Question

*Work the problems out in your notebook. First you will need to find a common denominator. Next you will rewrite the problems using equivalent fractions. Then add or subtract.

5 1/9 - 2 1/3
Answer:


2 ¼ + 8 ⅔
Answer:


4 ⅗ + 11 2/15
Answer:

Answer 1

To solve these problems, we first need to convert the mixed numbers into improper fractions, find a common denominator for the fractions involved, and then perform the addition or subtraction. Let’s work through each problem step-by-step.

### Problem 1: \( 5 \frac{1}{9} - 2 \frac{1}{3} \)

1. **Convert mixed numbers to improper fractions:**
- \( 5 \frac{1}{9} = \frac{5 \times 9 + 1}{9} = \frac{45 + 1}{9} = \frac{46}{9} \)
- \( 2 \frac{1}{3} = \frac{2 \times 3 + 1}{3} = \frac{6 + 1}{3} = \frac{7}{3} \)

2. **Find a common denominator:**
- The denominators are 9 and 3. The least common denominator (LCD) is 9.

3. **Rewrite \( \frac{7}{3} \) with a denominator of 9:**
\[
\frac{7}{3} = \frac{7 \times 3}{3 \times 3} = \frac{21}{9}
\]

4. **Now perform the subtraction:**
\[
\frac{46}{9} - \frac{21}{9} = \frac{46 - 21}{9} = \frac{25}{9}
\]

5. **Convert back to a mixed number:**
\[
\frac{25}{9} = 2 \frac{7}{9}
\]

**Answer:** \( 2 \frac{7}{9} \)

---

### Problem 2: \( 2 \frac{1}{4} + 8 \frac{2}{3} \)

1. **Convert mixed numbers to improper fractions:**
- \( 2 \frac{1}{4} = \frac{2 \times 4 + 1}{4} = \frac{8 + 1}{4} = \frac{9}{4} \)
- \( 8 \frac{2}{3} = \frac{8 \times 3 + 2}{3} = \frac{24 + 2}{3} = \frac{26}{3} \)

2. **Find a common denominator:**
- The denominators are 4 and 3. The least common denominator (LCD) is 12.

3. **Rewrite the fractions with a denominator of 12:**
\[
\frac{9}{4} = \frac{9 \times 3}{4 \times 3} = \frac{27}{12}
\]
\[
\frac{26}{3} = \frac{26 \times 4}{3 \times 4} = \frac{104}{12}
\]

4. **Now perform the addition:**
\[
\frac{27}{12} + \frac{104}{12} = \frac{27 + 104}{12} = \frac{131}{12}
\]

5. **Convert back to a mixed number:**
\[
\frac{131}{12} = 10 \frac{11}{12}
\]

**Answer:** \( 10 \frac{11}{12} \)

---

### Problem 3: \( 4 \frac{3}{5} + 11 \frac{2}{15} \)

1. **Convert mixed numbers to improper fractions:**
- \( 4 \frac{3}{5} = \frac{4 \times 5 + 3}{5} = \frac{20 + 3}{5} = \frac{23}{5} \)
- \( 11 \frac{2}{15} = \frac{11 \times 15 + 2}{15} = \frac{165 + 2}{15} = \frac{167}{15} \)

2. **Find a common denominator:**
- The denominators are 5 and 15. The least common denominator (LCD) is 15.

3. **Rewrite \( \frac{23}{5} \) with a denominator of 15:**
\[
\frac{23}{5} = \frac{23 \times 3}{5 \times 3} = \frac{69}{15}
\]

4. **Now perform the addition:**
\[
\frac{69}{15} + \frac{167}{15} = \frac{69 + 167}{15} = \frac{236}{15}
\]

5. **Convert back to a mixed number:**
\[
\frac{236}{15} = 15 \frac{11}{15}
\]

**Answer:** \( 15 \frac{11}{15} \)

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### Summary of Answers:
1. \( 2 \frac{7}{9} \)
2. \( 10 \frac{11}{12} \)
3. \( 15 \frac{11}{15} \)