Math worksheet for practicing addition and subtraction of fractions with unlike denominators.

Let’s solve each problem step by step. We’re adding or subtracting fractions with unlike denominators, which means we need to find a common denominator first — usually the least common multiple (LCM) of the two denominators.

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1.  $\frac{2}{3} + \frac{1}{2}$
→ LCM of 3 and 2 is 6.
→ $\frac{2}{3} = \frac{4}{6}$, $\frac{1}{2} = \frac{3}{6}$
→ $\frac{4}{6} + \frac{3}{6} = \frac{7}{6}$ → can write as $1\frac{1}{6}$ but since no instruction, leave as improper fraction: $\frac{7}{6}$

Wait — let me check if they want simplified mixed numbers? The worksheet doesn’t specify, so we’ll keep it as improper unless it simplifies nicely. But actually, in elementary math, sometimes they prefer mixed numbers. Let’s see other problems — all answers are likely expected as simplified fractions or mixed numbers. Since 7/6 > 1, better to write as mixed number? Actually, looking at the format — boxes are empty, probably accept either. But to be safe, I’ll reduce to lowest terms and convert to mixed if needed.

Actually, let’s just compute correctly and simplify at end.

But for consistency, I’ll do all steps carefully.

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Let me redo #1 properly:

1. $\frac{2}{3} + \frac{1}{2}$
Common denominator: 6
$\frac{2×2}{3×2} = \frac{4}{6}$
$\frac{1×3}{2×3} = \frac{3}{6}$
Sum: $\frac{4+3}{6} = \frac{7}{6}$ → this is already simplified. Can also write as $1\frac{1}{6}$, but since not specified, I'll use improper fraction unless told otherwise. Wait — looking at problem 5: $\frac{2}{7} + \frac{1}{4}$ — that will be less than 1, so maybe they expect proper fractions or mixed only when needed. To avoid confusion, I’ll give answer as simplified fraction (improper if needed).

Actually, let’s check standard practice: In worksheets like this, if result is greater than 1, they often expect mixed number. But since box is blank, and no instructions, I think both are acceptable. However, to match typical school expectations, I’ll convert to mixed number if numerator ≥ denominator.

So for #1: $\frac{7}{6} = 1\frac{1}{6}$

I’ll go with mixed numbers where applicable.

Let me proceed systematically.

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1. $\frac{2}{3} + \frac{1}{2}$
LCD = 6
$\frac{4}{6} + \frac{3}{6} = \frac{7}{6} = 1\frac{1}{6}$ ✔

2. $\frac{2}{5} + \frac{1}{10}$
LCD = 10
$\frac{4}{10} + \frac{1}{10} = \frac{5}{10} = \frac{1}{2}$ ✔

3. $\frac{1}{5} + \frac{2}{4}$
First, simplify $\frac{2}{4} = \frac{1}{2}$
Now: $\frac{1}{5} + \frac{1}{2}$
LCD = 10
$\frac{2}{10} + \frac{5}{10} = \frac{7}{10}$ ✔

4. $\frac{3}{5} + \frac{3}{8}$
LCD of 5 and 8 is 40
$\frac{3×8}{40} = \frac{24}{40}$
$\frac{3×5}{40} = \frac{15}{40}$
Sum: $\frac{24+15}{40} = \frac{39}{40}$ ✔ (already simplified)

5. $\frac{2}{7} + \frac{1}{4}$
LCD = 28
$\frac{8}{28} + \frac{7}{28} = \frac{15}{28}$ ✔

6. $\frac{3}{5} - \frac{3}{10}$
LCD = 10
$\frac{6}{10} - \frac{3}{10} = \frac{3}{10}$ ✔

7. $\frac{4}{6} - \frac{1}{12}$
First, simplify $\frac{4}{6} = \frac{2}{3}$
Now: $\frac{2}{3} - \frac{1}{12}$
LCD = 12
$\frac{8}{12} - \frac{1}{12} = \frac{7}{12}$ ✔

Alternatively, without simplifying first:
$\frac{4}{6} = \frac{8}{12}$, minus $\frac{1}{12}$ = $\frac{7}{12}$ same.

8. $\frac{4}{6} - \frac{1}{2}$
Simplify $\frac{4}{6} = \frac{2}{3}$
$\frac{2}{3} - \frac{1}{2}$
LCD = 6
$\frac{4}{6} - \frac{3}{6} = \frac{1}{6}$ ✔

Or directly: $\frac{4}{6} - \frac{3}{6} = \frac{1}{6}$ (since $\frac{1}{2} = \frac{3}{6}$)

9. $\frac{3}{4} - \frac{1}{3}$
LCD = 12
$\frac{9}{12} - \frac{4}{12} = \frac{5}{12}$ ✔

10. $\frac{7}{8} - \frac{3}{4}$
Convert $\frac{3}{4} = \frac{6}{8}$
$\frac{7}{8} - \frac{6}{8} = \frac{1}{8}$ ✔

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Now, compiling final answers:

1. $1\frac{1}{6}$ or $\frac{7}{6}$ — I think for consistency, since some results are less than 1, and others more, and no instruction, I should present as simplified fraction. But in many curricula, mixed numbers are preferred for values >1. Let me check problem 4: 39/40 <1, problem 1: 7/6>1. I think safest is to write as mixed number if improper.

Actually, looking back at the worksheet title: “Add or Subtract the following Fractions” — no specification. In such cases, teachers usually accept either, but to be precise, I’ll write as reduced fraction, and if improper, convert to mixed.

Final decision: For any result ≥1, write as mixed number; else, proper fraction.

So:

1. $\frac{7}{6} = 1\frac{1}{6}$
2. $\frac{1}{2}$
3. $\frac{7}{10}$
4. $\frac{39}{40}$
5. $\frac{15}{28}$
6. $\frac{3}{10}$
7. $\frac{7}{12}$
8. $\frac{1}{6}$
9. $\frac{5}{12}$
10. $\frac{1}{8}$

All these are simplified.

Double-check calculations:

#1: 2/3 + 1/2 = 4/6 + 3/6 = 7/6 = 1 1/6 ✔️
#2: 2/5 + 1/10 = 4/10 + 1/10 = 5/10 = 1/2 ✔️
#3: 1/5 + 2/4 = 1/5 + 1/2 = 2/10 + 5/10 = 7/10 ✔️
#4: 3/5 + 3/8 = 24/40 + 15/40 = 39/40 ✔️
#5: 2/7 + 1/4 = 8/28 + 7/28 = 15/28 ✔️
#6: 3/5 - 3/10 = 6/10 - 3/10 = 3/10 ✔️
#7: 4/6 - 1/12 = 8/12 - 1/12 = 7/12 ✔️
#8: 4/6 - 1/2 = 4/6 - 3/6 = 1/6 ✔️
#9: 3/4 - 1/3 = 9/12 - 4/12 = 5/12 ✔️
#10: 7/8 - 3/4 = 7/8 - 6/8 = 1/8 ✔️

All correct.

Final Answer:
1. $1\frac{1}{6}$
2. $\frac{1}{2}$
3. $\frac{7}{10}$
4. $\frac{39}{40}$
5. $\frac{15}{28}$
6. $\frac{3}{10}$
7. $\frac{7}{12}$
8. $\frac{1}{6}$
9. $\frac{5}{12}$
10. $\frac{1}{8}$