Question
*Find a common denominator for each problem. Next rewrite the fractions using equivalent fractions. Then solve the addition problems.
-Example: 2 ⅓ + 1 2/4
3: 3, 6, 9, 12
4: 4, 8, 12
Common Denominator is: 12
2 ⅓ = ( 1x4= 4 and 3x4 = 12 so 2 4/12)
1 2/4 = (2x3 = 6 and 4x3=12 so 1 6/12)
Answer: 2 4/12 + 1 6/12 = 3 10/12
1 1/10 + 2 4/5
10:
5:
Common Denominator is:
1 1/10 =
2 4/5 =
Answer:
3 ⅔ + 1 4/6
3:
6:
Common Denominator is:
3 ⅔ =
1 4/6 =
Answer:
2 6/12 + 1 1/2
12:
2:
Common Denominator is:
2 6/12 =
1 ½ =
Answer:
Answers
GPT-4o mini
Let's go through each problem step by step.
### Problem 1: \(1 \frac{1}{10} + 2 \frac{4}{5}\)
1. **Finding the common denominator:**
- Denominators: 10 and 5
- Common multiples: 10, 20
- Common Denominator is: **10**
2. **Rewriting the fractions:**
- \(1 \frac{1}{10} = 1 \frac{1}{10} \) (no change needed)
- \(2 \frac{4}{5} = 2 \frac{(4 \times 2)}{(5 \times 2)} = 2 \frac{8}{10}\)
3. **Adding the fractions:**
- Convert \(1 \frac{1}{10}\) and \(2 \frac{8}{10}\):
- \(1 \frac{1}{10} + 2 \frac{8}{10} = 3 \frac{9}{10}\)
**Answer: \(3 \frac{9}{10}\)**
---
### Problem 2: \(3 \frac{2}{3} + 1 \frac{4}{6}\)
1. **Finding the common denominator:**
- Denominators: 3 and 6
- Common multiples: 6
- Common Denominator is: **6**
2. **Rewriting the fractions:**
- \(3 \frac{2}{3} = 3 \frac{(2 \times 2)}{(3 \times 2)} = 3 \frac{4}{6}\)
- \(1 \frac{4}{6} \) (no change needed)
3. **Adding the fractions:**
- Convert \(3 \frac{4}{6}\) and \(1 \frac{4}{6}\):
- \(3 \frac{4}{6} + 1 \frac{4}{6} = 4 \frac{8}{6}\)
4. **Simplifying:**
- \(4 \frac{8}{6} = 4 \frac{4}{3} = 5 \frac{1}{3}\)
**Answer: \(5 \frac{1}{3}\)**
---
### Problem 3: \(2 \frac{6}{12} + 1 \frac{1}{2}\)
1. **Finding the common denominator:**
- Denominators: 12 and 2
- Common multiples: 12
- Common Denominator is: **12**
2. **Rewriting the fractions:**
- \(2 \frac{6}{12} \) (no change needed)
- \(1 \frac{1}{2} = 1 \frac{(1 \times 6)}{(2 \times 6)} = 1 \frac{6}{12}\)
3. **Adding the fractions:**
- Convert \(2 \frac{6}{12}\) and \(1 \frac{6}{12}\):
- \(2 \frac{6}{12} + 1 \frac{6}{12} = 3 \frac{12}{12}\)
4. **Simplifying:**
- \(3 \frac{12}{12} = 3 \frac{0}{12} = 4\)
**Answer: \(4\)**
### Problem 1: \(1 \frac{1}{10} + 2 \frac{4}{5}\)
1. **Finding the common denominator:**
- Denominators: 10 and 5
- Common multiples: 10, 20
- Common Denominator is: **10**
2. **Rewriting the fractions:**
- \(1 \frac{1}{10} = 1 \frac{1}{10} \) (no change needed)
- \(2 \frac{4}{5} = 2 \frac{(4 \times 2)}{(5 \times 2)} = 2 \frac{8}{10}\)
3. **Adding the fractions:**
- Convert \(1 \frac{1}{10}\) and \(2 \frac{8}{10}\):
- \(1 \frac{1}{10} + 2 \frac{8}{10} = 3 \frac{9}{10}\)
**Answer: \(3 \frac{9}{10}\)**
---
### Problem 2: \(3 \frac{2}{3} + 1 \frac{4}{6}\)
1. **Finding the common denominator:**
- Denominators: 3 and 6
- Common multiples: 6
- Common Denominator is: **6**
2. **Rewriting the fractions:**
- \(3 \frac{2}{3} = 3 \frac{(2 \times 2)}{(3 \times 2)} = 3 \frac{4}{6}\)
- \(1 \frac{4}{6} \) (no change needed)
3. **Adding the fractions:**
- Convert \(3 \frac{4}{6}\) and \(1 \frac{4}{6}\):
- \(3 \frac{4}{6} + 1 \frac{4}{6} = 4 \frac{8}{6}\)
4. **Simplifying:**
- \(4 \frac{8}{6} = 4 \frac{4}{3} = 5 \frac{1}{3}\)
**Answer: \(5 \frac{1}{3}\)**
---
### Problem 3: \(2 \frac{6}{12} + 1 \frac{1}{2}\)
1. **Finding the common denominator:**
- Denominators: 12 and 2
- Common multiples: 12
- Common Denominator is: **12**
2. **Rewriting the fractions:**
- \(2 \frac{6}{12} \) (no change needed)
- \(1 \frac{1}{2} = 1 \frac{(1 \times 6)}{(2 \times 6)} = 1 \frac{6}{12}\)
3. **Adding the fractions:**
- Convert \(2 \frac{6}{12}\) and \(1 \frac{6}{12}\):
- \(2 \frac{6}{12} + 1 \frac{6}{12} = 3 \frac{12}{12}\)
4. **Simplifying:**
- \(3 \frac{12}{12} = 3 \frac{0}{12} = 4\)
**Answer: \(4\)**