Mixed fractions addition worksheet with 15 problems and a hint for simplification.

Let’s solve each problem step by step. We’re adding fractions — some are proper, some improper, and we’ll simplify where needed.

We’ll find a common denominator for each pair, add the numerators, then simplify if possible.

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1) 1/3 + 1/2

LCM of 3 and 2 is 6
→ 1/3 = 2/6, 1/2 = 3/6
→ 2/6 + 3/6 = 5/6

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2) 1/5 + 1/4

LCM of 5 and 4 is 20
→ 1/5 = 4/20, 1/4 = 5/20
→ 4/20 + 5/20 = 9/20

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3) 1/7 + 1/2

LCM of 7 and 2 is 14
→ 1/7 = 2/14, 1/2 = 7/14
→ 2/14 + 7/14 = 9/14

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4) 1/5 + 1/9

LCM of 5 and 9 is 45
→ 1/5 = 9/45, 1/9 = 5/45
→ 9/45 + 5/45 = 14/45 (already simplified)

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5) 1/6 + 1/8

LCM of 6 and 8 is 24
→ 1/6 = 4/24, 1/8 = 3/24
→ 4/24 + 3/24 = 7/24

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6) 1/4 + 1/9

LCM of 4 and 9 is 36
→ 1/4 = 9/36, 1/9 = 4/36
→ 9/36 + 4/36 = 13/36

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7) 3/12 + 4/8

First, simplify before adding:
3/12 = 1/4, 4/8 = 1/2
Now: 1/4 + 1/2 → LCM 4
→ 1/4 + 2/4 = 3/4

*(Alternatively, without simplifying first: LCM of 12 and 8 is 24 → 6/24 + 12/24 = 18/24 = 3/4)*

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8) 6/3 + 7/14

Simplify first:
6/3 = 2, 7/14 = 1/2
So: 2 + 1/2 = 2 1/2 or 5/2

*(As improper fraction: 5/2)*

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9) 5/15 + 4/16

Simplify:
5/15 = 1/3, 4/16 = 1/4
LCM of 3 and 4 is 12
→ 1/3 = 4/12, 1/4 = 3/12
→ 4/12 + 3/12 = 7/12

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10) 10/30 + 6/9

Simplify:
10/30 = 1/3, 6/9 = 2/3
→ 1/3 + 2/3 = 3/3 = 1

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11) 2/18 + 9/4

Simplify 2/18 = 1/9
Now: 1/9 + 9/4
LCM of 9 and 4 is 36
→ 1/9 = 4/36, 9/4 = 81/36
→ 4/36 + 81/36 = 85/36

Can write as mixed number: 85 ÷ 36 = 2 with remainder 13 → 2 13/36

But since original problems didn’t specify format, we can leave as improper unless asked. Let’s keep as 85/36 for now.

Wait — let me double-check:

2/18 = 1/9 ✔️
9/4 stays ✔️
LCM 36 ✔️
1/9 = 4/36 ✔️
9/4 = (9×9)/(4×9)? No! Wait — 9/4 to 36ths: multiply numerator and denominator by 9? No!

Mistake here!

To convert 9/4 to 36ths:
4 × 9 = 36 → so multiply numerator and denominator by 9:
9 × 9 = 81 → yes, 81/36 ✔️
1/9 = 4/36 ✔️
Sum: 85/36 ✔️

Yes, correct.

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12) 5/25 + 11/22

Simplify:
5/25 = 1/5, 11/22 = 1/2
LCM of 5 and 2 is 10
→ 1/5 = 2/10, 1/2 = 5/10
→ 2/10 + 5/10 = 7/10

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13) 5/8 + 2/18

Simplify 2/18 = 1/9
Now: 5/8 + 1/9
LCM of 8 and 9 is 72
→ 5/8 = 45/72, 1/9 = 8/72
→ 45/72 + 8/72 = 53/72 (already simplified)

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14) 6/30 + 4/12

Simplify:
6/30 = 1/5, 4/12 = 1/3
LCM of 5 and 3 is 15
→ 1/5 = 3/15, 1/3 = 5/15
→ 3/15 + 5/15 = 8/15

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15) 9/10 + 8/20

Simplify 8/20 = 2/5
Now: 9/10 + 2/5
LCM of 10 and 5 is 10
→ 2/5 = 4/10
→ 9/10 + 4/10 = 13/10

Or as mixed number: 1 3/10

Again, unless specified, we can leave as improper. But since it's >1, maybe better as mixed? The worksheet says “Mixed Fractions Arithmetic” but all inputs are proper or improper fractions — outputs may be mixed.

Looking at problem 8: 6/3 + 7/14 = 2 + 0.5 = 2.5 → we wrote 5/2 or 2 1/2. Probably acceptable either way, but since title says “Mixed Fractions”, perhaps they expect mixed numbers when result >1.

Let’s check which answers are greater than 1:

- #8: 5/2 → 2 1/2
- #11: 85/36 → 2 13/36
- #15: 13/10 → 1 3/10

Others are less than 1.

Since the worksheet doesn’t specify output format, and hint says “simplify to make calculations easier”, I think leaving as simplified improper fractions is fine — but for consistency with “mixed fractions” in title, maybe convert those three to mixed numbers.

Actually, looking again: the title is “Mixed Fractions Arithmetic (Addition)” — but none of the problems have mixed numbers as input. All are simple fractions. So probably “mixed” refers to mixing different types of fractions, not that answers must be mixed numbers.

I’ll provide both forms for clarity, but final answer will use simplest form — improper if <1, mixed if >1? Or just always simplified fraction?

Let me see standard practice: usually, if result is improper, convert to mixed number unless told otherwise.

But in this case, since it’s arithmetic practice, and no instruction, I’ll give simplified fraction, and for >1, also show mixed number in parentheses? But user wants only final answer.

Re-reading instructions: “Provide only the final correct answer”

And “CRITICAL: First work through... ONLY THEN provide final answer”

Also, in math worksheets like this, often they accept either, but prefer mixed numbers for results >1.

Let me decide:

For #8: 5/2 → 2 1/2
#11: 85/36 → 2 13/36
#15: 13/10 → 1 3/10

Others stay as fractions.

But to be safe, since the problem didn't specify, and many are proper fractions, I'll present all as simplified fractions, and for improper ones, leave as improper — because converting to mixed might not be required.

Wait — look at problem 8: 6/3 is 2, which is whole number, plus 1/2 → clearly 2 1/2 is expected.

Similarly, #10: 10/30 + 6/9 = 1/3 + 2/3 = 1 → whole number.

So probably, they expect simplified form, including mixed numbers where appropriate.

I think best to follow convention: if result is improper fraction, convert to mixed number.

So let’s adjust:

#8: 5/2 = 2 1/2
#11: 85/36 = 2 * 36 = 72, 85-72=13 → 2 13/36
#15: 13/10 = 1 3/10

Others remain as fractions.

Now, compiling all answers:

1) 5/6
2) 9/20
3) 9/14
4) 14/45
5) 7/24
6) 13/36
7) 3/4
8) 2 1/2
9) 7/12
10) 1
11) 2 13/36
12) 7/10
13) 53/72
14) 8/15
15) 1 3/10

Double-checking a few:

#7: 3/12 + 4/8 = 1/4 + 1/2 = 3/4 ✔️
#10: 10/30=1/3, 6/9=2/3, sum=1 ✔️
#12: 5/25=1/5, 11/22=1/2, 1/5+1/2=2/10+5/10=7/10 ✔️
#14: 6/30=1/5, 4/12=1/3, 1/5+1/3=3/15+5/15=8/15 ✔️
#15: 9/10 + 8/20=9/10+4/10=13/10=1 3/10 ✔️

All good.

Final Answer:

1) \frac{5}{6}
2) \frac{9}{20}
3) \frac{9}{14}
4) \frac{14}{45}
5) \frac{7}{24}
6) \frac{13}{36}
7) \frac{3}{4}
8) 2\frac{1}{2}
9) \frac{7}{12}
10) 1
11) 2\frac{13}{36}
12) \frac{7}{10}
13) \frac{53}{72}
14) \frac{8}{15}
15) 1\frac{3}{10}