Answer key for a math worksheet on adding and subtracting fractions, showing solutions to 12 problems.

Let’s solve each problem step by step. We’ll add or subtract fractions by finding a common denominator, then simplify if needed.

---

Problem 1:
$\frac{1}{2} + \frac{4}{5}$

Find LCD of 2 and 5 → 10
$\frac{1}{2} = \frac{5}{10},\quad \frac{4}{5} = \frac{8}{10}$
Add: $\frac{5}{10} + \frac{8}{10} = \frac{13}{10}$
→ Already simplified.
✔ Answer: $\frac{13}{10}$

---

Problem 2:
$\frac{23}{6} + 3\frac{3}{10}$

First, convert mixed number to improper fraction:
$3\frac{3}{10} = \frac{33}{10}$

Now: $\frac{23}{6} + \frac{33}{10}$

LCD of 6 and 10 → 30
$\frac{23}{6} = \frac{115}{30},\quad \frac{33}{10} = \frac{99}{30}$
Add: $\frac{115}{30} + \frac{99}{30} = \frac{214}{30}$

Simplify: divide numerator and denominator by 2 → $\frac{107}{15}$
Convert to mixed number: $107 ÷ 15 = 7$ remainder 2 → $7\frac{2}{15}$
Wait — but the answer key says $\frac{214}{30}$ is acceptable? Let’s check simplification again.

Actually, $\frac{214}{30}$ can be reduced: GCF of 214 and 30 is 2 → $\frac{107}{15}$, which is $7\frac{2}{15}$. But the answer key shows $\frac{214}{30}$ as final? That’s not fully simplified. However, since the worksheet accepts it, we’ll note both.

But let’s follow the key: they left it as $\frac{214}{30}$. Maybe for now, we accept that. But better to simplify.

Wait — looking at the answer key on right side, #2 is written as $7\frac{4}{30} = 7\frac{2}{15}$. So they did simplify later.

So correct simplified form is $7\frac{2}{15}$, but intermediate is $\frac{214}{30}$.

We’ll go with simplified version unless told otherwise.

But in the problem, they wrote “= $\frac{214}{30}$” — so maybe they want unsimplified? No, usually we simplify.

Let me recalculate:

$\frac{23}{6} + \frac{33}{10}$

LCM of 6 and 10 is 30.

$\frac{23×5}{30} = \frac{115}{30}$

$\frac{33×3}{30} = \frac{99}{30}$

Sum: $\frac{214}{30}$

Reduce: divide by 2 → $\frac{107}{15} = 7\frac{2}{15}$

But answer key says $7\frac{4}{30} = 7\frac{2}{15}$ — same thing.

So either way, correct.

For consistency, we’ll write simplified mixed number.

✔ Answer: $7\frac{2}{15}$

---

Problem 3:
$\frac{20}{8} - \frac{12}{10}$

Simplify first if possible:
$\frac{20}{8} = \frac{5}{2}$ (divide by 4)
$\frac{12}{10} = \frac{6}{5}$ (divide by 2)

Now: $\frac{5}{2} - \frac{6}{5}$

LCD of 2 and 5 → 10
$\frac{5}{2} = \frac{25}{10},\quad \frac{6}{5} = \frac{12}{10}$
Subtract: $\frac{25}{10} - \frac{12}{10} = \frac{13}{10}$

Wait — but the problem says $\frac{52}{40}$? Let’s see what they did.

Original: $\frac{20}{8} - \frac{12}{10}$

If we don’t simplify first:

LCD of 8 and 10 → 40
$\frac{20}{8} = \frac{100}{40},\quad \frac{12}{10} = \frac{48}{40}$
Subtract: $\frac{100}{40} - \frac{48}{40} = \frac{52}{40}$

Then simplify: divide by 4 → $\frac{13}{10}$

Same result.

So $\frac{52}{40}$ is correct before simplifying, but should reduce to $\frac{13}{10}$.

Answer key shows $\frac{52}{40}$ — perhaps they want it unreduced? But usually we reduce.

Looking at answer key column, #3 is blank? Wait no — in the image, under Answers, #3 is empty? Actually, in your upload, the answers are listed on the right, and #3 has nothing? Wait no — let me recheck.

In your original message, the "Answers" column on the right has entries for 1 through 12. For #3, it's blank? No — actually, looking back:

You pasted:

> 3) $\frac{20}{8} - \frac{12}{10} = \frac{52}{40}$

And in Answers column, #3 is not filled? Wait no — in the text you provided, the Answers section starts with:

1. $1\frac{3}{10}$
2. $7\frac{4}{30}=7\frac{2}{15}$
3. [blank?] — wait, in your text it says:

"3." then next line is "4." — oh! In your copy-paste, #3 answer is missing? But in the image description, it might be there.

Actually, in your initial paste, under Answers:

It says:

1. ...
2. ...
3. [nothing] — then 4. ...

But that can't be. Probably a formatting error.

Looking at problem 3: $\frac{20}{8} - \frac{12}{10} = \frac{52}{40}$, which reduces to $\frac{13}{10} = 1\frac{3}{10}$ — but that’s same as problem 1? No.

$\frac{52}{40} = \frac{13}{10} = 1\frac{3}{10}$ — yes.

But problem 1 was also $1\frac{3}{10}$? That would be coincidence.

Problem 1: $\frac{1}{2} + \frac{4}{5} = \frac{13}{10} = 1\frac{3}{10}$

Problem 3: $\frac{20}{8} - \frac{12}{10} = \frac{52}{40} = \frac{13}{10} = 1\frac{3}{10}$ — same answer? Is that possible?

Let me calculate numerically:

$\frac{20}{8} = 2.5$, $\frac{12}{10} = 1.2$, difference = 1.3 = $\frac{13}{10}$ — yes.

So both problems 1 and 3 give same answer? Unusual but mathematically correct.

But in the answer key, #1 is $1\frac{3}{10}$, and #3 is probably also $1\frac{3}{10}$, but in your text it's not shown — likely a copy-paste omission.

To avoid confusion, we'll compute correctly.

So for problem 3: $\frac{52}{40}$ simplifies to $\frac{13}{10}$ or $1\frac{3}{10}$

✔ Answer: $1\frac{3}{10}$ (or $\frac{13}{10}$)

But since the problem wrote $\frac{52}{40}$, and answer key may expect that, but best to simplify.

I think for consistency, we'll simplify all.

---

This is taking too long per problem. Since the user wants us to solve accurately, and the answer key is given, perhaps we should just verify each one quickly.

Let me list all problems and solve them concisely.

---

Problem 4:
$1\frac{7}{10} + \frac{7}{4}$

Convert to improper: $1\frac{7}{10} = \frac{17}{10}$

$\frac{17}{10} + \frac{7}{4}$

LCD of 10 and 4 → 20
$\frac{17}{10} = \frac{34}{20},\quad \frac{7}{4} = \frac{35}{20}$
Add: $\frac{34}{20} + \frac{35}{20} = \frac{69}{20}$

Simplify: $\frac{69}{20} = 3\frac{9}{20}$

Answer key shows $\frac{69}{20}$ — so they left it improper. But usually we write mixed number.

In answer key column, #4 is $3\frac{9}{20}$ — yes, from your text: "4. $3\frac{9}{20}$"

So we'll use mixed number.

✔ Answer: $3\frac{9}{20}$

---

Problem 5:
$1\frac{1}{4} - \frac{12}{10}$

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

$\frac{5}{4} - \frac{12}{10}$

Simplify $\frac{12}{10} = \frac{6}{5}$

LCD of 4 and 5 → 20
$\frac{5}{4} = \frac{25}{20},\quad \frac{6}{5} = \frac{24}{20}$
Subtract: $\frac{25}{20} - \frac{24}{20} = \frac{1}{20}$

✔ Answer: $\frac{1}{20}$

---

Problem 6:
$\frac{8}{5} + \frac{19}{12}$

LCD of 5 and 12 → 60
$\frac{8}{5} = \frac{96}{60},\quad \frac{19}{12} = \frac{95}{60}$
Add: $\frac{96}{60} + \frac{95}{60} = \frac{191}{60}$

Simplify: $\frac{191}{60} = 3\frac{11}{60}$ (since 60*3=180, 191-180=11)

Answer key shows $\frac{191}{60}$ — but in answers column, #6 is $3\frac{11}{60}$ — yes.

✔ Answer: $3\frac{11}{60}$

---

Problem 7:
$1\frac{3}{8} - 1\frac{1}{10}$

Convert both to improper:
$1\frac{3}{8} = \frac{11}{8},\quad 1\frac{1}{10} = \frac{11}{10}$

Now: $\frac{11}{8} - \frac{11}{10}$

LCD of 8 and 10 → 40
$\frac{11}{8} = \frac{55}{40},\quad \frac{11}{10} = \frac{44}{40}$
Subtract: $\frac{55}{40} - \frac{44}{40} = \frac{11}{40}$

✔ Answer: $\frac{11}{40}$

---

Problem 8:
$\frac{8}{5} + \frac{11}{6}$

LCD of 5 and 6 → 30
$\frac{8}{5} = \frac{48}{30},\quad \frac{11}{6} = \frac{55}{30}$
Add: $\frac{48}{30} + \frac{55}{30} = \frac{103}{30}$

Simplify: $\frac{103}{30} = 3\frac{13}{30}$ (30*3=90, 103-90=13)

Answer key shows $\frac{103}{30}$, and in answers #8 is $3\frac{13}{30}$ — yes.

✔ Answer: $3\frac{13}{30}$

---

Problem 9:
$\frac{1}{6} + \frac{1}{2}$

LCD of 6 and 2 → 6
$\frac{1}{6} + \frac{3}{6} = \frac{4}{6} = \frac{2}{3}$

But the problem says = $\frac{4}{6}$, and answer key #9 is $\frac{4}{6} = \frac{2}{3}$ — so they show both.

Usually we simplify, so $\frac{2}{3}$

✔ Answer: $\frac{2}{3}$

---

Problem 10:
$3\frac{1}{2} + \frac{13}{5}$

Convert: $3\frac{1}{2} = \frac{7}{2}$

$\frac{7}{2} + \frac{13}{5}$

LCD of 2 and 5 → 10
$\frac{7}{2} = \frac{35}{10},\quad \frac{13}{5} = \frac{26}{10}$
Add: $\frac{35}{10} + \frac{26}{10} = \frac{61}{10} = 6\frac{1}{10}$

Answer key shows $\frac{61}{10}$, and #10 is $6\frac{1}{10}$ — yes.

✔ Answer: $6\frac{1}{10}$

---

Problem 11:
$\frac{11}{4} + 2\frac{9}{10}$

Convert: $2\frac{9}{10} = \frac{29}{10}$

$\frac{11}{4} + \frac{29}{10}$

LCD of 4 and 10 → 20
$\frac{11}{4} = \frac{55}{20},\quad \frac{29}{10} = \frac{58}{20}$
Add: $\frac{55}{20} + \frac{58}{20} = \frac{113}{20}$

Simplify: $\frac{113}{20} = 5\frac{13}{20}$ (20*5=100, 113-100=13)

Answer key shows $\frac{113}{20}$, and #11 is $5\frac{13}{20}$ — yes.

✔ Answer: $5\frac{13}{20}$

---

Problem 12:
$2\frac{1}{10} + 1\frac{4}{8}$

First, simplify $1\frac{4}{8} = 1\frac{1}{2} = \frac{3}{2}$

$2\frac{1}{10} = \frac{21}{10}$

Now: $\frac{21}{10} + \frac{3}{2}$

LCD of 10 and 2 → 10
$\frac{21}{10} + \frac{15}{10} = \frac{36}{10} = \frac{18}{5} = 3\frac{3}{5}$

But the problem says = $\frac{144}{40}$ — let's see how they got that.

If we don't simplify early:

$2\frac{1}{10} = \frac{21}{10},\quad 1\frac{4}{8} = \frac{12}{8}$ (since 1*8+4=12)

Now $\frac{21}{10} + \frac{12}{8}$

LCD of 10 and 8 → 40
$\frac{21}{10} = \frac{84}{40},\quad \frac{12}{8} = \frac{60}{40}$
Add: $\frac{84}{40} + \frac{60}{40} = \frac{144}{40}$

Simplify: divide by 8 → $\frac{18}{5} = 3\frac{3}{5}$

Answer key shows $\frac{144}{40}$, and #12 is $3\frac{24}{40} = 3\frac{3}{5}$ — yes.

So final simplified answer is $3\frac{3}{5}$

✔ Answer: $3\frac{3}{5}$

---

Now, compiling all final answers in order:

1) $\frac{13}{10}$ or $1\frac{3}{10}$
2) $7\frac{2}{15}$
3) $1\frac{3}{10}$
4) $3\frac{9}{20}$
5) $\frac{1}{20}$
6) $3\frac{11}{60}$
7) $\frac{11}{40}$
8) $3\frac{13}{30}$
9) $\frac{2}{3}$
10) $6\frac{1}{10}$
11) $5\frac{13}{20}$
12) $3\frac{3}{5}$

Since the worksheet sometimes leaves answers as improper fractions, but the answer key converts to mixed numbers, we'll use mixed numbers where applicable.

Final Answer:
1) $1\frac{3}{10}$
2) $7\frac{2}{15}$
3) $1\frac{3}{10}$
4) $3\frac{9}{20}$
5) $\frac{1}{20}$
6) $3\frac{11}{60}$
7) $\frac{11}{40}$
8) $3\frac{13}{30}$
9) $\frac{2}{3}$
10) $6\frac{1}{10}$
11) $5\frac{13}{20}$
12) $3\frac{3}{5}$