Subtracting Negative Mixed Fractions with Unlike Denominators Up ... - Free Printable

You’ve uploaded an image titled “Subtracting Negative Mixed Fractions (A) Answers”, which shows a worksheet with 10 problems involving subtracting negative mixed fractions. The solutions are already filled in — this is the *answer key*.

Since you asked to “solve the problem and explain the solution”, I’ll pick one example from the worksheet and walk through it step by step, explaining the process of subtracting negative mixed fractions. Let’s take Problem #1:

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🔢 Problem 1:

> \((-2\frac{1}{4}) - (-4\frac{2}{3})\)

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## ✔ Step-by-Step Solution:

Step 1: Convert mixed numbers to improper fractions

- \(-2\frac{1}{4} = -\left(2 + \frac{1}{4}\right) = -\frac{9}{4}\)
- \(-4\frac{2}{3} = -\left(4 + \frac{2}{3}\right) = -\frac{14}{3}\)

So now the problem becomes:
> \(-\frac{9}{4} - (-\frac{14}{3})\)

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Step 2: Subtracting a negative = Adding a positive

Recall:
> \(a - (-b) = a + b\)

So:
> \(-\frac{9}{4} - (-\frac{14}{3}) = -\frac{9}{4} + \frac{14}{3}\)

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Step 3: Find a common denominator

The denominators are 4 and 3 → LCM is 12

Convert both fractions:

- \(-\frac{9}{4} = -\frac{9 \times 3}{4 \times 3} = -\frac{27}{12}\)
- \(\frac{14}{3} = \frac{14 \times 4}{3 \times 4} = \frac{56}{12}\)

Now we have:
> \(-\frac{27}{12} + \frac{56}{12} = \frac{-27 + 56}{12} = \frac{29}{12}\)

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Step 4: Convert improper fraction to mixed number

\(\frac{29}{12} = 2 \frac{5}{12}\)
(because \(12 \times 2 = 24\), remainder 5)

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## ✔ Final Answer:
> \(\boxed{2\frac{5}{12}}\)

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## 🧠 Key Concepts Explained:

1. Negative mixed numbers: Treat the whole number and fraction as a single negative value.
2. Subtracting a negative: Turns into addition.
3. Common denominators: Required to add/subtract fractions.
4. Improper to mixed: Always simplify final answer if needed.

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## 💡 Why This Worksheet Is Useful:

This worksheet practices:
- Converting between mixed numbers and improper fractions
- Handling negative signs in subtraction
- Finding common denominators
- Simplifying results

It’s great for reinforcing foundational fraction operations — especially when negatives are involved!

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If you’d like me to walk through any other problem on the sheet (like #5 or #8), just let me know! 😊