Combine like terms to create an equivalent expression. Enter any coefficients as simplified proper or improper fractions or integers. -(6)/(5)-(2)/(3)v+(4)/(15)+(1)/(3)v

Identify like terms: Identify like terms in the expression. The expression given is -(6/5) - (2/3)v + (4/15) + (1/3)v. We need to combine like terms, which are terms that have the same variable part. In this case, the like terms are -(2/3)v and (1/3)v, which both have the variable 'v'. The other terms -(6/5) and (4/15) are constants and can be combined separately.Combine constant terms: Combine the constant terms. To combine the constants -(6/5) and (4/15), we need a common denominator. The least common denominator for 5 and 15 is 15. We convert -(6/5) to -(18/15) so that both fractions have the same denominator. Now we can combine the constants: -(18/15) + (4/15) = (-18 + 4)/15 = -14/15.Combine variable terms: Combine the variable terms. Now we combine the variable terms -(2/3)v and (1/3)v. Since they have the same variable part, we can simply add their coefficients: -(2/3) + (1/3) = (-2 + 1)/3 = -1/3. So the combined variable term is (-1/3)v.Write final simplified expression: Write the final simplified expression. We now have the combined constant term and the combined variable term. The final simplified expression is -14/15 - (1/3)v.

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Math Problems

Algebra 1

Simplify variable expressions involving like terms and the distributive property

Full solution

Q. Combine like terms to create an equivalent expression.

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

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-\frac{6}{5}-\frac{2}{3}v+\frac{4}{15}+\frac{1}{3}v

Identify like terms: Identify like terms in the expression. $\newline$ The expression given is $-\frac{6}{5}$ - $\frac{2}{3}v$ + $\frac{4}{15}$ + $\frac{1}{3}v$ . We need to combine like terms, which are terms that have the same variable part. In this case, the like terms are $-\frac{2}{3}v$ and $\frac{1}{3}v$ , which both have the variable 'v'. The other terms $-\frac{6}{5}$ and $\frac{4}{15}$ are constants and can be combined separately.
Combine constant terms: Combine the constant terms. $\newline$ To combine the constants $-\frac{6}{5}$ and $\frac{4}{15}$ , we need a common denominator. The least common denominator for $5$ and $15$ is $15$ . We convert $-\frac{6}{5}$ to $-\frac{18}{15}$ so that both fractions have the same denominator. $\newline$ Now we can combine the constants: $-\frac{18}{15} + \frac{4}{15} = \frac{-18 + 4}{15} = -\frac{14}{15}$ .
Combine variable terms: Combine the variable terms. $\newline$ Now we combine the variable terms $-\frac{2}{3}v$ and $\frac{1}{3}v$ . Since they have the same variable part, we can simply add their coefficients: $-\frac{2}{3} + \frac{1}{3} = \frac{-2 + 1}{3} = -\frac{1}{3}$ . $\newline$ So the combined variable term is $-\frac{1}{3}v$ .
Write final simplified expression: Write the final simplified expression. $\newline$ We now have the combined constant term and the combined variable term. The final simplified expression is $-\frac{14}{15} - \left(\frac{1}{3}\right)v$ .