Adding Fractions Worksheets with Answer Key - Free Printable
Educational worksheet: Adding Fractions Worksheets with Answer Key. Download and print for classroom or home learning activities.
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Step-by-step solution for: Adding Fractions Worksheets with Answer Key
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Show Answer Key & Explanations
Step-by-step solution for: Adding Fractions Worksheets with Answer Key
To solve these fraction addition problems, we need to find a common denominator for each pair of fractions. Once the denominators are the same, we can add the numerators and simplify if needed.
Let’s go step by step for each problem:
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Problem 1:
$\frac{1}{4} + \frac{1}{2}$
Common denominator = 4
Convert $\frac{1}{2}$ → $\frac{2}{4}$
Now: $\frac{1}{4} + \frac{2}{4} = \frac{3}{4}$ ✔
---
Problem 2:
$\frac{3}{4} + \frac{3}{8}$
Common denominator = 8
Convert $\frac{3}{4}$ → $\frac{6}{8}$
Now: $\frac{6}{8} + \frac{3}{8} = \frac{9}{8}$ → which is $1\frac{1}{8}$ ✔
---
Problem 3:
$\frac{2}{4} + \frac{5}{6}$
Simplify $\frac{2}{4}$ → $\frac{1}{2}$ first? Or just use LCD of 4 and 6 → 12
$\frac{2}{4} = \frac{6}{12}$, $\frac{5}{6} = \frac{10}{12}$
Add: $\frac{6}{12} + \frac{10}{12} = \frac{16}{12} = \frac{4}{3} = 1\frac{1}{3}$ ✔
*(Note: You could also simplify $\frac{2}{4}$ to $\frac{1}{2}$ first — then $\frac{1}{2} + \frac{5}{6} = \frac{3}{6} + \frac{5}{6} = \frac{8}{6} = \frac{4}{3}$ — same result.)*
---
Problem 4:
$\frac{3}{6} + \frac{1}{3}$
Simplify $\frac{3}{6}$ → $\frac{1}{2}$
Then: $\frac{1}{2} + \frac{1}{3}$ → LCD = 6
$\frac{3}{6} + \frac{2}{6} = \frac{5}{6}$ ✔
*(Alternatively, without simplifying: $\frac{3}{6} + \frac{2}{6} = \frac{5}{6}$ — same thing!)*
---
Problem 5:
$\frac{8}{3} + \frac{4}{5}$
LCD = 15
$\frac{8}{3} = \frac{40}{15}$, $\frac{4}{5} = \frac{12}{15}$
Add: $\frac{40}{15} + \frac{12}{15} = \frac{52}{15} = 3\frac{7}{15}$ ✔
---
Problem 6:
$\frac{2}{5} + \frac{5}{10}$
Simplify $\frac{5}{10}$ → $\frac{1}{2}$
Now: $\frac{2}{5} + \frac{1}{2}$ → LCD = 10
$\frac{4}{10} + \frac{5}{10} = \frac{9}{10}$ ✔
*(Or keep as is: $\frac{2}{5} = \frac{4}{10}, \frac{5}{10} = \frac{5}{10} → \frac{9}{10}$ — same!)*
---
Problem 7:
$\frac{2}{3} + \frac{1}{2}$
LCD = 6
$\frac{4}{6} + \frac{3}{6} = \frac{7}{6} = 1\frac{1}{6}$ ✔
---
Problem 8:
$\frac{4}{6} + \frac{5}{8}$
Simplify $\frac{4}{6}$ → $\frac{2}{3}$
Now: $\frac{2}{3} + \frac{5}{8}$ → LCD = 24
$\frac{16}{24} + \frac{15}{24} = \frac{31}{24} = 1\frac{7}{24}$ ✔
*(Without simplifying: $\frac{4}{6} = \frac{16}{24}, \frac{5}{8} = \frac{15}{24} → \frac{31}{24}$ — same!)*
---
Problem 9:
$\frac{3}{9} + \frac{1}{3}$
Simplify $\frac{3}{9}$ → $\frac{1}{3}$
So: $\frac{1}{3} + \frac{1}{3} = \frac{2}{3}$ ✔
---
Problem 10:
$\frac{6}{4} + \frac{5}{12}$
Simplify $\frac{6}{4}$ → $\frac{3}{2}$
Now: $\frac{3}{2} + \frac{5}{12}$ → LCD = 12
$\frac{18}{12} + \frac{5}{12} = \frac{23}{12} = 1\frac{11}{12}$ ✔
*(Without simplifying: $\frac{6}{4} = \frac{18}{12}, \frac{5}{12} = \frac{5}{12} → \frac{23}{12}$ — same!)*
---
Problem 11:
$\frac{4}{6} + \frac{2}{9}$
Simplify $\frac{4}{6}$ → $\frac{2}{3}$
Now: $\frac{2}{3} + \frac{2}{9}$ → LCD = 9
$\frac{6}{9} + \frac{2}{9} = \frac{8}{9}$ ✔
*(Without simplifying: $\frac{4}{6} = \frac{12}{18}, \frac{2}{9} = \frac{4}{18} → \frac{16}{18} = \frac{8}{9}$ — same!)*
---
Problem 12:
$\frac{9}{2} + \frac{2}{8}$
Simplify $\frac{2}{8}$ → $\frac{1}{4}$
Now: $\frac{9}{2} + \frac{1}{4}$ → LCD = 4
$\frac{18}{4} + \frac{1}{4} = \frac{19}{4} = 4\frac{3}{4}$ ✔
*(Without simplifying: $\frac{9}{2} = \frac{36}{8}, \frac{2}{8} = \frac{2}{8} → \frac{38}{8} = \frac{19}{4}$ — same!)*
---
Final Answers (in order):
1. $\frac{3}{4}$
2. $1\frac{1}{8}$ or $\frac{9}{8}$
3. $1\frac{1}{3}$ or $\frac{4}{3}$
4. $\frac{5}{6}$
5. $3\frac{7}{15}$ or $\frac{52}{15}$
6. $\frac{9}{10}$
7. $1\frac{1}{6}$ or $\frac{7}{6}$
8. $1\frac{7}{24}$ or $\frac{31}{24}$
9. $\frac{2}{3}$
10. $1\frac{11}{12}$ or $\frac{23}{12}$
11. $\frac{8}{9}$
12. $4\frac{3}{4}$ or $\frac{19}{4}$
Since the worksheet doesn’t specify whether to leave as improper fractions or mixed numbers, both forms are correct. But in elementary math, mixed numbers are often preferred when the numerator is larger than the denominator.
We’ll write them as mixed numbers where applicable.
──────────────────────────────────────
Final Answer:
1. $\frac{3}{4}$
2. $1\frac{1}{8}$
3. $1\frac{1}{3}$
4. $\frac{5}{6}$
5. $3\frac{7}{15}$
6. $\frac{9}{10}$
7. $1\frac{1}{6}$
8. $1\frac{7}{24}$
9. $\frac{2}{3}$
10. $1\frac{11}{12}$
11. $\frac{8}{9}$
12. $4\frac{3}{4}$
Let’s go step by step for each problem:
---
Problem 1:
$\frac{1}{4} + \frac{1}{2}$
Common denominator = 4
Convert $\frac{1}{2}$ → $\frac{2}{4}$
Now: $\frac{1}{4} + \frac{2}{4} = \frac{3}{4}$ ✔
---
Problem 2:
$\frac{3}{4} + \frac{3}{8}$
Common denominator = 8
Convert $\frac{3}{4}$ → $\frac{6}{8}$
Now: $\frac{6}{8} + \frac{3}{8} = \frac{9}{8}$ → which is $1\frac{1}{8}$ ✔
---
Problem 3:
$\frac{2}{4} + \frac{5}{6}$
Simplify $\frac{2}{4}$ → $\frac{1}{2}$ first? Or just use LCD of 4 and 6 → 12
$\frac{2}{4} = \frac{6}{12}$, $\frac{5}{6} = \frac{10}{12}$
Add: $\frac{6}{12} + \frac{10}{12} = \frac{16}{12} = \frac{4}{3} = 1\frac{1}{3}$ ✔
*(Note: You could also simplify $\frac{2}{4}$ to $\frac{1}{2}$ first — then $\frac{1}{2} + \frac{5}{6} = \frac{3}{6} + \frac{5}{6} = \frac{8}{6} = \frac{4}{3}$ — same result.)*
---
Problem 4:
$\frac{3}{6} + \frac{1}{3}$
Simplify $\frac{3}{6}$ → $\frac{1}{2}$
Then: $\frac{1}{2} + \frac{1}{3}$ → LCD = 6
$\frac{3}{6} + \frac{2}{6} = \frac{5}{6}$ ✔
*(Alternatively, without simplifying: $\frac{3}{6} + \frac{2}{6} = \frac{5}{6}$ — same thing!)*
---
Problem 5:
$\frac{8}{3} + \frac{4}{5}$
LCD = 15
$\frac{8}{3} = \frac{40}{15}$, $\frac{4}{5} = \frac{12}{15}$
Add: $\frac{40}{15} + \frac{12}{15} = \frac{52}{15} = 3\frac{7}{15}$ ✔
---
Problem 6:
$\frac{2}{5} + \frac{5}{10}$
Simplify $\frac{5}{10}$ → $\frac{1}{2}$
Now: $\frac{2}{5} + \frac{1}{2}$ → LCD = 10
$\frac{4}{10} + \frac{5}{10} = \frac{9}{10}$ ✔
*(Or keep as is: $\frac{2}{5} = \frac{4}{10}, \frac{5}{10} = \frac{5}{10} → \frac{9}{10}$ — same!)*
---
Problem 7:
$\frac{2}{3} + \frac{1}{2}$
LCD = 6
$\frac{4}{6} + \frac{3}{6} = \frac{7}{6} = 1\frac{1}{6}$ ✔
---
Problem 8:
$\frac{4}{6} + \frac{5}{8}$
Simplify $\frac{4}{6}$ → $\frac{2}{3}$
Now: $\frac{2}{3} + \frac{5}{8}$ → LCD = 24
$\frac{16}{24} + \frac{15}{24} = \frac{31}{24} = 1\frac{7}{24}$ ✔
*(Without simplifying: $\frac{4}{6} = \frac{16}{24}, \frac{5}{8} = \frac{15}{24} → \frac{31}{24}$ — same!)*
---
Problem 9:
$\frac{3}{9} + \frac{1}{3}$
Simplify $\frac{3}{9}$ → $\frac{1}{3}$
So: $\frac{1}{3} + \frac{1}{3} = \frac{2}{3}$ ✔
---
Problem 10:
$\frac{6}{4} + \frac{5}{12}$
Simplify $\frac{6}{4}$ → $\frac{3}{2}$
Now: $\frac{3}{2} + \frac{5}{12}$ → LCD = 12
$\frac{18}{12} + \frac{5}{12} = \frac{23}{12} = 1\frac{11}{12}$ ✔
*(Without simplifying: $\frac{6}{4} = \frac{18}{12}, \frac{5}{12} = \frac{5}{12} → \frac{23}{12}$ — same!)*
---
Problem 11:
$\frac{4}{6} + \frac{2}{9}$
Simplify $\frac{4}{6}$ → $\frac{2}{3}$
Now: $\frac{2}{3} + \frac{2}{9}$ → LCD = 9
$\frac{6}{9} + \frac{2}{9} = \frac{8}{9}$ ✔
*(Without simplifying: $\frac{4}{6} = \frac{12}{18}, \frac{2}{9} = \frac{4}{18} → \frac{16}{18} = \frac{8}{9}$ — same!)*
---
Problem 12:
$\frac{9}{2} + \frac{2}{8}$
Simplify $\frac{2}{8}$ → $\frac{1}{4}$
Now: $\frac{9}{2} + \frac{1}{4}$ → LCD = 4
$\frac{18}{4} + \frac{1}{4} = \frac{19}{4} = 4\frac{3}{4}$ ✔
*(Without simplifying: $\frac{9}{2} = \frac{36}{8}, \frac{2}{8} = \frac{2}{8} → \frac{38}{8} = \frac{19}{4}$ — same!)*
---
Final Answers (in order):
1. $\frac{3}{4}$
2. $1\frac{1}{8}$ or $\frac{9}{8}$
3. $1\frac{1}{3}$ or $\frac{4}{3}$
4. $\frac{5}{6}$
5. $3\frac{7}{15}$ or $\frac{52}{15}$
6. $\frac{9}{10}$
7. $1\frac{1}{6}$ or $\frac{7}{6}$
8. $1\frac{7}{24}$ or $\frac{31}{24}$
9. $\frac{2}{3}$
10. $1\frac{11}{12}$ or $\frac{23}{12}$
11. $\frac{8}{9}$
12. $4\frac{3}{4}$ or $\frac{19}{4}$
Since the worksheet doesn’t specify whether to leave as improper fractions or mixed numbers, both forms are correct. But in elementary math, mixed numbers are often preferred when the numerator is larger than the denominator.
We’ll write them as mixed numbers where applicable.
──────────────────────────────────────
Final Answer:
1. $\frac{3}{4}$
2. $1\frac{1}{8}$
3. $1\frac{1}{3}$
4. $\frac{5}{6}$
5. $3\frac{7}{15}$
6. $\frac{9}{10}$
7. $1\frac{1}{6}$
8. $1\frac{7}{24}$
9. $\frac{2}{3}$
10. $1\frac{11}{12}$
11. $\frac{8}{9}$
12. $4\frac{3}{4}$
Parent Tip: Review the logic above to help your child master the concept of worksheet addition of fractions with unlike denominators.
![Adding Fractions with Unlike Denominators Worksheets [PDFs] Brighterly](/images2/worksheet-addition-of-fractions-with-unlike-denominators/worksheet-addition-of-fractions-with-unlike-denominators-30.jpg)
