Adding Fractions with Unlike Denominators - Worksheet Digital - Free Printable
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Step-by-step solution for: Adding Fractions with Unlike Denominators - Worksheet Digital
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Show Answer Key & Explanations
Step-by-step solution for: Adding Fractions with Unlike Denominators - Worksheet Digital
To solve the problem of adding unlike fractions, we need to follow these steps:
1. Find a Common Denominator: The denominators of the fractions must be made the same so that they can be added directly.
2. Adjust the Numerators: Once the common denominator is found, adjust the numerators of the fractions accordingly.
3. Add the Fractions: Add the adjusted numerators and keep the common denominator.
4. Simplify the Result: If possible, simplify the resulting fraction.
Let's solve each problem step by step.
---
- Step 1: Find the Least Common Denominator (LCD)
The denominators are 2 and 3. The LCD is 6.
- Step 2: Adjust the Fractions
Convert \( \frac{1}{2} \) to \( \frac{3}{6} \) (multiply numerator and denominator by 3).
Convert \( \frac{1}{3} \) to \( \frac{2}{6} \) (multiply numerator and denominator by 2).
- Step 3: Add the Fractions
\( \frac{3}{6} + \frac{2}{6} = \frac{5}{6} \)
- Step 4: Simplify
\( \frac{5}{6} \) is already in simplest form.
Answer: \( \frac{5}{6} \)
---
- Step 1: Find the LCD
The denominators are 3 and 5. The LCD is 15.
- Step 2: Adjust the Fractions
Convert \( \frac{1}{3} \) to \( \frac{5}{15} \) (multiply numerator and denominator by 5).
Convert \( \frac{3}{5} \) to \( \frac{9}{15} \) (multiply numerator and denominator by 3).
- Step 3: Add the Fractions
\( \frac{5}{15} + \frac{9}{15} = \frac{14}{15} \)
- Step 4: Simplify
\( \frac{14}{15} \) is already in simplest form.
Answer: \( \frac{14}{15} \)
---
- Step 1: Find the LCD
The denominators are 2 and 3. The LCD is 6.
- Step 2: Adjust the Fractions
Convert \( \frac{1}{2} \) to \( \frac{3}{6} \) (multiply numerator and denominator by 3).
Convert \( \frac{2}{3} \) to \( \frac{4}{6} \) (multiply numerator and denominator by 2).
- Step 3: Add the Fractions
\( \frac{3}{6} + \frac{4}{6} = \frac{7}{6} \)
- Step 4: Simplify
\( \frac{7}{6} \) is an improper fraction and can be written as \( 1 \frac{1}{6} \).
Answer: \( \frac{7}{6} \) or \( 1 \frac{1}{6} \)
---
- Step 1: Find the LCD
The denominators are 5 and 6. The LCD is 30.
- Step 2: Adjust the Fractions
Convert \( \frac{2}{5} \) to \( \frac{12}{30} \) (multiply numerator and denominator by 6).
Convert \( \frac{5}{6} \) to \( \frac{25}{30} \) (multiply numerator and denominator by 5).
- Step 3: Add the Fractions
\( \frac{12}{30} + \frac{25}{30} = \frac{37}{30} \)
- Step 4: Simplify
\( \frac{37}{30} \) is an improper fraction and can be written as \( 1 \frac{7}{30} \).
Answer: \( \frac{37}{30} \) or \( 1 \frac{7}{30} \)
---
- Step 1: Find the LCD
The denominators are 6 and 5. The LCD is 30.
- Step 2: Adjust the Fractions
Convert \( \frac{5}{6} \) to \( \frac{25}{30} \) (multiply numerator and denominator by 5).
Convert \( \frac{2}{5} \) to \( \frac{12}{30} \) (multiply numerator and denominator by 6).
- Step 3: Add the Fractions
\( \frac{25}{30} + \frac{12}{30} = \frac{37}{30} \)
- Step 4: Simplify
\( \frac{37}{30} \) is an improper fraction and can be written as \( 1 \frac{7}{30} \).
Answer: \( \frac{37}{30} \) or \( 1 \frac{7}{30} \)
---
- Step 1: Find the LCD
The denominators are 4 and 6. The LCD is 12.
- Step 2: Adjust the Fractions
Convert \( \frac{1}{4} \) to \( \frac{3}{12} \) (multiply numerator and denominator by 3).
Convert \( \frac{1}{6} \) to \( \frac{2}{12} \) (multiply numerator and denominator by 2).
- Step 3: Add the Fractions
\( \frac{3}{12} + \frac{2}{12} = \frac{5}{12} \)
- Step 4: Simplify
\( \frac{5}{12} \) is already in simplest form.
Answer: \( \frac{5}{12} \)
---
- Step 1: Find the LCD
The denominators are 7 and 5. The LCD is 35.
- Step 2: Adjust the Fractions
Convert \( \frac{3}{7} \) to \( \frac{15}{35} \) (multiply numerator and denominator by 5).
Convert \( \frac{3}{5} \) to \( \frac{21}{35} \) (multiply numerator and denominator by 7).
- Step 3: Add the Fractions
\( \frac{15}{35} + \frac{21}{35} = \frac{36}{35} \)
- Step 4: Simplify
\( \frac{36}{35} \) is an improper fraction and can be written as \( 1 \frac{1}{35} \).
Answer: \( \frac{36}{35} \) or \( 1 \frac{1}{35} \)
---
- Step 1: Find the LCD
The denominators are 5 and 9. The LCD is 45.
- Step 2: Adjust the Fractions
Convert \( \frac{2}{5} \) to \( \frac{18}{45} \) (multiply numerator and denominator by 9).
Convert \( \frac{5}{9} \) to \( \frac{25}{45} \) (multiply numerator and denominator by 5).
- Step 3: Add the Fractions
\( \frac{18}{45} + \frac{25}{45} = \frac{43}{45} \)
- Step 4: Simplify
\( \frac{43}{45} \) is already in simplest form.
Answer: \( \frac{43}{45} \)
---
- Step 1: Find the LCD
The denominators are 8 and 2. The LCD is 8.
- Step 2: Adjust the Fractions
Convert \( \frac{1}{2} \) to \( \frac{4}{8} \) (multiply numerator and denominator by 4).
\( \frac{5}{8} \) remains \( \frac{5}{8} \).
- Step 3: Add the Fractions
\( \frac{5}{8} + \frac{4}{8} = \frac{9}{8} \)
- Step 4: Simplify
\( \frac{9}{8} \) is an improper fraction and can be written as \( 1 \frac{1}{8} \).
Answer: \( \frac{9}{8} \) or \( 1 \frac{1}{8} \)
---
- Step 1: Find the LCD
The denominators are 6 and 4. The LCD is 12.
- Step 2: Adjust the Fractions
Convert \( \frac{1}{6} \) to \( \frac{2}{12} \) (multiply numerator and denominator by 2).
Convert \( \frac{3}{4} \) to \( \frac{9}{12} \) (multiply numerator and denominator by 3).
- Step 3: Add the Fractions
\( \frac{2}{12} + \frac{9}{12} = \frac{11}{12} \)
- Step 4: Simplify
\( \frac{11}{12} \) is already in simplest form.
Answer: \( \frac{11}{12} \)
---
\[
\boxed{
\begin{array}{cc}
\frac{1}{2} + \frac{1}{3} = \frac{5}{6} & \frac{1}{3} + \frac{3}{5} = \frac{14}{15} \\
\frac{1}{2} + \frac{2}{3} = \frac{7}{6} & \frac{2}{5} + \frac{5}{6} = \frac{37}{30} \\
\frac{5}{6} + \frac{2}{5} = \frac{37}{30} & \frac{1}{4} + \frac{1}{6} = \frac{5}{12} \\
\frac{3}{7} + \frac{3}{5} = \frac{36}{35} & \frac{2}{5} + \frac{5}{9} = \frac{43}{45} \\
\frac{5}{8} + \frac{1}{2} = \frac{9}{8} & \frac{1}{6} + \frac{3}{4} = \frac{11}{12}
\end{array}
}
\]
1. Find a Common Denominator: The denominators of the fractions must be made the same so that they can be added directly.
2. Adjust the Numerators: Once the common denominator is found, adjust the numerators of the fractions accordingly.
3. Add the Fractions: Add the adjusted numerators and keep the common denominator.
4. Simplify the Result: If possible, simplify the resulting fraction.
Let's solve each problem step by step.
---
Problem 1: \( \frac{1}{2} + \frac{1}{3} \)
- Step 1: Find the Least Common Denominator (LCD)
The denominators are 2 and 3. The LCD is 6.
- Step 2: Adjust the Fractions
Convert \( \frac{1}{2} \) to \( \frac{3}{6} \) (multiply numerator and denominator by 3).
Convert \( \frac{1}{3} \) to \( \frac{2}{6} \) (multiply numerator and denominator by 2).
- Step 3: Add the Fractions
\( \frac{3}{6} + \frac{2}{6} = \frac{5}{6} \)
- Step 4: Simplify
\( \frac{5}{6} \) is already in simplest form.
Answer: \( \frac{5}{6} \)
---
Problem 2: \( \frac{1}{3} + \frac{3}{5} \)
- Step 1: Find the LCD
The denominators are 3 and 5. The LCD is 15.
- Step 2: Adjust the Fractions
Convert \( \frac{1}{3} \) to \( \frac{5}{15} \) (multiply numerator and denominator by 5).
Convert \( \frac{3}{5} \) to \( \frac{9}{15} \) (multiply numerator and denominator by 3).
- Step 3: Add the Fractions
\( \frac{5}{15} + \frac{9}{15} = \frac{14}{15} \)
- Step 4: Simplify
\( \frac{14}{15} \) is already in simplest form.
Answer: \( \frac{14}{15} \)
---
Problem 3: \( \frac{1}{2} + \frac{2}{3} \)
- Step 1: Find the LCD
The denominators are 2 and 3. The LCD is 6.
- Step 2: Adjust the Fractions
Convert \( \frac{1}{2} \) to \( \frac{3}{6} \) (multiply numerator and denominator by 3).
Convert \( \frac{2}{3} \) to \( \frac{4}{6} \) (multiply numerator and denominator by 2).
- Step 3: Add the Fractions
\( \frac{3}{6} + \frac{4}{6} = \frac{7}{6} \)
- Step 4: Simplify
\( \frac{7}{6} \) is an improper fraction and can be written as \( 1 \frac{1}{6} \).
Answer: \( \frac{7}{6} \) or \( 1 \frac{1}{6} \)
---
Problem 4: \( \frac{2}{5} + \frac{5}{6} \)
- Step 1: Find the LCD
The denominators are 5 and 6. The LCD is 30.
- Step 2: Adjust the Fractions
Convert \( \frac{2}{5} \) to \( \frac{12}{30} \) (multiply numerator and denominator by 6).
Convert \( \frac{5}{6} \) to \( \frac{25}{30} \) (multiply numerator and denominator by 5).
- Step 3: Add the Fractions
\( \frac{12}{30} + \frac{25}{30} = \frac{37}{30} \)
- Step 4: Simplify
\( \frac{37}{30} \) is an improper fraction and can be written as \( 1 \frac{7}{30} \).
Answer: \( \frac{37}{30} \) or \( 1 \frac{7}{30} \)
---
Problem 5: \( \frac{5}{6} + \frac{2}{5} \)
- Step 1: Find the LCD
The denominators are 6 and 5. The LCD is 30.
- Step 2: Adjust the Fractions
Convert \( \frac{5}{6} \) to \( \frac{25}{30} \) (multiply numerator and denominator by 5).
Convert \( \frac{2}{5} \) to \( \frac{12}{30} \) (multiply numerator and denominator by 6).
- Step 3: Add the Fractions
\( \frac{25}{30} + \frac{12}{30} = \frac{37}{30} \)
- Step 4: Simplify
\( \frac{37}{30} \) is an improper fraction and can be written as \( 1 \frac{7}{30} \).
Answer: \( \frac{37}{30} \) or \( 1 \frac{7}{30} \)
---
Problem 6: \( \frac{1}{4} + \frac{1}{6} \)
- Step 1: Find the LCD
The denominators are 4 and 6. The LCD is 12.
- Step 2: Adjust the Fractions
Convert \( \frac{1}{4} \) to \( \frac{3}{12} \) (multiply numerator and denominator by 3).
Convert \( \frac{1}{6} \) to \( \frac{2}{12} \) (multiply numerator and denominator by 2).
- Step 3: Add the Fractions
\( \frac{3}{12} + \frac{2}{12} = \frac{5}{12} \)
- Step 4: Simplify
\( \frac{5}{12} \) is already in simplest form.
Answer: \( \frac{5}{12} \)
---
Problem 7: \( \frac{3}{7} + \frac{3}{5} \)
- Step 1: Find the LCD
The denominators are 7 and 5. The LCD is 35.
- Step 2: Adjust the Fractions
Convert \( \frac{3}{7} \) to \( \frac{15}{35} \) (multiply numerator and denominator by 5).
Convert \( \frac{3}{5} \) to \( \frac{21}{35} \) (multiply numerator and denominator by 7).
- Step 3: Add the Fractions
\( \frac{15}{35} + \frac{21}{35} = \frac{36}{35} \)
- Step 4: Simplify
\( \frac{36}{35} \) is an improper fraction and can be written as \( 1 \frac{1}{35} \).
Answer: \( \frac{36}{35} \) or \( 1 \frac{1}{35} \)
---
Problem 8: \( \frac{2}{5} + \frac{5}{9} \)
- Step 1: Find the LCD
The denominators are 5 and 9. The LCD is 45.
- Step 2: Adjust the Fractions
Convert \( \frac{2}{5} \) to \( \frac{18}{45} \) (multiply numerator and denominator by 9).
Convert \( \frac{5}{9} \) to \( \frac{25}{45} \) (multiply numerator and denominator by 5).
- Step 3: Add the Fractions
\( \frac{18}{45} + \frac{25}{45} = \frac{43}{45} \)
- Step 4: Simplify
\( \frac{43}{45} \) is already in simplest form.
Answer: \( \frac{43}{45} \)
---
Problem 9: \( \frac{5}{8} + \frac{1}{2} \)
- Step 1: Find the LCD
The denominators are 8 and 2. The LCD is 8.
- Step 2: Adjust the Fractions
Convert \( \frac{1}{2} \) to \( \frac{4}{8} \) (multiply numerator and denominator by 4).
\( \frac{5}{8} \) remains \( \frac{5}{8} \).
- Step 3: Add the Fractions
\( \frac{5}{8} + \frac{4}{8} = \frac{9}{8} \)
- Step 4: Simplify
\( \frac{9}{8} \) is an improper fraction and can be written as \( 1 \frac{1}{8} \).
Answer: \( \frac{9}{8} \) or \( 1 \frac{1}{8} \)
---
Problem 10: \( \frac{1}{6} + \frac{3}{4} \)
- Step 1: Find the LCD
The denominators are 6 and 4. The LCD is 12.
- Step 2: Adjust the Fractions
Convert \( \frac{1}{6} \) to \( \frac{2}{12} \) (multiply numerator and denominator by 2).
Convert \( \frac{3}{4} \) to \( \frac{9}{12} \) (multiply numerator and denominator by 3).
- Step 3: Add the Fractions
\( \frac{2}{12} + \frac{9}{12} = \frac{11}{12} \)
- Step 4: Simplify
\( \frac{11}{12} \) is already in simplest form.
Answer: \( \frac{11}{12} \)
---
Final Answers
\[
\boxed{
\begin{array}{cc}
\frac{1}{2} + \frac{1}{3} = \frac{5}{6} & \frac{1}{3} + \frac{3}{5} = \frac{14}{15} \\
\frac{1}{2} + \frac{2}{3} = \frac{7}{6} & \frac{2}{5} + \frac{5}{6} = \frac{37}{30} \\
\frac{5}{6} + \frac{2}{5} = \frac{37}{30} & \frac{1}{4} + \frac{1}{6} = \frac{5}{12} \\
\frac{3}{7} + \frac{3}{5} = \frac{36}{35} & \frac{2}{5} + \frac{5}{9} = \frac{43}{45} \\
\frac{5}{8} + \frac{1}{2} = \frac{9}{8} & \frac{1}{6} + \frac{3}{4} = \frac{11}{12}
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of adding unlike fractions.
