Kaplan Nursing Entrance Practice Exam

How is "nine times the difference of a number and 10" expressed mathematically?

1. 9a + 10

2. 9(a - 10)

3. 10 - 9a

4. (a - 10)9

The correct answer is: 9(a - 10)

The statement "nine times the difference of a number and 10" can be broken down into its components. First, we identify "the difference of a number and 10," which is expressed mathematically as \( a - 10 \), where \( a \) represents the number. Next, the phrase "nine times" indicates that we need to multiply this difference, \( a - 10 \), by 9. Thus, when we combine these parts, we have \( 9 \times (a - 10) \). This corresponds perfectly to the expression \( 9(a - 10) \). It shows that the entire difference \( (a - 10) \) is being multiplied by 9, confirming that this formulation accurately captures the original statement. The other choices fail to represent the situation correctly; for instance, \( 9a + 10 \) suggests an addition rather than a difference being multiplied, while \( 10 - 9a \) incorrectly rearranges and misinterprets the situation. Lastly, \( (a - 10)9 \) is mathematically equivalent to \( 9(a - 10) \) but is not in the conventional form typically preferred for clarity in