Question

PE teachers need volleyballs and basketballs for practice. The ratio of volleyballs to basketballs is 9:12. Select all the statements that are correct about the balls.

A.The ratio of basketballs to volleyballs is 4:3.
B.The ratio of basketballs to volleyballs is 12:9.
C.There are always 3 fewer volleyballs
D.The ratio of volleyballs to basketballs is 18:24.

Answer 1

The correct statements about the ratio of volleyballs to basketballs are statements A (the ratio is 4:3), B (it is 12:9), and D (it is 18:24), which are different ways of expressing the same ratio.

Step-by-step explanation:

The question involves understanding the concept of a ratio in mathematics. A ratio compares the quantities of two different types of items. Here, we are looking at the ratio of volleyballs to basketballs, which is given as 9:12. To answer the question, we'll examine the given statements one by one.

1. The ratio of basketballs to volleyballs can be found by inverting the given ratio, resulting in 12:9, which simplifies to 4:3. So, statement A is correct.
2. Statement B simply restates the given ratio in reverse order, so it is also correct.
3. Statement C suggests a fixed difference in the number of balls, which is incorrect as the ratio only shows a relative comparison, not a fixed difference. The actual numbers could be any multiples of 9 and 12, and the difference does not have to be 3.
4. Lastly, statement D is another way of expressing the given ratio (9:12), just scaled up by a factor of 2. So, it is equivalent to the given ratio and is therefore correct.

Therefore, the correct statements about the ratio of volleyballs to basketballs are A, B, and D.