Adding Fractions Worksheets - Free Printable

Let’s solve each problem one by one. We’ll simplify algebraic fractions by combining them over a common denominator, then simplifying the numerator and reducing if possible.

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Problem 1:
$\frac{3x}{7} + \frac{x + 3}{7}$

Same denominator → just add numerators:
= $\frac{3x + x + 3}{7} = \frac{4x + 3}{7}$

Already in lowest terms.

✔ Answer: $\frac{4x + 3}{7}$

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Problem 2:
$\frac{8x}{3} + \frac{x - 3}{12}$

Find LCD of 3 and 12 → it’s 12.

Convert first fraction:
$\frac{8x}{3} = \frac{8x \cdot 4}{3 \cdot 4} = \frac{32x}{12}$

Now add:
$\frac{32x}{12} + \frac{x - 3}{12} = \frac{32x + x - 3}{12} = \frac{33x - 3}{12}$

Factor numerator: $3(11x - 1)$
Denominator: $12 = 3 \cdot 4$

Cancel 3:
= $\frac{11x - 1}{4}$

✔ Answer: $\frac{11x - 1}{4}$

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Problem 3:
$\frac{9x}{8} - \frac{x - 5}{16}$

LCD of 8 and 16 → 16.

Convert first fraction:
$\frac{9x}{8} = \frac{9x \cdot 2}{8 \cdot 2} = \frac{18x}{16}$

Now subtract:
$\frac{18x}{16} - \frac{x - 5}{16} = \frac{18x - (x - 5)}{16} = \frac{18x - x + 5}{16} = \frac{17x + 5}{16}$

No common factors → done.

✔ Answer: $\frac{17x + 5}{16}$

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Problem 4:
$\frac{x + 7}{3} + \frac{3x - 2}{18}$

LCD of 3 and 18 → 18.

Convert first fraction:
$\frac{x + 7}{3} = \frac{(x + 7) \cdot 6}{3 \cdot 6} = \frac{6x + 42}{18}$

Add:
$\frac{6x + 42}{18} + \frac{3x - 2}{18} = \frac{6x + 42 + 3x - 2}{18} = \frac{9x + 40}{18}$

Check for simplification: 9 and 18 share factor 9? But 40 not divisible by 9 → no.

Wait — actually, check GCF of all coefficients: 9, 40, 18 → GCF is 1. So leave as is.

But wait — can we reduce? Let's see:

Numerator: 9x + 40
Denominator: 18

No common factor between entire numerator and denominator → so answer is $\frac{9x + 40}{18}$

BUT — let me double-check arithmetic:

6x + 3x = 9x
42 - 2 = 40 → correct.

Yes.

✔ Answer: $\frac{9x + 40}{18}$

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Problem 5:
$\frac{7x}{8} + \frac{3x}{10} - \frac{x}{5}$

Need LCD of 8, 10, 5.

Prime factors:
8 = 2³
10 = 2·5
5 = 5
→ LCD = 2³ · 5 = 40

Convert each:

$\frac{7x}{8} = \frac{7x \cdot 5}{40} = \frac{35x}{40}$
$\frac{3x}{10} = \frac{3x \cdot 4}{40} = \frac{12x}{40}$
$\frac{x}{5} = \frac{x \cdot 8}{40} = \frac{8x}{40}$

Now combine:
$\frac{35x + 12x - 8x}{40} = \frac{39x}{40}$

39 and 40 have no common factors → done.

✔ Answer: $\frac{39x}{40}$

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Problem 6:
$\frac{2x}{11} - \frac{5(x - 2)}{11}$

Same denominator → combine numerators:

= $\frac{2x - 5(x - 2)}{11}$

Distribute the -5:
= $\frac{2x - 5x + 10}{11} = \frac{-3x + 10}{11}$

Or write as $\frac{10 - 3x}{11}$ — both are fine. Usually prefer positive leading term if possible, but not required.

We’ll leave as $\frac{-3x + 10}{11}$ or rearrange to $\frac{10 - 3x}{11}$ — either is acceptable. I’ll use the latter for neatness.

✔ Answer: $\frac{10 - 3x}{11}$

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Problem 7:
$\frac{2}{x} - \frac{3}{x} + \frac{7}{2x}$

All denominators involve x. LCD is 2x.

Convert each:

$\frac{2}{x} = \frac{4}{2x}$
$\frac{3}{x} = \frac{6}{2x}$
$\frac{7}{2x}$ stays same.

Now:
$\frac{4}{2x} - \frac{6}{2x} + \frac{7}{2x} = \frac{4 - 6 + 7}{2x} = \frac{5}{2x}$

Done.

✔ Answer: $\frac{5}{2x}$

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Problem 8:
$\frac{4x}{7} - \frac{x - 3}{8}$

LCD of 7 and 8 → 56.

Convert:

$\frac{4x}{7} = \frac{4x \cdot 8}{56} = \frac{32x}{56}$
$\frac{x - 3}{8} = \frac{(x - 3) \cdot 7}{56} = \frac{7x - 21}{56}$

Subtract:
$\frac{32x}{56} - \frac{7x - 21}{56} = \frac{32x - (7x - 21)}{56} = \frac{32x - 7x + 21}{56} = \frac{25x + 21}{56}$

Check for simplification: 25, 21, 56 → GCF is 1 → done.

✔ Answer: $\frac{25x + 21}{56}$

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Final Answer:
1. $\frac{4x + 3}{7}$
2. $\frac{11x - 1}{4}$
3. $\frac{17x + 5}{16}$
4. $\frac{9x + 40}{18}$
5. $\frac{39x}{40}$
6. $\frac{10 - 3x}{11}$
7. $\frac{5}{2x}$
8. $\frac{25x + 21}{56}$