Add or subtract these 7ractions.-you answer in simplets form and as a mixed number where appropriate. a) $$ 1 \frac{4}{5}+\frac{3}{4} $$ e) $$ 5 \frac{2}{9}-\frac{1}{3} $$ F) $$ 1 \frac{1}{4}+2 \frac{2}{5} $$ g) $$ 3 \frac{5}{6}-1 \frac{4}{5} $$ h) $$ 2 \frac{4}{7}-1 \frac{4}{5} $$

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Let's solve each of the problems step by step, converting mixed numbers to improper fractions where necessary and then performing the addition or subtraction.

### a) $$ 1 \frac{4}{5} + \frac{3}{4} $$

1. Convert $$ 1 \frac{4}{5} $$ to an improper fraction:
   $$
   1 \frac{4}{5} = \frac{1 \times 5 + 4}{5} = \frac{9}{5}
   $$

2. Find a common denominator for $$ \frac{9}{5} $$ and $$ \frac{3}{4} $$. The least common multiple of 5 and 4 is 20.

3. Convert both fractions:
   $$
   \frac{9}{5} = \frac{9 \times 4}{5 \times 4} = \frac{36}{20}
   $$
   $$
   \frac{3}{4} = \frac{3 \times 5}{4 \times 5} = \frac{15}{20}
   $$

4. Add the fractions:
   $$
   \frac{36}{20} + \frac{15}{20} = \frac{51}{20}
   $$

5. Convert to a mixed number:
   $$
   \frac{51}{20} = 2 \frac{11}{20}
   $$

### e) $$ 5 \frac{2}{9} - \frac{1}{3} $$

1. Convert $$ 5 \frac{2}{9} $$ to an improper fraction:
   $$
   5 \frac{2}{9} = \frac{5 \times 9 + 2}{9} = \frac{47}{9}
   $$

2. Find a common denominator for $$ \frac{47}{9} $$ and $$ \frac{1}{3} $$. The least common multiple of 9 and 3 is 9.

3. Convert $$ \frac{1}{3} $$:
   $$
   \frac{1}{3} = \frac{1 \times 3}{3 \times 3} = \frac{3}{9}
   $$

4. Subtract the fractions:
   $$
   \frac{47}{9} - \frac{3}{9} = \frac{44}{9}
   $$

5. Convert to a mixed number:
   $$
   \frac{44}{9} = 4 \frac{8}{9}
   $$

### f) $$ 1 \frac{1}{4} + 2 \frac{2}{5} $$

1. Convert both mixed numbers to improper fractions:
   $$
   1 \frac{1}{4} = \frac{1 \times 4 + 1}{4} = \frac{5}{4}
   $$
   $$
   2 \frac{2}{5} = \frac{2 \times 5 + 2}{5} = \frac{12}{5}
   $$

2. Find a common denominator for $$ \frac{5}{4} $$ and $$ \frac{12}{5} $$. The least common multiple of 4 and 5 is 20.

3. Convert both fractions:
   $$
   \frac{5}{4} = \frac{5 \times 5}{4 \times 5} = \frac{25}{20}
   $$
   $$
   \frac{12}{5} = \frac{12 \times 4}{5 \times 4} = \frac{48}{20}
   $$

4. Add the fractions:
   $$
   \frac{25}{20} + \frac{48}{20} = \frac{73}{20}
   $$

5. Convert to a mixed number:
   $$
   \frac{73}{20} = 3 \frac{13}{20}
   $$

### g) $$ 3 \frac{5}{6} - 1 \frac{4}{5} $$

1. Convert both mixed numbers to improper fractions:
   $$
   3 \frac{5}{6} = \frac{3 \times 6 + 5}{6} = \frac{23}{6}
   $$
   $$
   1 \frac{4}{5} = \frac{1 \times 5 + 4}{5} = \frac{9}{5}
   $$

2. Find a common denominator for $$ \frac{23}{6} $$ and $$ \frac{9}{5} $$. The least common multiple of 6 and 5 is 30.

3. Convert both fractions:
   $$
   \frac{23}{6} = \frac{23 \times 5}{6 \times 5} = \frac{115}{30}
   $$
   $$
   \frac{9}{5} = \frac{9 \times 6}{5 \times 6} = \frac{54}{30}
   $$

4. Subtract the fractions:
   $$
   \frac{115}{30} - \frac{54}{30} = \frac{61}{30}
   $$

5. Convert to a mixed number:
   $$
   \frac{61}{30} = 2 \frac{1}{30}
   $$

### h) $$ 2 \frac{4}{7} - 1 \frac{4}{5} $$

1. Convert both mixed numbers to improper fractions:
   $$
   2 \frac{4}{7} = \frac{2 \times 7 + 4}{7} = \frac{18}{7}
   $$
   $$
   1 \frac{4}{5} = \frac{1 \times 5 + 4}{5} = \frac{9}{5}
   $$

2. Find a common denominator for $$ \frac{18}{7} $$ and $$ \frac{9}{5} $$. The least common multiple of 7 and 5 is 35.

3. Convert both fractions:
   $$
   \frac{18}{7} = \frac{18 \times 5}{7 \times 5} = \frac{90}{35}
   $$
   $$
   \frac{9}{5} = \frac{9 \times 7}{5 \times 7} = \frac{63}{35}
   $$

4. Subtract the fractions:
   $$
   \frac{90}{35} - \frac{63}{35} = \frac{27}{35}
   $$

5. This fraction is already in simplest form and does not need to be converted to a mixed number.

### Summary of Results:
- a) $$ 1 \frac{4}{5} + \frac{3}{4} = 2 \frac{11}{20} $$
- e) $$ 5 \frac{2}{
- a) $$ 1 \frac{4}{5} + \frac{3}{4} = 2 \frac{11}{20} $$ - e) $$ 5 \frac{2}{9} - \frac{1}{3} = 4 \frac{8}{9} $$ - f) $$ 1 \frac{1}{4} + 2 \frac{2}{5} = 3 \frac{13}{20} $$ - g) $$ 3 \frac{5}{6} - 1 \frac{4}{5} = 2 \frac{1}{30} $$ - h) $$ 2 \frac{4}{7} - 1 \frac{4}{5} = \frac{27}{35} $$

Add or subtract these 7ractions.-you answer in simplets form and as a mixed number where appropriate. a) \( 1 \frac{4}{5}+\frac{3}{4} \) e) \( 5 \frac{2}{9}-\frac{1}{3} \) F) \( 1 \frac{1}{4}+2 \frac{2}{5} \) g) \( 3 \frac{5}{6}-1 \frac{4}{5} \) h) \( 2 \frac{4}{7}-1 \frac{4}{5} \)

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