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$Combine like terms to create an equivalent expression. Enter any coefficients as simplified proper or improper fractions or integers. -(2)/(3)a+(5)/(6)a-(1)/(6)$

Combine like terms to create an equivalent expression. $\newline$ Enter any coefficients as simplified proper or improper fractions or integers. $\newline$ $-\frac{2}{3}a+\frac{5}{6}a-\frac{1}{6}$

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Math Problems

Algebra 1

Simplify variable expressions involving like terms and the distributive property

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Q. Combine like terms to create an equivalent expression.

\newline

Enter any coefficients as simplified proper or improper fractions or integers.

\newline

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

Identify Like Terms: Identify like terms in the expression. $\newline$ The like terms in the expression are the terms that contain the variable $a$ . In this case, $-\left(\frac{2}{3}\right)a$ and $\left(\frac{5}{6}\right)a$ are like terms. The constant term $-\left(\frac{1}{6}\right)$ does not have a like term to combine with.
Combine Like Terms: Combine the like terms by adding their coefficients. $\newline$ To combine the terms, we add the coefficients of $a$ together. This means adding $-\frac{2}{3}$ and $\frac{5}{6}$ .
Find Common Denominator: Find a common denominator for the fractions to add them. $\newline$ The common denominator for $3$ and $6$ is $6$ . We need to convert $-(\frac{2}{3})$ into a fraction with a denominator of $6$ before adding it to $(\frac{5}{6})$ .
Convert to Common Denominator: Convert $-\frac{2}{3}$ to a fraction with a denominator of $6$ . $\newline$ To convert $-\frac{2}{3}$ to a fraction with a denominator of $6$ , we multiply both the numerator and the denominator by $2$ . This gives us $-\frac{4}{6}$ .
Add Converted Fractions: Add the converted fraction to $(5/6)$ . $\newline$ Now we add $-(4/6)$ to $(5/6)$ : $\newline$ $-(4/6) + (5/6) = (5/6) - (4/6) = (1/6)$ a
Write Final Expression: Write the final expression. $\newline$ The final expression after combining like terms is: $\newline$ $(\frac{1}{6})a - (\frac{1}{6})$