Solve: (-2/3x)-(-7⅔x) | Combining Like Terms with Negative Fractions

Q: Can I work with mixed numbers directly?

It's possible, but much harder! Converting to improper fractions first makes the arithmetic cleaner and reduces mistakes when combining like terms.

Q: How do I add fractions with different denominators?

Find a common denominator first. Here, $ 9x = \frac{27}{3}x $, so both terms have denominator 3: $ \frac{27}{3}x - \frac{2}{3}x = \frac{25}{3}x $.

Q: Should my final answer be improper or mixed?

Both are correct! $ \frac{25}{3}x $ and $ 8\frac{1}{3}x $ are equivalent. Choose the form that matches your teacher's preference or the answer choices given.

Subtracting Negative Terms with Mixed Numbers

Solve the following exercise:

$(-\frac{2}{3}x)-(-7\frac{6}{3}x)=$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following exercise:

$(-\frac{2}{3}x)-(-7\frac{6}{3}x)=$

Step-by-step solution

First, we'll perform the operations inside of the parentheses, remembering the rule:

$-(-x)=+x$

This leaves us with the exercise:

$-\frac{2}{3}x+7\frac{6}{3}x=$

Now we'll address the mixed fraction and convert it into an improper fraction:

$7\frac{6}{3}x=\frac{7\times3+6}{3}x=\frac{21+6}{3}x=\frac{27}{3}x=9x$

Now we have the exercise:

$-\frac{2}{3}x+9x=$

Finally, we'll use the distributive property to get the answer:

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

Final Answer

$8\frac{1}{3}x$

Key Points to Remember

Essential concepts to master this topic

Double Negative Rule: Subtracting a negative equals adding positive
Technique: Convert $7\frac{6}{3}x$ to $9x$ before combining
Check: Final answer $8\frac{1}{3}x$ equals $\frac{25}{3}x$ ✓

Common Mistakes

Avoid these frequent errors

Keeping the subtraction sign when dealing with negative terms
Don't leave it as $-\frac{2}{3}x - 7\frac{6}{3}x$ = $-9\frac{8}{3}x$ ! The double negative rule means subtracting a negative becomes addition. Always change $-(-7\frac{6}{3}x)$ to $+7\frac{6}{3}x$ first.

Practice Quiz

Test your knowledge with interactive questions

Convert $\frac{7}{2}$ into its reciprocal form:

FAQ

Everything you need to know about this question

Why does subtracting a negative become positive?

Think of it as removing a debt! If you owe -$5 (negative), and that debt is removed (subtracted), you actually gain $5 (positive). The rule $-(-x) = +x$ works the same way.

How do I convert mixed numbers to improper fractions?

Multiply the whole number by the denominator, then add the numerator: $7\frac{6}{3} = \frac{7 \times 3 + 6}{3} = \frac{27}{3} = 9$ . Always simplify when possible!

Can I work with mixed numbers directly?

It's possible, but much harder! Converting to improper fractions first makes the arithmetic cleaner and reduces mistakes when combining like terms.

How do I add fractions with different denominators?

Find a common denominator first. Here, $9x = \frac{27}{3}x$ , so both terms have denominator 3: $\frac{27}{3}x - \frac{2}{3}x = \frac{25}{3}x$ .

Should my final answer be improper or mixed?

Both are correct! $\frac{25}{3}x$ and $8\frac{1}{3}x$ are equivalent. Choose the form that matches your teacher's preference or the answer choices given.

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