Adding & Subtracting with Mixed Numbers - Use visual models to solve fraction problems.

To solve the problems involving mixed numbers using the visual models, let's go through each problem step by step.

Problem 1:

Visual Model:
- First circle: Fully shaded (1 whole)
- Second circle: Half shaded ($\frac{1}{4}$)
- Third circle: Fully shaded (1 whole)
- Fourth circle: Three-quarters shaded ($\frac{3}{4}$)

Mixed Numbers:
\[ 1 \frac{1}{4} + 1 \frac{3}{4} \]

Solution:
1. Add the whole numbers: \(1 + 1 = 2\)
2. Add the fractions: \(\frac{1}{4} + \frac{3}{4} = \frac{4}{4} = 1\)
3. Combine the results: \(2 + 1 = 3\)

Answer:
\[ 1 \frac{1}{4} + 1 \frac{3}{4} = 3 \]

Problem 2:

Visual Model:
- First set: 2 wholes and 3 out of 4 parts shaded
- Second set: 1 whole and 1 out of 4 parts shaded

Mixed Numbers:
\[ 2 \frac{3}{4} - 1 \frac{1}{4} \]

Solution:
1. Subtract the whole numbers: \(2 - 1 = 1\)
2. Subtract the fractions: \(\frac{3}{4} - \frac{1}{4} = \frac{2}{4} = \frac{1}{2}\)
3. Combine the results: \(1 + \frac{1}{2} = 1 \frac{1}{2}\)

Answer:
\[ 2 \frac{3}{4} - 1 \frac{1}{4} = 1 \frac{1}{2} \]

Problem 3:

Visual Model:
- First set: 2 wholes and 3 out of 6 parts shaded
- Second set: 1 whole and 2 out of 6 parts shaded

Mixed Numbers:
\[ 2 \frac{3}{6} + 1 \frac{2}{6} \]

Solution:
1. Add the whole numbers: \(2 + 1 = 3\)
2. Add the fractions: \(\frac{3}{6} + \frac{2}{6} = \frac{5}{6}\)
3. Combine the results: \(3 + \frac{5}{6} = 3 \frac{5}{6}\)

Answer:
\[ 2 \frac{3}{6} + 1 \frac{2}{6} = 3 \frac{5}{6} \]

Problem 4:

Visual Model:
- First set: 2 wholes and 6 out of 8 parts shaded
- Second set: 1 whole and 4 out of 8 parts shaded

Mixed Numbers:
\[ 2 \frac{6}{8} - 1 \frac{4}{8} \]

Solution:
1. Subtract the whole numbers: \(2 - 1 = 1\)
2. Subtract the fractions: \(\frac{6}{8} - \frac{4}{8} = \frac{2}{8} = \frac{1}{4}\)
3. Combine the results: \(1 + \frac{1}{4} = 1 \frac{1}{4}\)

Answer:
\[ 2 \frac{6}{8} - 1 \frac{4}{8} = 1 \frac{1}{4} \]

Problem 5:

Visual Model:
- First set: 2 wholes and 7 out of 10 parts shaded
- Second set: 1 whole and 7 out of 10 parts shaded

Mixed Numbers:
\[ 2 \frac{7}{10} - 1 \frac{7}{10} \]

Solution:
1. Subtract the whole numbers: \(2 - 1 = 1\)
2. Subtract the fractions: \(\frac{7}{10} - \frac{7}{10} = 0\)
3. Combine the results: \(1 + 0 = 1\)

Answer:
\[ 2 \frac{7}{10} - 1 \frac{7}{10} = 1 \]

Final Answers:

1. \( 1 \frac{1}{4} + 1 \frac{3}{4} = \boxed{3} \)
2. \( 2 \frac{3}{4} - 1 \frac{1}{4} = \boxed{1 \frac{1}{2}} \)
3. \( 2 \frac{3}{6} + 1 \frac{2}{6} = \boxed{3 \frac{5}{6}} \)
4. \( 2 \frac{6}{8} - 1 \frac{4}{8} = \boxed{1 \frac{1}{4}} \)
5. \( 2 \frac{7}{10} - 1 \frac{7}{10} = \boxed{1} \)