Adding Fractions Answer Key - 12 problems with solutions for practice and review.

It looks like you've uploaded an answer key for a worksheet titled *"Adding Fractions"*, which includes 12 problems with their solutions. However, since the image shows only the answers, and not the original problems or any specific question you'd like solved, I’ll help by:

1. Reviewing the correctness of each answer.
2. Explaining how to solve each type of problem (adding fractions).
3. Highlighting any potential errors.

Let’s go through each problem one by one and verify the answers.

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🔹 Problem 1:

$\frac{3}{4} + \frac{1}{4} = \frac{4}{4} = 1$ ✔
✔ Correct. Same denominator → add numerators: $3+1=4$, so $\frac{4}{4}=1$

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🔹 Problem 2:

$\frac{12}{25} + \frac{8}{25} = \frac{20}{25} = \frac{4}{5}$ ✔
✔ Correct. Add numerators: $12+8=20$, then simplify $\frac{20}{25} = \frac{4}{5}$

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🔹 Problem 3:

$\frac{10}{13} + \frac{2}{13} = \frac{12}{13}$ ✔
✔ Correct. Same denominator → $10+2=12$, so $\frac{12}{13}$

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🔹 Problem 4:

$\frac{40}{85} + \frac{60}{85} = \frac{100}{85} = \frac{20}{17}$ ✔
✔ Correct. Add numerators: $40+60=100$, then simplify:
- $\frac{100}{85} = \frac{20}{17}$ (divided numerator and denominator by 5)
- $\frac{20}{17}$ is improper but acceptable unless specified otherwise.

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🔹 Problem 5:

$\frac{10}{2} + \frac{4}{2} = \frac{12}{4} = 7$ ✘
✘ Incorrect!

Let's check:
- $\frac{10}{2} = 5$, $\frac{4}{2} = 2$, so $5 + 2 = 7$
- But the answer key says $\frac{12}{4} = 7$, which is true numerically, but $\frac{12}{4}$ simplifies to 3, not 7!

Wait — there's a mistake here.

Actually:
$$
\frac{10}{2} + \frac{4}{2} = \frac{14}{2} = 7
$$
But the answer key says $\frac{12}{4} = 7$, which is wrong because:
- $\frac{12}{4} = 3$, not 7.

So this is incorrect.

✔ Correct Answer:
$$
\frac{10}{2} + \frac{4}{2} = \frac{14}{2} = 7
$$

The answer key incorrectly writes $\frac{12}{4}$ instead of $\frac{14}{2}$. This is a mistake.

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🔹 Problem 6:

$\frac{10}{42} + \frac{25}{42} = \frac{35}{42} = \frac{5}{6}$ ✔
✔ Correct. Add numerators: $10+25=35$, then simplify:
- $\frac{35}{42} = \frac{5}{6}$ (divide numerator and denominator by 7)

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🔹 Problem 7:

$\frac{2}{3} + \frac{1}{6} = \frac{5}{6}$ ✔
✔ Correct. Find common denominator (LCM of 3 and 6 is 6):
- $\frac{2}{3} = \frac{4}{6}$, $\frac{1}{6} = \frac{1}{6}$
- $\frac{4}{6} + \frac{1}{6} = \frac{5}{6}$

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🔹 Problem 8:

$\frac{3}{4} + \frac{5}{8} = \frac{11}{8}$ ✔
✔ Correct. Common denominator: LCM of 4 and 8 is 8:
- $\frac{3}{4} = \frac{6}{8}$, $\frac{5}{8} = \frac{5}{8}$
- $\frac{6}{8} + \frac{5}{8} = \frac{11}{8}$

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🔹 Problem 9:

$\frac{2}{18} + \frac{2}{9} = \frac{11}{18}$ ✘
✘ Incorrect

Check:
- $\frac{2}{18} = \frac{1}{9}$, $\frac{2}{9} = \frac{2}{9}$
- So $\frac{1}{9} + \frac{2}{9} = \frac{3}{9} = \frac{1}{3}$

But the answer key says $\frac{11}{18}$ — that's wrong.

Let’s do it properly:
- Convert both to denominator 18:
- $\frac{2}{18}$ stays
- $\frac{2}{9} = \frac{4}{18}$
- So $\frac{2}{18} + \frac{4}{18} = \frac{6}{18} = \frac{1}{3}$

✔ Correct Answer: $\frac{1}{3}$

Answer key has a mistake here.

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🔹 Problem 10:

$\frac{2}{4} + \frac{2}{3} = \frac{14}{12} = \frac{7}{6}$ ✘
✘ Incorrect

Wait — let’s see:
- $\frac{2}{4} = \frac{1}{2}$, $\frac{2}{3}$ remains
- Common denominator: 6
- $\frac{1}{2} = \frac{3}{6}$, $\frac{2}{3} = \frac{4}{6}$
- Sum: $\frac{3}{6} + \frac{4}{6} = \frac{7}{6}$

But the answer key says:
$$
\frac{2}{4} + \frac{2}{3} = \frac{14}{12} = \frac{7}{6}
$$

But $\frac{2}{4} + \frac{2}{3} = ?$

Let’s compute:
- $\frac{2}{4} = \frac{1}{2} = \frac{3}{6}$
- $\frac{2}{3} = \frac{4}{6}$
- Total: $\frac{7}{6}$ — correct

But how did they get $\frac{14}{12}$?

Let’s try adding directly:
- $\frac{2}{4} + \frac{2}{3} = \frac{2 \cdot 3}{4 \cdot 3} + \frac{2 \cdot 4}{3 \cdot 4} = \frac{6}{12} + \frac{8}{12} = \frac{14}{12} = \frac{7}{6}$

Ah! So $\frac{14}{12}$ is correct, and reduces to $\frac{7}{6}$.

So even though the intermediate step shows $\frac{14}{12}$, it's mathematically valid.

✔ So Problem 10 is actually correct, despite seeming odd.

Note: The answer key wrote:
> $\frac{2}{4} + \frac{2}{3} = \frac{14}{12} = \frac{7}{6}$

That’s fine — it's just using 12 as the common denominator.

✔ Correct

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🔹 Problem 11:

$\frac{2}{7} + \frac{5}{9} = \frac{53}{63}$ ✔
✔ Correct. LCM of 7 and 9 is 63:
- $\frac{2}{7} = \frac{18}{63}$, $\frac{5}{9} = \frac{35}{63}$
- $18 + 35 = 53$, so $\frac{53}{63}$

✔️ Correct.

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🔹 Problem 12:

$\frac{8}{11} + \frac{1}{4} = \frac{43}{44}$ ✘
✘ Incorrect

Check:
- LCM of 11 and 4 is 44
- $\frac{8}{11} = \frac{32}{44}$, $\frac{1}{4} = \frac{11}{44}$
- Sum: $\frac{32 + 11}{44} = \frac{43}{44}$

Wait — that seems correct.

But let’s double-check:
- $8 \times 4 = 32$, yes
- $1 \times 11 = 11$, yes
- $32 + 11 = 43$, so $\frac{43}{44}$

✔ So this is correct.

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## ✔ Final Summary: Which Answers Are Wrong?

| Problem | Status | Explanation |
|--------|--------|-----------|
| 1 | ✔ Correct | Good |
| 2 | ✔ Correct | Good |
| 3 | ✔ Correct | Good |
| 4 | ✔ Correct | Good |
| 5 | ✘ Incorrect | Should be $\frac{14}{2} = 7$, not $\frac{12}{4} = 3$ |
| 6 | ✔ Correct | Good |
| 7 | ✔ Correct | Good |
| 8 | ✔ Correct | Good |
| 9 | ✘ Incorrect | Should be $\frac{6}{18} = \frac{1}{3}$, not $\frac{11}{18}$ |
| 10 | ✔ Correct | $\frac{14}{12} = \frac{7}{6}$ is valid |
| 11 | ✔ Correct | Good |
| 12 | ✔ Correct | Good |

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🚫 Errors in the Answer Key:

- Problem 5: Incorrectly states $\frac{12}{4} = 7$ (should be $\frac{14}{2} = 7$)
- Problem 9: Incorrectly states $\frac{11}{18}$ (should be $\frac{6}{18} = \frac{1}{3}$)

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✔ How to Add Fractions (Quick Guide):

1. Same Denominator: Add numerators, keep denominator.
- Example: $\frac{a}{c} + \frac{b}{c} = \frac{a+b}{c}$

2. Different Denominators:
- Find LCM (Least Common Multiple) of denominators
- Convert both fractions to have same denominator
- Add numerators
- Simplify if possible

3. Mixed Numbers: Convert to improper fractions first.

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💡 Final Advice:

This appears to be a published answer key, possibly from Mometrix, and contains two errors (Problems 5 and 9). If you're using this for study, double-check these two.

Would you like me to generate a corrected version of this answer key?