimal to a percentage.

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

Do the same thing for $\frac{3}{9}$

$\frac{3}{9}$ = 0.33 = 33 %

Now compare the percentages.

50 % 33 %

33 % is smaller than 50 %

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 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) 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 17 to 7. In the fourth grade, the ratio is 34 to 14.

We want to figure out which ratio is higher:

$\frac{17}{7}$ or $\frac{34}{14}$

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

First write the ratio $\frac{17}{7}$ as a decimal. Then convert the decimal to a percentage.

$\frac{17}{7}$ = 2.43 = 243 %

Do the same thing for $\frac{34}{14}$

$\frac{34}{14}$ = 2.43 = 243 %

Now compare the percentages.

243 % 243 %

243 % is equal to 243 %

Neither ratio is lower; the ratios are equivalent.

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 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) 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 20 to 8. At Grant County University, it is 18 to 9.

We want to figure out which ratio is higher:

$\frac{20}{8}$ or $\frac{18}{9}$

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

First write the ratio $\frac{20}{8}$ as a decimal. Then convert the decimal to a percentage.

$\frac{20}{8}$ = 2.5000 = 250 %

Do the same thing for $\frac{18}{9}$

$\frac{18}{9}$ = 2.0000 = 200 %

Now compare the percentages.

250 % 200 %

200 % is smaller than 250 %

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 20 to 6. In the fourth grade, the ratio is 60 to 18.

We want to figure out which ratio is higher:

$\frac{20}{6}$ or $\frac{60}{18}$

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

First write the ratio $\frac{20}{6}$ as a decimal. Then convert the decimal to a percentage.

$\frac{20}{6}$ = 3.33 = 333 %

Do the same thing for $\frac{60}{18}$

$\frac{60}{18}$ = 3.33 = 333 %

Now compare the percentages.

333 % 333 %

333 % is equal to 333 %

Neither ratio is lower; the ratios are equivalent.

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 6. Among 16-year-olds, the ratio is 4 to 7.

We want to figure out which ratio is higher:

$\frac{5}{6}$ or $\frac{4}{7}$

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

First write the ratio $\frac{5}{6}$ as a decimal. Then convert the decimal to a percentage.

$\frac{5}{6}$ = 0.83 = 83 %

Do the same thing for $\frac{4}{7}$

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

Now compare the percentages.

83 % 57 %

57 % is smaller than 83 %

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

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

Answer: 3

SOLUTION 1 :

Solve:

The ratio of men to women in a typical class at Summerfield Technical University is 15 to 5. At Grant County University, it is 13 to 6.

We want to figure out which ratio is higher:

$\frac{15}{5}$ or $\frac{13}{6}$

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

First write the ratio $\frac{15}{5}$ as a decimal. Then convert the decimal to a percentage.

$\frac{15}{5}$ = 3.0000 = 300 %

Do the same thing for $\frac{13}{6}$

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

Now compare the percentages.

300 % 216.67 %

216.67 % is smaller than 300 %

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

10)

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 15 to 7. In the fourth grade, the ratio is 30 to 14.

We want to figure out which ratio is higher:

$\frac{15}{7}$ or $\frac{30}{14}$

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

First write the ratio $\frac{15}{7}$ as a decimal. Then convert the decimal to a percentage.

$\frac{15}{7}$ = 2.14 = 214 %

Do the same thing for $\frac{30}{14}$

$\frac{30}{14}$ = 2.14 = 214 %

Now compare the percentages.

214 % 214 %

214 % is equal to 214 %

Neither ratio is lower; the ratios are equivalent.