The ratio of orange juice to cranberry juice is 3 to 2. The total parts of the mixture are 3 + 2 = 5 parts. This means the ratio of orange juice to the total punch is 3 to 5. Statement D correctly expresses this relationship: out of 5 cups of total punch, 3 cups are orange juice.

The ratio of cows to sheep is 36 to 48. To find the simplest form, find the greatest common factor (GCF) of 36 and 48. The GCF is 12. Divide both numbers by 12: 36 ÷ 12 = 3 and 48 ÷ 12 = 4. The simplest ratio is 3 to 4.

First, find the number of boys: 28 total students - 16 girls = 12 boys. The ratio of boys to the total number of students is 12 to 28. To simplify, find the greatest common factor of 12 and 28, which is 4. Divide both numbers by 4: 12 ÷ 4 = 3 and 28 ÷ 4 = 7. The simplified ratio is 3 to 7.

First, find the total number of fruits: 8 apples + 12 bananas + 4 oranges = 24 fruits. The ratio of bananas to the total number of fruits is 12 to 24. To simplify, divide both numbers by their greatest common factor, which is 12. 12 ÷ 12 = 1 and 24 ÷ 12 = 2. The simplified ratio is 1 to 2.

First, find the number of cats: 30 total animals - 18 dogs = 12 cats. The ratio of cats to dogs is 12 to 18. The greatest common factor of 12 and 18 is 6. Simplify the ratio by dividing both numbers by 6: 12 ÷ 6 = 2 and 18 ÷ 6 = 3. The ratio is 2 to 3.

The question provides the number of sides for each shape. A hexagon has 6 sides and a pentagon has 5 sides. The ratio of the number of sides of a hexagon to the number of sides of a pentagon is 6 to 5. This ratio is already in its simplest form because 6 and 5 have no common factors other than 1.

When you encounter ratio problems, you need to carefully identify what groups you're comparing and count each group accurately.

Let's organize the given information: There are 10 rose bushes (4 red, 6 not red) and 15 tulip plants (9 red, 6 not red). You need the ratio of red flowers to non-red flowers.

First, count the red flowers: 4 red roses + 9 red tulips = 13 red flowers total.

Next, count the non-red flowers: 6 non-red roses + 6 non-red tulips = 12 non-red flowers total.

Therefore, the ratio of red flowers to non-red flowers is 13 to 12.

Looking at the wrong answers: Choice A (13 to 25) incorrectly compares red flowers to the total number of plants instead of just the non-red flowers. Choice B (12 to 13) reverses the ratio by putting non-red flowers first instead of red flowers first. Choice C (4 to 9) only compares red roses to red tulips, completely ignoring the non-red flowers that should be in the denominator.

Study tip: In ratio problems, always double-check that you're comparing the right groups in the right order. Write down what each part of your ratio represents before calculating, and make sure your categories don't overlap and account for all items mentioned in the problem.

First, find the total number of books: 10 + 14 + 6 = 30 books. The ratio of books on the first shelf to the total number of books is 10 to 30. To simplify, divide both numbers by their greatest common factor, 10. 10 ÷ 10 = 1 and 30 ÷ 10 = 3. The simplified ratio is 1 to 3.

First, find the number of children wearing hats: 24 children × (1/3) = 8 children. Next, find the number of children not wearing hats: 24 total - 8 with hats = 16 children. The ratio of children not wearing hats to children wearing hats is 16 to 8. To simplify, divide both numbers by their greatest common factor, 8. 16 ÷ 8 = 2 and 8 ÷ 8 = 1. The ratio is 2 to 1.

First, find the time for the credits: 90 total minutes - 60 minutes of story = 30 minutes of credits. The ratio of credit time to total time is 30 to 90. To simplify, divide both numbers by their greatest common factor, 30. 30 ÷ 30 = 1 and 90 ÷ 30 = 3. The simplified ratio is 1 to 3.