Grade 6 math worksheet on adding mixed numbers with eight practice problems.

Problem: Addition with Mixed Numbers

The task is to solve the addition of mixed numbers for each given problem. Let's solve them step by step.

#### Step-by-Step Solution:

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i. \( 3 \frac{1}{2} + 2 \frac{2}{3} \)

1. Convert mixed numbers to improper fractions:
- \( 3 \frac{1}{2} = 3 + \frac{1}{2} = \frac{6}{2} + \frac{1}{2} = \frac{7}{2} \)
- \( 2 \frac{2}{3} = 2 + \frac{2}{3} = \frac{6}{3} + \frac{2}{3} = \frac{8}{3} \)

2. Find a common denominator:
- The denominators are 2 and 3. The least common denominator (LCD) is 6.
- Convert each fraction:
- \( \frac{7}{2} = \frac{7 \times 3}{2 \times 3} = \frac{21}{6} \)
- \( \frac{8}{3} = \frac{8 \times 2}{3 \times 2} = \frac{16}{6} \)

3. Add the fractions:
- \( \frac{21}{6} + \frac{16}{6} = \frac{21 + 16}{6} = \frac{37}{6} \)

4. Convert back to a mixed number:
- \( \frac{37}{6} = 6 \frac{1}{6} \) (since \( 37 \div 6 = 6 \) remainder 1)

Answer: \( 6 \frac{1}{6} \)

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ii. \( 2 \frac{2}{3} + 4 \frac{1}{2} \)

1. Convert mixed numbers to improper fractions:
- \( 2 \frac{2}{3} = 2 + \frac{2}{3} = \frac{6}{3} + \frac{2}{3} = \frac{8}{3} \)
- \( 4 \frac{1}{2} = 4 + \frac{1}{2} = \frac{8}{2} + \frac{1}{2} = \frac{9}{2} \)

2. Find a common denominator:
- The denominators are 3 and 2. The least common denominator (LCD) is 6.
- Convert each fraction:
- \( \frac{8}{3} = \frac{8 \times 2}{3 \times 2} = \frac{16}{6} \)
- \( \frac{9}{2} = \frac{9 \times 3}{2 \times 3} = \frac{27}{6} \)

3. Add the fractions:
- \( \frac{16}{6} + \frac{27}{6} = \frac{16 + 27}{6} = \frac{43}{6} \)

4. Convert back to a mixed number:
- \( \frac{43}{6} = 7 \frac{1}{6} \) (since \( 43 \div 6 = 7 \) remainder 1)

Answer: \( 7 \frac{1}{6} \)

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iii. \( 2 \frac{1}{3} + 4 \frac{1}{2} \)

1. Convert mixed numbers to improper fractions:
- \( 2 \frac{1}{3} = 2 + \frac{1}{3} = \frac{6}{3} + \frac{1}{3} = \frac{7}{3} \)
- \( 4 \frac{1}{2} = 4 + \frac{1}{2} = \frac{8}{2} + \frac{1}{2} = \frac{9}{2} \)

2. Find a common denominator:
- The denominators are 3 and 2. The least common denominator (LCD) is 6.
- Convert each fraction:
- \( \frac{7}{3} = \frac{7 \times 2}{3 \times 2} = \frac{14}{6} \)
- \( \frac{9}{2} = \frac{9 \times 3}{2 \times 3} = \frac{27}{6} \)

3. Add the fractions:
- \( \frac{14}{6} + \frac{27}{6} = \frac{14 + 27}{6} = \frac{41}{6} \)

4. Convert back to a mixed number:
- \( \frac{41}{6} = 6 \frac{5}{6} \) (since \( 41 \div 6 = 6 \) remainder 5)

Answer: \( 6 \frac{5}{6} \)

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iv. \( 4 \frac{1}{2} + 2 \frac{2}{3} \)

1. Convert mixed numbers to improper fractions:
- \( 4 \frac{1}{2} = 4 + \frac{1}{2} = \frac{8}{2} + \frac{1}{2} = \frac{9}{2} \)
- \( 2 \frac{2}{3} = 2 + \frac{2}{3} = \frac{6}{3} + \frac{2}{3} = \frac{8}{3} \)

2. Find a common denominator:
- The denominators are 2 and 3. The least common denominator (LCD) is 6.
- Convert each fraction:
- \( \frac{9}{2} = \frac{9 \times 3}{2 \times 3} = \frac{27}{6} \)
- \( \frac{8}{3} = \frac{8 \times 2}{3 \times 2} = \frac{16}{6} \)

3. Add the fractions:
- \( \frac{27}{6} + \frac{16}{6} = \frac{27 + 16}{6} = \frac{43}{6} \)

4. Convert back to a mixed number:
- \( \frac{43}{6} = 7 \frac{1}{6} \) (since \( 43 \div 6 = 7 \) remainder 1)

Answer: \( 7 \frac{1}{6} \)

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v. \( 2 \frac{1}{2} + 4 \frac{1}{2} \)

1. Convert mixed numbers to improper fractions:
- \( 2 \frac{1}{2} = 2 + \frac{1}{2} = \frac{4}{2} + \frac{1}{2} = \frac{5}{2} \)
- \( 4 \frac{1}{2} = 4 + \frac{1}{2} = \frac{8}{2} + \frac{1}{2} = \frac{9}{2} \)

2. Add the fractions:
- Since the denominators are the same, add the numerators directly:
- \( \frac{5}{2} + \frac{9}{2} = \frac{5 + 9}{2} = \frac{14}{2} \)

3. Simplify the fraction:
- \( \frac{14}{2} = 7 \)

Answer: \( 7 \)

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vi. \( 4 \frac{1}{2} + 2 \frac{1}{4} \)

1. Convert mixed numbers to improper fractions:
- \( 4 \frac{1}{2} = 4 + \frac{1}{2} = \frac{8}{2} + \frac{1}{2} = \frac{9}{2} \)
- \( 2 \frac{1}{4} = 2 + \frac{1}{4} = \frac{8}{4} + \frac{1}{4} = \frac{9}{4} \)

2. Find a common denominator:
- The denominators are 2 and 4. The least common denominator (LCD) is 4.
- Convert each fraction:
- \( \frac{9}{2} = \frac{9 \times 2}{2 \times 2} = \frac{18}{4} \)
- \( \frac{9}{4} \) remains \( \frac{9}{4} \)

3. Add the fractions:
- \( \frac{18}{4} + \frac{9}{4} = \frac{18 + 9}{4} = \frac{27}{4} \)

4. Convert back to a mixed number:
- \( \frac{27}{4} = 6 \frac{3}{4} \) (since \( 27 \div 4 = 6 \) remainder 3)

Answer: \( 6 \frac{3}{4} \)

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vii. \( 3 \frac{1}{2} + 2 \frac{1}{2} \)

1. Convert mixed numbers to improper fractions:
- \( 3 \frac{1}{2} = 3 + \frac{1}{2} = \frac{6}{2} + \frac{1}{2} = \frac{7}{2} \)
- \( 2 \frac{1}{2} = 2 + \frac{1}{2} = \frac{4}{2} + \frac{1}{2} = \frac{5}{2} \)

2. Add the fractions:
- Since the denominators are the same, add the numerators directly:
- \( \frac{7}{2} + \frac{5}{2} = \frac{7 + 5}{2} = \frac{12}{2} \)

3. Simplify the fraction:
- \( \frac{12}{2} = 6 \)

Answer: \( 6 \)

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viii. \( 2 \frac{1}{4} + 4 \frac{1}{2} \)

1. Convert mixed numbers to improper fractions:
- \( 2 \frac{1}{4} = 2 + \frac{1}{4} = \frac{8}{4} + \frac{1}{4} = \frac{9}{4} \)
- \( 4 \frac{1}{2} = 4 + \frac{1}{2} = \frac{8}{2} + \frac{1}{2} = \frac{9}{2} \)

2. Find a common denominator:
- The denominators are 4 and 2. The least common denominator (LCD) is 4.
- Convert each fraction:
- \( \frac{9}{4} \) remains \( \frac{9}{4} \)
- \( \frac{9}{2} = \frac{9 \times 2}{2 \times 2} = \frac{18}{4} \)

3. Add the fractions:
- \( \frac{9}{4} + \frac{18}{4} = \frac{9 + 18}{4} = \frac{27}{4} \)

4. Convert back to a mixed number:
- \( \frac{27}{4} = 6 \frac{3}{4} \) (since \( 27 \div 4 = 6 \) remainder 3)

Answer: \( 6 \frac{3}{4} \)

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Final Answers:

\[
\boxed{
\begin{aligned}
&\text{i. } 6 \frac{1}{6} \\
&\text{ii. } 7 \frac{1}{6} \\
&\text{iii. } 6 \frac{5}{6} \\
&\text{iv. } 7 \frac{1}{6} \\
&\text{v. } 7 \\
&\text{vi. } 6 \frac{3}{4} \\
&\text{vii. } 6 \\
&\text{viii. } 6 \frac{3}{4}
\end{aligned}
}
\]