Worksheet with answers for adding negative fractions, showing step-by-step solutions and final results.

It looks like you've uploaded an image of a completed worksheet titled "Adding Negative Fractions (A) Answers" from Math-Drills.com, which shows the solutions to 10 problems involving the addition of negative fractions.

Since this is already a solved worksheet, I'll go through each problem and explain the solution process step by step so you understand how the answers were derived. This will help reinforce the concept of adding negative fractions.

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🔢 General Rule for Adding Fractions:

To add fractions:
1. Find a common denominator.
2. Convert each fraction to have that common denominator.
3. Add the numerators.
4. Simplify the result if needed.

When dealing with negative fractions, remember:
- A negative sign can be in front of the whole fraction or in the numerator.
- Adding a negative is the same as subtracting a positive.

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Let’s walk through each problem:

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1.

$$
\left(-\frac{2}{6}\right) + \frac{3}{5}
$$

Step 1: Simplify $-\frac{2}{6} = -\frac{1}{3}$, but we’ll keep it as $-\frac{2}{6}$ for now.

Step 2: Find LCD of 6 and 5 → 30

Convert:
- $-\frac{2}{6} = -\frac{10}{30}$
- $\frac{3}{5} = \frac{18}{30}$

Add:
$$
-\frac{10}{30} + \frac{18}{30} = \frac{8}{30} = \frac{4}{15}
$$

✔ Answer: $ \boxed{\frac{4}{15}} $

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2.

$$
\left(-\frac{3}{5}\right) + \frac{1}{2}
$$

LCD of 5 and 2 → 10

Convert:
- $-\frac{3}{5} = -\frac{6}{10}$
- $\frac{1}{2} = \frac{5}{10}$

Add:
$$
-\frac{6}{10} + \frac{5}{10} = -\frac{1}{10}
$$

✔ Answer: $ \boxed{-\frac{1}{10}} $

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3.

$$
\left(-\frac{5}{6}\right) + \frac{2}{5}
$$

LCD of 6 and 5 → 30

Convert:
- $-\frac{5}{6} = -\frac{25}{30}$
- $\frac{2}{5} = \frac{12}{30}$

Add:
$$
-\frac{25}{30} + \frac{12}{30} = -\frac{13}{30}
$$

✔ Answer: $ \boxed{-\frac{13}{30}} $

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4.

$$
\left(-\frac{1}{6}\right) + \frac{2}{5}
$$

LCD of 6 and 5 → 30

Convert:
- $-\frac{1}{6} = -\frac{5}{30}$
- $\frac{2}{5} = \frac{12}{30}$

Add:
$$
-\frac{5}{30} + \frac{12}{30} = \frac{7}{30}
$$

✔ Answer: $ \boxed{\frac{7}{30}} $

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5.

$$
\left(-\frac{1}{2}\right) + \left(-\frac{1}{3}\right)
$$

LCD of 2 and 3 → 6

Convert:
- $-\frac{1}{2} = -\frac{3}{6}$
- $-\frac{1}{3} = -\frac{2}{6}$

Add:
$$
-\frac{3}{6} + (-\frac{2}{6}) = -\frac{5}{6}
$$

✔ Answer: $ \boxed{-\frac{5}{6}} $

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6.

$$
\left(-\frac{1}{3}\right) + \left(-\frac{1}{5}\right)
$$

LCD of 3 and 5 → 15

Convert:
- $-\frac{1}{3} = -\frac{5}{15}$
- $-\frac{1}{5} = -\frac{3}{15}$

Add:
$$
-\frac{5}{15} + (-\frac{3}{15}) = -\frac{8}{15}
$$

✔ Answer: $ \boxed{-\frac{8}{15}} $

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7.

$$
\left(-\frac{3}{6}\right) + \frac{1}{5}
$$

Simplify $-\frac{3}{6} = -\frac{1}{2}$, but let's use original.

LCD of 6 and 5 → 30

Convert:
- $-\frac{3}{6} = -\frac{15}{30}$
- $\frac{1}{5} = \frac{6}{30}$

Add:
$$
-\frac{15}{30} + \frac{6}{30} = -\frac{9}{30} = -\frac{3}{10}
$$

✔ Answer: $ \boxed{-\frac{3}{10}} $

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8.

$$
\left(-\frac{1}{5}\right) + \left(-\frac{1}{4}\right)
$$

LCD of 5 and 4 → 20

Convert:
- $-\frac{1}{5} = -\frac{4}{20}$
- $-\frac{1}{4} = -\frac{5}{20}$

Add:
$$
-\frac{4}{20} + (-\frac{5}{20}) = -\frac{9}{20}
$$

✔ Answer: $ \boxed{-\frac{9}{20}} $

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9.

$$
\left(-\frac{1}{5}\right) + \frac{1}{2}
$$

LCD of 5 and 2 → 10

Convert:
- $-\frac{1}{5} = -\frac{2}{10}$
- $\frac{1}{2} = \frac{5}{10}$

Add:
$$
-\frac{2}{10} + \frac{5}{10} = \frac{3}{10}
$$

✔ Answer: $ \boxed{\frac{3}{10}} $

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10.

$$
\left(-\frac{3}{5}\right) + \frac{4}{6}
$$

Simplify $\frac{4}{6} = \frac{2}{3}$, but we’ll proceed.

LCD of 5 and 6 → 30

Convert:
- $-\frac{3}{5} = -\frac{18}{30}$
- $\frac{4}{6} = \frac{20}{30}$

Add:
$$
-\frac{18}{30} + \frac{20}{30} = \frac{2}{30} = \frac{1}{15}
$$

✔ Answer: $ \boxed{\frac{1}{15}} $

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✔ Summary of Key Concepts:

- Always find a common denominator.
- Convert both fractions.
- Add the numerators, keeping signs in mind.
- Simplify the final answer.
- Adding two negatives gives a more negative number.
- Adding a negative and a positive is like subtraction.

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