Ratios And Proportions Math 6

1. There are 12 trucks and 5 cars. What is the ratio of trucks to cars?

5:12

12:5

1/2

The ratio of trucks to cars is 12:5 because there are 12 trucks and 5 cars.

Explanation

The ratio of trucks to cars is 12:5 because there are 12 trucks and 5 cars.

2. Which of the following ratios is equivalent to 3/5?

6/7

9/15

9/8

The ratio 3/5 is equivalent to the ratio 9/15 because both ratios simplify to 3/5 when divided by their greatest common divisor, which is 3.

Explanation

The ratio 3/5 is equivalent to the ratio 9/15 because both ratios simplify to 3/5 when divided by their greatest common divisor, which is 3.

3. There are 5 red cars, 6 blue cars, 8 silver cars, and 4 black cars. What is the ratio of blue cars to black cars?

6/8

6:2

6:4

The ratio of blue cars to black cars is 6:4. This means that for every 6 blue cars, there are 4 black cars.

Explanation

The ratio of blue cars to black cars is 6:4. This means that for every 6 blue cars, there are 4 black cars.

4. There are: 12 trucks 5 cars 16 vans 3 monkeys 4 penguins 8 parrots
What is the ratio of vehicles (all motorized machines for transportation) to total animals?

33 to 15

12 to 15

33 to 3

The ratio of vehicles to total animals can be calculated by adding up the number of vehicles (12 trucks, 5 cars, and 16 vans) and dividing it by the total number of animals (3 monkeys, 4 penguins, and 8 parrots). This gives us a ratio of 33 to 15.

Explanation

The ratio of vehicles to total animals can be calculated by adding up the number of vehicles (12 trucks, 5 cars, and 16 vans) and dividing it by the total number of animals (3 monkeys, 4 penguins, and 8 parrots). This gives us a ratio of 33 to 15.

5. Are the following ratios equivalent? 2:3 and 6:9

Remember, you need to rewrite these ratios in fraction form to solve this problem.

Yes

No

The given ratios 2:3 and 6:9 are equivalent because when we rewrite them in fraction form, we get 2/3 and 6/9 respectively. By simplifying the fraction 6/9, we can see that it is equal to 2/3. Therefore, the ratios are equivalent.

Explanation

The given ratios 2:3 and 6:9 are equivalent because when we rewrite them in fraction form, we get 2/3 and 6/9 respectively. By simplifying the fraction 6/9, we can see that it is equal to 2/3. Therefore, the ratios are equivalent.

6. Which of the following ratios is equivalent to 8/9?

22/27

24/27

16/17

The ratio 8/9 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 1. Therefore, the simplified ratio is 8/9. The ratio 24/27 can also be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 3. This results in the simplified ratio of 8/9. Thus, the ratio 24/27 is equivalent to 8/9.

Explanation

The ratio 8/9 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 1. Therefore, the simplified ratio is 8/9. The ratio 24/27 can also be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 3. This results in the simplified ratio of 8/9. Thus, the ratio 24/27 is equivalent to 8/9.

7.

Find the value of n in this proportion.

300

20

150

In a proportion, the two ratios are equal. In this case, the ratio of 300 to 20 is equal to the ratio of 150 to n. To find the value of n, we can set up the equation 300/20 = 150/n. Cross multiplying, we get 300n = 20 * 150. Dividing both sides by 300, we find that n = 20.

Explanation

In a proportion, the two ratios are equal. In this case, the ratio of 300 to 20 is equal to the ratio of 150 to n. To find the value of n, we can set up the equation 300/20 = 150/n. Cross multiplying, we get 300n = 20 * 150. Dividing both sides by 300, we find that n = 20.

8. At the local zoo, there are 4 penguins, 8 parrots, and 3 monkeys. What is the ratio of monkeys to total animals?

3/15

3/4

1/4

The correct ratio of monkeys to total animals is 3/15. To calculate this ratio, we need to determine the total number of animals and then divide the number of monkeys by the total.

Total animals = 4 penguins + 8 parrots + 3 monkeys = 15 animals

Monkeys / Total animals = 3 / 15

So, the ratio of monkeys to total animals is 3/15, which can also be simplified to 1/5. This means that for every 1 monkey, there are 5 animals in total.

Explanation

The correct ratio of monkeys to total animals is 3/15. To calculate this ratio, we need to determine the total number of animals and then divide the number of monkeys by the total.

Total animals = 4 penguins + 8 parrots + 3 monkeys = 15 animals

Monkeys / Total animals = 3 / 15

So, the ratio of monkeys to total animals is 3/15, which can also be simplified to 1/5. This means that for every 1 monkey, there are 5 animals in total.

9. Find the value of n in this proportion.

3

36

48

In this proportion, the value of n can be found by comparing the ratios of the numbers. The ratio between 3 and 36 is the same as the ratio between 36 and 48. By setting up the proportion 3/36 = 36/48, we can cross multiply and solve for n. Multiplying 3 by 48 gives us 144, and multiplying 36 by n gives us 36n. Setting these equal to each other, we get 144 = 36n. Dividing both sides by 36, we find that n is equal to 4. Therefore, the value of n in this proportion is 48.

Explanation

In this proportion, the value of n can be found by comparing the ratios of the numbers. The ratio between 3 and 36 is the same as the ratio between 36 and 48. By setting up the proportion 3/36 = 36/48, we can cross multiply and solve for n. Multiplying 3 by 48 gives us 144, and multiplying 36 by n gives us 36n. Setting these equal to each other, we get 144 = 36n. Dividing both sides by 36, we find that n is equal to 4. Therefore, the value of n in this proportion is 48.

10. Reduce the following ratio to lowest terms 6/12.

3/4

1/2

1/4

The given ratio 6/12 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 6. When we simplify, we get the ratio 1/2. This means that the fraction 6/12 is equivalent to 1/2.

Explanation

The given ratio 6/12 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 6. When we simplify, we get the ratio 1/2. This means that the fraction 6/12 is equivalent to 1/2.

11. Which of the following statements is true regarding equivalent ratios.

Equivalent ratios always have equal cross products.

Equivalent ratios always have different cross products.

Equivalent ratios are ratios that represent the same relationship between two quantities. When two ratios are equivalent, their cross products, which are obtained by multiplying the numerator of one ratio by the denominator of the other ratio, are always equal. This is because the cross products represent the same value in both ratios, ensuring that the ratios are equivalent. Therefore, the statement "Equivalent ratios always have equal cross products" is true.

Explanation

Equivalent ratios are ratios that represent the same relationship between two quantities. When two ratios are equivalent, their cross products, which are obtained by multiplying the numerator of one ratio by the denominator of the other ratio, are always equal. This is because the cross products represent the same value in both ratios, ensuring that the ratios are equivalent. Therefore, the statement "Equivalent ratios always have equal cross products" is true.