Math Test: Ratio And Proportion Quiz For Grade 7

To simplify a ratio, find the greatest common factor (GCF) of both sides of the ratio and divide both sides by the GCF. The GCF of 6 and 42 is 6. Dividing both sides of 6:42 by 6 gives 1:7.

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.

The ratio 20:45 represents a comparison between two quantities, where the first quantity is 20 units and the second quantity is 45 units. To simplify this ratio, we need to find the greatest common factor (GCF) of 20 and 45, which is 5. Dividing both sides of the ratio by 5 gives us 4:9. This simplified ratio represents the same proportional relationship between the two quantities, but with smaller, more manageable numbers.

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.

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.

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.

The cost of feeding a family of 3 for one week is $90. To find the cost for a family of 5, we first determine the cost per person, which is $90 divided by 3, or $30. Then, we multiply the cost per person by 5 to get the total cost for a family of 5, which is $150.

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.

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.

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.

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.

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.

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.

The given proportion, 3:5 = x:35, states that the ratio of 3 to 5 is equal to the ratio of x to 35. To find the value of x, we can use the property that the product of the means (5 and x) is equal to the product of the extremes (3 and 35). This gives us the equation 5x = 105. Dividing both sides by 5, we get x = 21. Therefore, the value of x that satisfies the proportion is 21.

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.

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.

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.

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.

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.