Question

Combine like terms to create an equivalent expression.\[{-\dfrac{2}{3}a+\dfrac{5}6a-\dfrac{1}6}\]

Answer 1

The equivalent expression after combining like terms is \dfrac{3}{2}a - \dfrac{1}{6}.

Explanation:

To combine like terms in the expression {-\dfrac{2}{3}a+\dfrac{5}{6}a-\dfrac{1}{6}}, we need to add or subtract the coefficients of the like terms.

The like terms in the expression are the terms with the same variable, which in this case is 'a'.

Let's add the coefficients of the like terms:

- \dfrac{2}{3}a + \dfrac{5}{6}a - \dfrac{1}{6}

To add the coefficients, we need a common denominator. The least common multiple of 3 and 6 is 6.

Rewriting the fractions with a common denominator:

- \dfrac{4}{6}a + \dfrac{5}{6}a - \dfrac{1}{6}

Now we can combine the like terms:

- \dfrac{4}{6}a + \dfrac{5}{6}a - \dfrac{1}{6} = (\dfrac{4}{6} + \dfrac{5}{6})a - \dfrac{1}{6} = \dfrac{9}{6}a - \dfrac{1}{6}

Simplifying the fraction:

\dfrac{9}{6}a - \dfrac{1}{6} = \dfrac{3}{2}a - \dfrac{1}{6}

Therefore, the equivalent expression after combining like terms is \dfrac{3}{2}a - \dfrac{1}{6}.

Answer 2

To combine like terms in the expression \({-\frac{2}{3}a+\frac{5}{6}a-\frac{1}{6}}\), we need to add or subtract the coefficients of the same variable. In this case, the variable is \(a\). Step 1: Start by adding the coefficients of the \(a\) terms. The coefficients are \(-\frac{2}{3}\) and \(\frac{5}{6}\). \({-\frac{2}{3}a+\frac{5}{6}a-\frac{1}{6}} = \left(-\frac{2}{3} + \frac{5}{6}\right)a - \frac{1}{6}\) Step 2: To add the fractions, we need a common denominator. The least common denominator for \(\frac{2}{3}\) and \(\frac{5}{6}\) is 6. \(\left(-\frac{2}{3} + \frac{5}{6}\right)a - \frac{1}{6} = \left(-\frac{4}{6} + \frac{5}{6}\right)a - \frac{1}{6}\) Step 3: Combine the fractions. \(\left(-\frac{4}{6} + \frac{5}{6}\right)a - \frac{1}{6} = \left(\frac{1}{6}\right)a - \frac{1}{6}\) Step 4: Simplify the expression. Since \(\frac{1}{6}a\) and \(-\frac{1}{6}\) have the same denominator, we can write the expression as: \(\frac{1}{6}a - \frac{1}{6}\) So, the combined expression is \(\frac{1}{6}a - \frac{1}{6}\).

Explanation: