a) $$ 4 \frac{2}{3} $$ b) $$ 1 \frac{1}{9} $$ C) $$ 3 \frac{6}{7} $$ d) $$ 2 \frac{14}{15} $$ e) $$ 5 \frac{3}{15} $$ f) $$ 10 \frac{7}{8} $$ 3. Convert these improper fractions to mixed numbers: a) $$ \frac{14}{5} $$ b) $$ \frac{7}{2} $$ C) $$ \frac{21}{4} $$ d) $$ \frac{36}{7} $$ e) $$ \frac{19}{8} $$ f) $$ \frac{9}{5} $$ 4. Add or subtract these fractions. Write your answer in simplest form, and as mixed number: where appropriate: c) $$ \frac{4}{5}-\frac{1}{3} $$ a) $$ \frac{1}{5}+\frac{3}{5} $$ b) $$ \frac{5}{9}+\frac{4}{9} $$ d) $$ \frac{1}{6}+\frac{2}{3} $$ e) $$ \frac{7}{10}-\frac{2}{5} $$ f) $$ \frac{2}{5}+\frac{3}{4} $$ g) $$ \frac{1}{2}-\frac{3}{7} $$ h) $$ \frac{1}{6}+\frac{1}{5} $$ (LCM) of the denominators. Spot On Mathematics Grade 8

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UpStudy AI · Accepted Answer

Let's break down the problem step by step.

### Step 1: Convert Mixed Numbers to Improper Fractions

1. **Convert $$ 4 \frac{2}{3} $$**:
   $$
   4 \frac{2}{3} = 4 \times 3 + 2 = 12 + 2 = \frac{14}{3}
   $$

2. **Convert $$ 1 \frac{1}{9} $$**:
   $$
   1 \frac{1}{9} = 1 \times 9 + 1 = 9 + 1 = \frac{10}{9}
   $$

3. **Convert $$ 3 \frac{6}{7} $$**:
   $$
   3 \frac{6}{7} = 3 \times 7 + 6 = 21 + 6 = \frac{27}{7}
   $$

4. **Convert $$ 2 \frac{14}{15} $$**:
   $$
   2 \frac{14}{15} = 2 \times 15 + 14 = 30 + 14 = \frac{44}{15}
   $$

5. **Convert $$ 5 \frac{3}{15} $$**:
   $$
   5 \frac{3}{15} = 5 \times 15 + 3 = 75 + 3 = \frac{78}{15}
   $$

6. **Convert $$ 10 \frac{7}{8} $$**:
   $$
   10 \frac{7}{8} = 10 \times 8 + 7 = 80 + 7 = \frac{87}{8}
   $$

### Step 2: Convert Improper Fractions to Mixed Numbers

1. **Convert $$ \frac{14}{5} $$**:
   $$
   14 \div 5 = 2 \quad \text{(remainder 4)} \quad \Rightarrow \quad 2 \frac{4}{5}
   $$

2. **Convert $$ \frac{7}{2} $$**:
   $$
   7 \div 2 = 3 \quad \text{(remainder 1)} \quad \Rightarrow \quad 3 \frac{1}{2}
   $$

3. **Convert $$ \frac{21}{4} $$**:
   $$
   21 \div 4 = 5 \quad \text{(remainder 1)} \quad \Rightarrow \quad 5 \frac{1}{4}
   $$

4. **Convert $$ \frac{36}{7} $$**:
   $$
   36 \div 7 = 5 \quad \text{(remainder 1)} \quad \Rightarrow \quad 5 \frac{1}{7}
   $$

5. **Convert $$ \frac{19}{8} $$**:
   $$
   19 \div 8 = 2 \quad \text{(remainder 3)} \quad \Rightarrow \quad 2 \frac{3}{8}
   $$

6. **Convert $$ \frac{9}{5} $$**:
   $$
   9 \div 5 = 1 \quad \text{(remainder 4)} \quad \Rightarrow \quad 1 \frac{4}{5}
   $$

### Step 3: Add or Subtract the Fractions

1. **Calculate $$ \frac{4}{5} - \frac{1}{3} $$**:
   - LCM of 5 and 3 is 15.
   $$
   \frac{4}{5} = \frac{12}{15}, \quad \frac{1}{3} = \frac{5}{15} \quad \Rightarrow \quad \frac{12}{15} - \frac{5}{15} = \frac{7}{15}
   $$

2. **Calculate $$ \frac{1}{5} + \frac{3}{5} $$**:
   $$
   \frac{1}{5} + \frac{3}{5} = \frac{4}{5}
   $$

3. **Calculate $$ \frac{5}{9} + \frac{4}{9} $$**:
   $$
   \frac{5}{9} + \frac{4}{9} = \frac{9}{9} = 1
   $$

4. **Calculate $$ \frac{1}{6} + \frac{2}{3} $$**:
   - LCM of 6 and 3 is 6.
   $$
   \frac{1}{6} + \frac{4}{6} = \frac{5}{6}
   $$

5. **Calculate $$ \frac{7}{10} - \frac{2}{5} $$**:
   - LCM of 10 and 5 is 10.
   $$
   \frac{7}{10} - \frac{4}{10} = \frac{3}{10}
   $$

6. **Calculate $$ \frac{2}{5} + \frac{3}{4} $$**:
   - LCM of 5 and 4 is 20.
   $$
   \frac{8}{20} + \frac{15}{20} = \frac{23}{20} = 1 \frac{3}{20}
   $$

7. **Calculate $$ \frac{1}{2} - \frac{3}{7} $$**:
   - LCM of 2 and 7 is 14.
   $$
   \frac{7}{14} - \frac{6}{14} = \frac{1}{14}
   $$

8. **Calculate $$ \frac{1}{6} + \frac{1}{5} $$**:
   - LCM of 6 and 5 is 30.
   $$
   \frac{5}{30} + \frac{6}{30} = \frac{11}{30}
   $$

### Summary of Results

**Mixed Numbers to Improper Fractions:**
- $$ 4 \frac{2}{3} = \frac{14}{3} $$
- $$ 1 \frac{1}{9} = \frac{10}{9} $$
- $$ 3 \frac{6}{7} = \frac{27}{7} $$
- $$ 2 \frac{14}{15} = \frac{44}{15} $$
- $$ 5 \frac{3}{15} = \frac{78}{15} $$
- $$ 10 \frac{7}{8} = \frac{87}{8} $$

**Improper Fractions to Mixed Numbers:**
- $$ \frac{14}{5} = 2 \frac{4}{5} $$
- $$ \frac{7}{2} = 3 \frac{1}{2} $$
- $$ \frac{
**Mixed Numbers to Improper Fractions:** - $$ 4 \frac{2}{3} = \frac{14}{3} $$ - $$ 1 \frac{1}{9} = \frac{10}{9} $$ - $$ 3 \frac{6}{7} = \frac{27}{7} $$ - $$ 2 \frac{14}{15} = \frac{44}{15} $$ - $$ 5 \frac{3}{15} = \frac{78}{15} $$ - $$ 10 \frac{7}{8} = \frac{87}{8} $$ **Improper Fractions to Mixed Numbers:** - $$ \frac{14}{5} = 2 \frac{4}{5} $$ - $$ \frac{7}{2} = 3 \frac{1}{2} $$ - $$ \frac{21}{4} = 5 \frac{1}{4} $$ - $$ \frac{36}{7} = 5 \frac{1}{7} $$ - $$ \frac{19}{8} = 2 \frac{3}{8} $$ - $$ \frac{9}{5} = 1 \frac{4}{5} $$ **Addition and Subtraction of Fractions:** 1. $$ \frac{4}{5} - \frac{1}{3} = \frac{7}{15} $$ 2. $$ \frac{1}{5} + \frac{3}{5} = \frac{4}{5} $$ 3. $$ \frac{5}{9} + \frac{4}{9} = 1 $$ 4. $$ \frac{1}{6} + \frac{2}{3} = \frac{5}{6} $$ 5. $$ \frac{7}{10} - \frac{2}{5} = \frac{3}{10} $$ 6. $$ \frac{2}{5} + \frac{3}{4} = 1 \frac{3}{20} $$ 7. $$ \frac{1}{2} - \frac{3}{7} = \frac{1}{14} $$ 8. $$ \frac{1}{6} + \frac{1}{5} = \frac{11}{30} $$

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