Ratio And Proportion - Grade 7

Explanation
The given ratios 8 to 15, 15:8, and 8:15 are all equivalent and represent the same ratio. However, the ratio 15:8 is different from the others as it is the inverse or reciprocal of the other ratios. In the other ratios, the numerator is 8 and the denominator is 15, whereas in the ratio 15:8, the numerator is 15 and the denominator is 8.

Explanation
The ratio 21 to 28 is equal to the ratio 15 to 20 because both ratios can be simplified to 3 to 4. To simplify the ratio 21 to 28, we divide both numbers by the greatest common divisor, which is 7. This gives us the simplified ratio of 3 to 4. Similarly, when we simplify the ratio 15 to 20, we also divide both numbers by the greatest common divisor, which is 5. This also gives us the simplified ratio of 3 to 4. Therefore, the ratio 21 to 28 is equal to the ratio 15 to 20.

Explanation
The ratio 8:23 compares the number of cats to the total number of animals in the pet store. The ratio tells us that for every 8 cats, there are 23 animals in total, which includes cats, dogs, and rabbits.

Explanation
In the word BALLOONS, there are 3 vowels (A, O, O) and 5 consonants (B, L, L, N, S). The ratio of vowels to consonants can be expressed as 3/5.

Explanation
The ratio of red marbles to green marbles is 7:5. This is because there are 35 red marbles and 25 green marbles. To simplify the ratio, we divide both numbers by their greatest common divisor, which is 5. Dividing 35 by 5 gives us 7, and dividing 25 by 5 gives us 5. Therefore, the simplest form of the ratio is 7:5.

Explanation
The cost to feed a family of 3 for one week is $90. To find the cost to feed a family of 5 for one week, we can assume that the cost increases proportionally with the number of family members. Therefore, we can set up a proportion: 3/90 = 5/x, where x represents the cost to feed a family of 5 for one week. Cross-multiplying, we get 3x = 450, and dividing both sides by 3, we find that x = 150. Therefore, it will cost $150.00 to feed a family of 5 for one week.

Explanation
The given ratio 6:42 can be simplified by dividing both numbers by their greatest common divisor, which is 6. Dividing 6 by 6 gives us 1, and dividing 42 by 6 gives us 7. Therefore, the simplified ratio is 1:7.

Explanation
To simplify the ratio 20:45, we need to find the greatest common divisor (GCD) of the two numbers and divide both numbers by it. The GCD of 20 and 45 is 5. Dividing both numbers by 5 gives us 4 and 9. Therefore, the simplified ratio is 4:9.

Explanation
To find out how much gas will be needed to travel 260 miles, we can set up a proportion using the given information. We know that the car can travel 300 miles on 30 gallons of gas. So, we can set up the proportion: 300 miles / 30 gallons = 260 miles / x gallons. Cross multiplying, we get 300x = 30 * 260. Solving for x, we get x = (30 * 260) / 300 = 26 gallons. Therefore, the car will need 26 gallons of gas to go 260 miles.

Explanation
Marlo can run 2 miles in 15 minutes. To find out how many miles Marlo can run in 60 minutes, we can set up a proportion. Since 15 minutes is to 2 miles, then 60 minutes would be to x miles. Cross-multiplying, we get 15x = 120. Dividing both sides by 15, we find that x = 8. Therefore, Marlo can run 8 miles in 60 minutes.

Explanation
Ratios can compare parts to a whole, such as the ratio of the number of boys to the total number of students in a class. They can also compare a whole to a part, such as the ratio of the total revenue to the revenue generated by a specific product. Additionally, ratios can compare part to a part, for example, the ratio of the number of red cars to the number of blue cars in a parking lot. Therefore, all of the given options are valid explanations of what ratios can compare.

Explanation
The ratio of monkeys to total animals can be found by dividing the number of monkeys (3) by the total number of animals (4 lions + 8 parrots + 3 monkeys = 15 animals). So, the ratio of monkeys to total animals is 3/15.

Explanation
The ratio 5/4 is in proportion to 20:16 because when we simplify the ratio 20:16, we get 5:4. This means that every 5 parts of the first ratio corresponds to 4 parts of the second ratio. Therefore, the ratio 5/4 is in proportion to 20:16.

Explanation
The given answer is true because 5 is equivalent to 35 when multiplied by 7, and 4 is equivalent to 28 when multiplied by 7 as well. Therefore, the ratio of 5 to 4 is the same as the ratio of 35 to 28, making them proportional.

Explanation
The statement "4/3 = 24/30" is false. To determine if two fractions are equal, we need to find their simplest form. Simplifying 4/3 gives us 4/3, while simplifying 24/30 gives us 4/5. Since 4/3 and 4/5 are not equal, the statement is false.

Explanation
To find the distance Jack drove, we need to multiply his speed (50 miles per hour) by the time he traveled (4 1/2 hours). To convert 4 1/2 hours to a mixed number, we multiply the whole number (4) by the denominator (2) and add the numerator (1), which gives us 9/2 hours. Multiplying 50 miles per hour by 9/2 hours gives us 450/2 miles, which simplifies to 225 miles. Therefore, Jack drove 225 miles.

Explanation
The ratio compares the number of people who voted (210) to the number of possible voters (1260). To simplify the ratio, we divide both numbers by their greatest common divisor, which is 210. This gives us a simplified ratio of 1/6, meaning that for every 1 person who voted, there were 6 possible voters.

Explanation
To find the ratio of each type of sock to the total number of pairs, we first need to determine the total number of pairs of socks Derrick has:

Total pairs = 14 (white) + 22 (navy blue) = 36 pairs

Now, we'll determine the ratio for each type:

1. White socks:
14 pairs of white socks to 36 total pairs = 14:36
When reduced (by dividing each by 2), the ratio becomes 7:18.

2. Navy blue socks:
22 pairs of navy blue socks to 36 total pairs = 22:36
When reduced (by dividing each by 2), the ratio becomes 11:18.

So, the ratio of white socks to the total number of pairs is 7:18, and the ratio of navy blue socks to the total number of pairs is 11:18.

Explanation
If Nick makes 8 baskets for every 12 shots, you can set up a proportion to find out how many baskets he would make if he took 60 shots:

(8 baskets / 12 shots) = (x baskets / 60 shots)

Now, cross-multiply and solve for x:

8 * 60 = 12 * x

480 = 12 * x

Now, divide both sides by 12 to isolate x:

x = 480 / 12

x = 40

Nick would make 40 baskets if he took 60 shots.