Question

what are the coefficients in this expression?
$6a - \frac{3}{4} + 7.5 - \frac{b}{3}$
$\bigcirc\\ -\frac{3}{4}$ and $-\frac{1}{3}$
$\bigcirc\\ -\frac{3}{4}$ and $7.5$
$\bigcirc\\ 6$ and $-3$
$\bigcirc\\ 6$ and $-\frac{1}{3}$

Explanation:

Step1: Recall the definition of a coefficient

A coefficient is a numerical or constant quantity placed before and multiplying the variable in an algebraic expression (e.g., \(4\) in \(4x\)).

Step2: Analyze each term in the expression \(6a-\frac{3}{4}+7.5-\frac{b}{3}\)

• For the term \(6a\), the variable is \(a\), and the coefficient is \(6\) (since \(6\) is multiplying \(a\)).
• For the term \(-\frac{b}{3}\), we can rewrite it as \(-\frac{1}{3}b\), so the coefficient of \(b\) is \(-\frac{1}{3}\).
• The terms \(-\frac{3}{4}\) and \(7.5\) are constants (they don't have variables multiplied by them), so they are not coefficients.

Answer:

6 and \(-\frac{1}{3}\) (corresponding to the last option: 6 and \(-\frac{1}{3}\))