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.
JPG
742×1050
113 KB
Free · Personal Use
Quality Assured by Worksheets Library Team
Reviewed for educational accuracy and age-appropriateness
ID: #932637
⭐
Show Answer Key & Explanations
Step-by-step solution for: Adding Fractions Worksheets with Answer Key
▼
Show Answer Key & Explanations
Step-by-step solution for: Adding Fractions Worksheets with Answer Key
To solve the given problems involving the addition of fractions, we need to follow these steps:
1. Find a common denominator for the fractions.
2. Rewrite each fraction with the common denominator.
3. Add the numerators while keeping the denominator the same.
4. Simplify the resulting fraction if possible.
Let's solve each problem step by step.
---
- Step 1: Find the least common denominator (LCD) of 6 and 8.
- The LCD of 6 and 8 is 24.
- Step 2: Rewrite each fraction with the denominator 24.
- \( \frac{3}{6} = \frac{3 \times 4}{6 \times 4} = \frac{12}{24} \)
- \( \frac{2}{8} = \frac{2 \times 3}{8 \times 3} = \frac{6}{24} \)
- Step 3: Add the fractions.
- \( \frac{12}{24} + \frac{6}{24} = \frac{12 + 6}{24} = \frac{18}{24} \)
- Step 4: Simplify the fraction.
- \( \frac{18}{24} = \frac{18 \div 6}{24 \div 6} = \frac{3}{4} \)
Answer: \( \frac{3}{4} \)
---
- Step 1: Find the LCD of 8 and 12.
- The LCD of 8 and 12 is 24.
- Step 2: Rewrite each fraction with the denominator 24.
- \( \frac{5}{8} = \frac{5 \times 3}{8 \times 3} = \frac{15}{24} \)
- \( \frac{6}{12} = \frac{6 \times 2}{12 \times 2} = \frac{12}{24} \)
- Step 3: Add the fractions.
- \( \frac{15}{24} + \frac{12}{24} = \frac{15 + 12}{24} = \frac{27}{24} \)
- Step 4: Simplify the fraction.
- \( \frac{27}{24} = \frac{27 \div 3}{24 \div 3} = \frac{9}{8} \)
Answer: \( \frac{9}{8} \)
---
- Step 1: Find the LCD of 6 and 5.
- The LCD of 6 and 5 is 30.
- Step 2: Rewrite each fraction with the denominator 30.
- \( \frac{1}{6} = \frac{1 \times 5}{6 \times 5} = \frac{5}{30} \)
- \( \frac{2}{5} = \frac{2 \times 6}{5 \times 6} = \frac{12}{30} \)
- Step 3: Add the fractions.
- \( \frac{5}{30} + \frac{12}{30} = \frac{5 + 12}{30} = \frac{17}{30} \)
- Step 4: Simplify the fraction.
- \( \frac{17}{30} \) is already in simplest form.
Answer: \( \frac{17}{30} \)
---
- Step 1: Find the LCD of 2 and 8.
- The LCD of 2 and 8 is 8.
- Step 2: Rewrite each fraction with the denominator 8.
- \( \frac{1}{2} = \frac{1 \times 4}{2 \times 4} = \frac{4}{8} \)
- \( \frac{2}{8} = \frac{2}{8} \)
- Step 3: Add the fractions.
- \( \frac{4}{8} + \frac{2}{8} = \frac{4 + 2}{8} = \frac{6}{8} \)
- Step 4: Simplify the fraction.
- \( \frac{6}{8} = \frac{6 \div 2}{8 \div 2} = \frac{3}{4} \)
Answer: \( \frac{3}{4} \)
---
- Step 1: Simplify each fraction.
- \( \frac{8}{2} = 4 \)
- \( \frac{6}{3} = 2 \)
- Step 2: Add the simplified values.
- \( 4 + 2 = 6 \)
Answer: \( 6 \)
---
- Step 1: Simplify each fraction.
- \( \frac{4}{6} = \frac{2}{3} \)
- \( \frac{5}{10} = \frac{1}{2} \)
- Step 2: Find the LCD of 3 and 2.
- The LCD of 3 and 2 is 6.
- Step 3: Rewrite each fraction with the denominator 6.
- \( \frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6} \)
- \( \frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6} \)
- Step 4: Add the fractions.
- \( \frac{4}{6} + \frac{3}{6} = \frac{4 + 3}{6} = \frac{7}{6} \)
Answer: \( \frac{7}{6} \)
---
- Step 1: Simplify \( \frac{8}{14} \).
- \( \frac{8}{14} = \frac{4}{7} \)
- Step 2: Add the fractions.
- \( \frac{3}{7} + \frac{4}{7} = \frac{3 + 4}{7} = \frac{7}{7} = 1 \)
Answer: \( 1 \)
---
- Step 1: Simplify \( \frac{2}{8} \).
- \( \frac{2}{8} = \frac{1}{4} \)
- Step 2: Find the LCD of 4 and 7.
- The LCD of 4 and 7 is 28.
- Step 3: Rewrite each fraction with the denominator 28.
- \( \frac{1}{4} = \frac{1 \times 7}{4 \times 7} = \frac{7}{28} \)
- \( \frac{3}{7} = \frac{3 \times 4}{7 \times 4} = \frac{12}{28} \)
- Step 4: Add the fractions.
- \( \frac{7}{28} + \frac{12}{28} = \frac{7 + 12}{28} = \frac{19}{28} \)
Answer: \( \frac{19}{28} \)
---
- Step 1: Find the LCD of 21 and 6.
- The LCD of 21 and 6 is 42.
- Step 2: Rewrite each fraction with the denominator 42.
- \( \frac{4}{21} = \frac{4 \times 2}{21 \times 2} = \frac{8}{42} \)
- \( \frac{1}{6} = \frac{1 \times 7}{6 \times 7} = \frac{7}{42} \)
- Step 3: Add the fractions.
- \( \frac{8}{42} + \frac{7}{42} = \frac{8 + 7}{42} = \frac{15}{42} \)
- Step 4: Simplify the fraction.
- \( \frac{15}{42} = \frac{15 \div 3}{42 \div 3} = \frac{5}{14} \)
Answer: \( \frac{5}{14} \)
---
- Step 1: Find the LCD of 9 and 36.
- The LCD of 9 and 36 is 36.
- Step 2: Rewrite each fraction with the denominator 36.
- \( \frac{4}{9} = \frac{4 \times 4}{9 \times 4} = \frac{16}{36} \)
- \( \frac{7}{36} = \frac{7}{36} \)
- Step 3: Add the fractions.
- \( \frac{16}{36} + \frac{7}{36} = \frac{16 + 7}{36} = \frac{23}{36} \)
- Step 4: Simplify the fraction.
- \( \frac{23}{36} \) is already in simplest form.
Answer: \( \frac{23}{36} \)
---
- Step 1: Find the LCD of 3 and 18.
- The LCD of 3 and 18 is 18.
- Step 2: Rewrite each fraction with the denominator 18.
- \( \frac{2}{3} = \frac{2 \times 6}{3 \times 6} = \frac{12}{18} \)
- \( \frac{7}{18} = \frac{7}{18} \)
- Step 3: Add the fractions.
- \( \frac{12}{18} + \frac{7}{18} = \frac{12 + 7}{18} = \frac{19}{18} \)
Answer: \( \frac{19}{18} \)
---
- Step 1: Find the LCD of 4 and 12.
- The LCD of 4 and 12 is 12.
- Step 2: Rewrite each fraction with the denominator 12.
- \( \frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12} \)
- \( \frac{5}{12} = \frac{5}{12} \)
- Step 3: Add the fractions.
- \( \frac{3}{12} + \frac{5}{12} = \frac{3 + 5}{12} = \frac{8}{12} \)
- Step 4: Simplify the fraction.
- \( \frac{8}{12} = \frac{8 \div 4}{12 \div 4} = \frac{2}{3} \)
Answer: \( \frac{2}{3} \)
---
\[
\boxed{
\begin{array}{lll}
1. & \frac{3}{4} & 2. & \frac{9}{8} & 3. & \frac{17}{30} \\
4. & \frac{3}{4} & 5. & 6 & 6. & \frac{7}{6} \\
7. & 1 & 8. & \frac{19}{28} & 9. & \frac{5}{14} \\
10. & \frac{23}{36} & 11. & \frac{19}{18} & 12. & \frac{2}{3}
\end{array}
}
\]
1. Find a common denominator for the fractions.
2. Rewrite each fraction with the common denominator.
3. Add the numerators while keeping the denominator the same.
4. Simplify the resulting fraction if possible.
Let's solve each problem step by step.
---
Problem 1: \( \frac{3}{6} + \frac{2}{8} \)
- Step 1: Find the least common denominator (LCD) of 6 and 8.
- The LCD of 6 and 8 is 24.
- Step 2: Rewrite each fraction with the denominator 24.
- \( \frac{3}{6} = \frac{3 \times 4}{6 \times 4} = \frac{12}{24} \)
- \( \frac{2}{8} = \frac{2 \times 3}{8 \times 3} = \frac{6}{24} \)
- Step 3: Add the fractions.
- \( \frac{12}{24} + \frac{6}{24} = \frac{12 + 6}{24} = \frac{18}{24} \)
- Step 4: Simplify the fraction.
- \( \frac{18}{24} = \frac{18 \div 6}{24 \div 6} = \frac{3}{4} \)
Answer: \( \frac{3}{4} \)
---
Problem 2: \( \frac{5}{8} + \frac{6}{12} \)
- Step 1: Find the LCD of 8 and 12.
- The LCD of 8 and 12 is 24.
- Step 2: Rewrite each fraction with the denominator 24.
- \( \frac{5}{8} = \frac{5 \times 3}{8 \times 3} = \frac{15}{24} \)
- \( \frac{6}{12} = \frac{6 \times 2}{12 \times 2} = \frac{12}{24} \)
- Step 3: Add the fractions.
- \( \frac{15}{24} + \frac{12}{24} = \frac{15 + 12}{24} = \frac{27}{24} \)
- Step 4: Simplify the fraction.
- \( \frac{27}{24} = \frac{27 \div 3}{24 \div 3} = \frac{9}{8} \)
Answer: \( \frac{9}{8} \)
---
Problem 3: \( \frac{1}{6} + \frac{2}{5} \)
- Step 1: Find the LCD of 6 and 5.
- The LCD of 6 and 5 is 30.
- Step 2: Rewrite each fraction with the denominator 30.
- \( \frac{1}{6} = \frac{1 \times 5}{6 \times 5} = \frac{5}{30} \)
- \( \frac{2}{5} = \frac{2 \times 6}{5 \times 6} = \frac{12}{30} \)
- Step 3: Add the fractions.
- \( \frac{5}{30} + \frac{12}{30} = \frac{5 + 12}{30} = \frac{17}{30} \)
- Step 4: Simplify the fraction.
- \( \frac{17}{30} \) is already in simplest form.
Answer: \( \frac{17}{30} \)
---
Problem 4: \( \frac{1}{2} + \frac{2}{8} \)
- Step 1: Find the LCD of 2 and 8.
- The LCD of 2 and 8 is 8.
- Step 2: Rewrite each fraction with the denominator 8.
- \( \frac{1}{2} = \frac{1 \times 4}{2 \times 4} = \frac{4}{8} \)
- \( \frac{2}{8} = \frac{2}{8} \)
- Step 3: Add the fractions.
- \( \frac{4}{8} + \frac{2}{8} = \frac{4 + 2}{8} = \frac{6}{8} \)
- Step 4: Simplify the fraction.
- \( \frac{6}{8} = \frac{6 \div 2}{8 \div 2} = \frac{3}{4} \)
Answer: \( \frac{3}{4} \)
---
Problem 5: \( \frac{8}{2} + \frac{6}{3} \)
- Step 1: Simplify each fraction.
- \( \frac{8}{2} = 4 \)
- \( \frac{6}{3} = 2 \)
- Step 2: Add the simplified values.
- \( 4 + 2 = 6 \)
Answer: \( 6 \)
---
Problem 6: \( \frac{4}{6} + \frac{5}{10} \)
- Step 1: Simplify each fraction.
- \( \frac{4}{6} = \frac{2}{3} \)
- \( \frac{5}{10} = \frac{1}{2} \)
- Step 2: Find the LCD of 3 and 2.
- The LCD of 3 and 2 is 6.
- Step 3: Rewrite each fraction with the denominator 6.
- \( \frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6} \)
- \( \frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6} \)
- Step 4: Add the fractions.
- \( \frac{4}{6} + \frac{3}{6} = \frac{4 + 3}{6} = \frac{7}{6} \)
Answer: \( \frac{7}{6} \)
---
Problem 7: \( \frac{3}{7} + \frac{8}{14} \)
- Step 1: Simplify \( \frac{8}{14} \).
- \( \frac{8}{14} = \frac{4}{7} \)
- Step 2: Add the fractions.
- \( \frac{3}{7} + \frac{4}{7} = \frac{3 + 4}{7} = \frac{7}{7} = 1 \)
Answer: \( 1 \)
---
Problem 8: \( \frac{2}{8} + \frac{3}{7} \)
- Step 1: Simplify \( \frac{2}{8} \).
- \( \frac{2}{8} = \frac{1}{4} \)
- Step 2: Find the LCD of 4 and 7.
- The LCD of 4 and 7 is 28.
- Step 3: Rewrite each fraction with the denominator 28.
- \( \frac{1}{4} = \frac{1 \times 7}{4 \times 7} = \frac{7}{28} \)
- \( \frac{3}{7} = \frac{3 \times 4}{7 \times 4} = \frac{12}{28} \)
- Step 4: Add the fractions.
- \( \frac{7}{28} + \frac{12}{28} = \frac{7 + 12}{28} = \frac{19}{28} \)
Answer: \( \frac{19}{28} \)
---
Problem 9: \( \frac{4}{21} + \frac{1}{6} \)
- Step 1: Find the LCD of 21 and 6.
- The LCD of 21 and 6 is 42.
- Step 2: Rewrite each fraction with the denominator 42.
- \( \frac{4}{21} = \frac{4 \times 2}{21 \times 2} = \frac{8}{42} \)
- \( \frac{1}{6} = \frac{1 \times 7}{6 \times 7} = \frac{7}{42} \)
- Step 3: Add the fractions.
- \( \frac{8}{42} + \frac{7}{42} = \frac{8 + 7}{42} = \frac{15}{42} \)
- Step 4: Simplify the fraction.
- \( \frac{15}{42} = \frac{15 \div 3}{42 \div 3} = \frac{5}{14} \)
Answer: \( \frac{5}{14} \)
---
Problem 10: \( \frac{4}{9} + \frac{7}{36} \)
- Step 1: Find the LCD of 9 and 36.
- The LCD of 9 and 36 is 36.
- Step 2: Rewrite each fraction with the denominator 36.
- \( \frac{4}{9} = \frac{4 \times 4}{9 \times 4} = \frac{16}{36} \)
- \( \frac{7}{36} = \frac{7}{36} \)
- Step 3: Add the fractions.
- \( \frac{16}{36} + \frac{7}{36} = \frac{16 + 7}{36} = \frac{23}{36} \)
- Step 4: Simplify the fraction.
- \( \frac{23}{36} \) is already in simplest form.
Answer: \( \frac{23}{36} \)
---
Problem 11: \( \frac{2}{3} + \frac{7}{18} \)
- Step 1: Find the LCD of 3 and 18.
- The LCD of 3 and 18 is 18.
- Step 2: Rewrite each fraction with the denominator 18.
- \( \frac{2}{3} = \frac{2 \times 6}{3 \times 6} = \frac{12}{18} \)
- \( \frac{7}{18} = \frac{7}{18} \)
- Step 3: Add the fractions.
- \( \frac{12}{18} + \frac{7}{18} = \frac{12 + 7}{18} = \frac{19}{18} \)
Answer: \( \frac{19}{18} \)
---
Problem 12: \( \frac{1}{4} + \frac{5}{12} \)
- Step 1: Find the LCD of 4 and 12.
- The LCD of 4 and 12 is 12.
- Step 2: Rewrite each fraction with the denominator 12.
- \( \frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12} \)
- \( \frac{5}{12} = \frac{5}{12} \)
- Step 3: Add the fractions.
- \( \frac{3}{12} + \frac{5}{12} = \frac{3 + 5}{12} = \frac{8}{12} \)
- Step 4: Simplify the fraction.
- \( \frac{8}{12} = \frac{8 \div 4}{12 \div 4} = \frac{2}{3} \)
Answer: \( \frac{2}{3} \)
---
Final Answers:
\[
\boxed{
\begin{array}{lll}
1. & \frac{3}{4} & 2. & \frac{9}{8} & 3. & \frac{17}{30} \\
4. & \frac{3}{4} & 5. & 6 & 6. & \frac{7}{6} \\
7. & 1 & 8. & \frac{19}{28} & 9. & \frac{5}{14} \\
10. & \frac{23}{36} & 11. & \frac{19}{18} & 12. & \frac{2}{3}
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of math worksheet adding fractions.
