Question

Which expression correctly represents “nine less than the quotient of a number and four, increased by three”?
StartFraction n Over 4 EndFraction minus 9 + 3
StartFraction 4 Over n EndFraction minus 9 + 3
9 minus StartFraction n Over 4 EndFraction + 3
9 minus StartFraction 4 Over n EndFraction + 3

Answer 1

To translate the phrase “nine less than the quotient of a number and four, increased by three” into a mathematical expression, we can break it down step by step:

1. "the quotient of a number and four": This is represented as \( \frac{n}{4} \).
2. "nine less than the quotient of a number and four": This means we subtract 9 from the quotient, making it \( \frac{n}{4} - 9 \).
3. "increased by three": Finally, we add 3 to the result, giving us \( \frac{n}{4} - 9 + 3 \).

Now simplifying the expression:
\[
\frac{n}{4} - 9 + 3 = \frac{n}{4} - 6
\]

Looking at the provided options, the correct expression that matches the phrase is:
**StartFraction n Over 4 EndFraction minus 9 + 3**

So, the correct choice is:
\( \frac{n}{4} - 9 + 3 \).