Adding Fractions With Unlike Denominators Practice Activities for ... - Free Printable

It looks like you've uploaded a worksheet titled "Adding Fractions With Unlike Denominators" that contains several problems where students are required to add fractions with different denominators. Since I can't view images directly, I'll explain how to solve such problems step-by-step and then walk through examples based on the typical format of these worksheets.

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🔧 How to Add Fractions with Unlike Denominators

To add fractions with unlike denominators (e.g., 1/4 + 1/3), follow these steps:

#### ✔ Step 1: Find the Least Common Denominator (LCD)
- The LCD is the smallest number that both denominators divide into evenly.
- You can find it by listing multiples or using prime factorization.

#### ✔ Step 2: Convert Each Fraction
- Rewrite each fraction so that they have the same denominator (the LCD).
- Multiply numerator and denominator by the same number.

#### ✔ Step 3: Add the Numerators
- Keep the common denominator and add only the numerators.

#### ✔ Step 4: Simplify the Result
- Reduce the fraction if possible.

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Let’s go through some sample problems from the worksheet format you provided.

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📌 Example Problems (Based on Worksheet Layout)

#### Problem 1:
\[
\frac{1}{6} + \frac{1}{10}
\]

Step 1: Find LCD of 6 and 10
Multiples of 6: 6, 12, 18, 24, 30, ...
Multiples of 10: 10, 20, 30, ...
→ LCD = 30

Step 2: Convert fractions
\[
\frac{1}{6} = \frac{5}{30}, \quad \frac{1}{10} = \frac{3}{30}
\]

Step 3: Add
\[
\frac{5}{30} + \frac{3}{30} = \frac{8}{30}
\]

Step 4: Simplify
\[
\frac{8}{30} = \frac{4}{15}
\]

✔ Answer: $\boxed{\frac{4}{15}}$

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#### Problem 2:
\[
\frac{1}{9} + \frac{1}{15}
\]

LCD of 9 and 15:
9 = 3×3, 15 = 3×5 → LCM = 3×3×5 = 45

Convert:
\[
\frac{1}{9} = \frac{5}{45}, \quad \frac{1}{15} = \frac{3}{45}
\]
Add:
\[
\frac{5}{45} + \frac{3}{45} = \frac{8}{45}
\]

✔ Answer: $\boxed{\frac{8}{45}}$ (already simplified)

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#### Problem 3:
\[
\frac{1}{2} + \frac{1}{3} + \frac{1}{6}
\]

LCD of 2, 3, 6 = 6

Convert:
\[
\frac{1}{2} = \frac{3}{6}, \quad \frac{1}{3} = \frac{2}{6}, \quad \frac{1}{6} = \frac{1}{6}
\]

Add:
\[
\frac{3}{6} + \frac{2}{6} + \frac{1}{6} = \frac{6}{6} = 1
\]

✔ Answer: $\boxed{1}$

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#### Problem 4:
\[
\frac{3}{10} + \frac{1}{12}
\]

LCD of 10 and 12:
10 = 2×5, 12 = 2²×3 → LCM = 2²×3×5 = 60

Convert:
\[
\frac{3}{10} = \frac{18}{60}, \quad \frac{1}{12} = \frac{5}{60}
\]

Add:
\[
\frac{18}{60} + \frac{5}{60} = \frac{23}{60}
\]

✔ Answer: $\boxed{\frac{23}{60}}$

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#### Problem 5:
\[
\frac{1}{2} + \frac{1}{4} + \frac{1}{8}
\]

LCD of 2, 4, 8 = 8

Convert:
\[
\frac{1}{2} = \frac{4}{8}, \quad \frac{1}{4} = \frac{2}{8}, \quad \frac{1}{8} = \frac{1}{8}
\]

Add:
\[
\frac{4}{8} + \frac{2}{8} + \frac{1}{8} = \frac{7}{8}
\]

✔ Answer: $\boxed{\frac{7}{8}}$

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📘 Tips for Solving These Problems

- Always check if the answer can be simplified.
- Use cross-multiplication or prime factorization to find LCD efficiently.
- For more than two fractions, find the LCD of all denominators at once.

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