Solve: Combining (-2/3x) and (-8⅓x) Like Terms in Algebra

Q: How do I convert a mixed number to an improper fraction?

Multiply the whole number by the denominator, then add the numerator. For $ 8\frac{1}{3} $: 8 × 3 = 24, then 24 + 1 = 25, so it becomes $ \frac{25}{3} $.

Q: Why can't I just work with the mixed number as is?

Mixed numbers make it confusing to combine terms because you have to deal with whole parts and fractional parts separately. Converting to improper fractions lets you add coefficients directly.

Q: Do I need a common denominator here?

No! Both terms already have the same denominator (3). You can add $ -\frac{2}{3}x $ and $ -\frac{25}{3}x $ directly by adding the numerators: -2 + (-25) = -27.

Q: Should my final answer be a mixed number or improper fraction?

For algebraic expressions, keep it as the simplest form. Since $ -\frac{27}{3} = -9 $, the answer is simply $ -9x $.

Q: What if the denominators were different?

Then you'd need to find the least common denominator (LCD) first, convert both fractions, and then combine. But here, both have denominator 3, making it easier!

Like Terms with Mixed Numbers

$(-\frac{2}{3}x)+(-8\frac{1}{3}x)=$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Simply

00:04 Positive times negative is always negative

00:23 Collect terms

00:35 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$(-\frac{2}{3}x)+(-8\frac{1}{3}x)=$

Step-by-step solution

Let's remember the rule:

$+(-x)=-x$

Now let's write the exercise in the appropriate form and solve it:

$-\frac{2}{3}x-8\frac{1}{3}x=-9x$

Final Answer

$-9x$

Key Points to Remember

Essential concepts to master this topic

Rule: Convert mixed numbers to improper fractions before combining
Technique: $8\frac{1}{3} = \frac{25}{3}$ , so coefficients become $-\frac{2}{3} - \frac{25}{3}$
Check: Add numerators with same denominator: $-\frac{27}{3} = -9$ ✓

Common Mistakes

Avoid these frequent errors

Adding whole numbers and fractions separately
Don't add 8 + (-2/3) = 7⅓! This ignores the fractional part of the mixed number and gives a completely wrong answer. Always convert mixed numbers to improper fractions first, then combine like terms by adding the coefficients.

Practice Quiz

Test your knowledge with interactive questions

a is negative number.

b is negative number.

What is the sum of a+b?

FAQ

Everything you need to know about this question

How do I convert a mixed number to an improper fraction?

Multiply the whole number by the denominator, then add the numerator. For $8\frac{1}{3}$ : 8 × 3 = 24, then 24 + 1 = 25, so it becomes $\frac{25}{3}$ .

Why can't I just work with the mixed number as is?

Mixed numbers make it confusing to combine terms because you have to deal with whole parts and fractional parts separately. Converting to improper fractions lets you add coefficients directly.

Do I need a common denominator here?

No! Both terms already have the same denominator (3). You can add $-\frac{2}{3}x$ and $-\frac{25}{3}x$ directly by adding the numerators: -2 + (-25) = -27.

Should my final answer be a mixed number or improper fraction?

For algebraic expressions, keep it as the simplest form. Since $-\frac{27}{3} = -9$ , the answer is simply $-9x$ .

What if the denominators were different?

Then you'd need to find the least common denominator (LCD) first, convert both fractions, and then combine. But here, both have denominator 3, making it easier!

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Signed Numbers (Positive and Negative) questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime