Question
Find the sum of the mixed numbers. Work the problems out in your notebook or you can type the work on here. First you will need to rewrite the problems out using common denominators and equivalent fractions. Then you can add.
1 ⅞ + 1 ¼
Answer:
2 ⅖ + 5 5/6
Answer:
4 1/10 + 6 1/2
Answer:
1 ⅞ + 1 ¼
Answer:
2 ⅖ + 5 5/6
Answer:
4 1/10 + 6 1/2
Answer:
Answers
GPT-4o mini
To add the mixed numbers, we first need to rewrite them as improper fractions with common denominators, and then we can combine them.
### Problem 1: \( 1 \frac{7}{8} + 1 \frac{1}{4} \)
1. Convert the mixed numbers to improper fractions.
- \( 1 \frac{7}{8} = \frac{8 \times 1 + 7}{8} = \frac{15}{8} \)
- \( 1 \frac{1}{4} = \frac{4 \times 1 + 1}{4} = \frac{5}{4} \)
2. Find a common denominator. The least common multiple of 8 and 4 is 8. We convert \( \frac{5}{4} \) to eighths.
- \( \frac{5}{4} = \frac{5 \times 2}{4 \times 2} = \frac{10}{8} \)
3. Now we can add the fractions:
\[
\frac{15}{8} + \frac{10}{8} = \frac{15 + 10}{8} = \frac{25}{8}
\]
4. Convert \( \frac{25}{8} \) back to a mixed number:
- \( 25 \div 8 = 3 \) remainder \( 1 \), so \( \frac{25}{8} = 3 \frac{1}{8} \)
**Answer:** \( 3 \frac{1}{8} \)
---
### Problem 2: \( 2 \frac{2}{5} + 5 \frac{5}{6} \)
1. Convert the mixed numbers to improper fractions.
- \( 2 \frac{2}{5} = \frac{5 \times 2 + 2}{5} = \frac{12}{5} \)
- \( 5 \frac{5}{6} = \frac{6 \times 5 + 5}{6} = \frac{35}{6} \)
2. Find a common denominator. The least common multiple of 5 and 6 is 30. We convert both fractions:
- \( \frac{12}{5} = \frac{12 \times 6}{5 \times 6} = \frac{72}{30} \)
- \( \frac{35}{6} = \frac{35 \times 5}{6 \times 5} = \frac{175}{30} \)
3. Now we can add the fractions:
\[
\frac{72}{30} + \frac{175}{30} = \frac{72 + 175}{30} = \frac{247}{30}
\]
4. Convert \( \frac{247}{30} \) back to a mixed number:
- \( 247 \div 30 = 8 \) remainder \( 7 \), so \( \frac{247}{30} = 8 \frac{7}{30} \)
**Answer:** \( 8 \frac{7}{30} \)
---
### Problem 3: \( 4 \frac{1}{10} + 6 \frac{1}{2} \)
1. Convert the mixed numbers to improper fractions.
- \( 4 \frac{1}{10} = \frac{10 \times 4 + 1}{10} = \frac{41}{10} \)
- \( 6 \frac{1}{2} = \frac{2 \times 6 + 1}{2} = \frac{13}{2} \)
2. Find a common denominator. The least common multiple of 10 and 2 is 10. We convert \( \frac{13}{2} \) to tenths:
- \( \frac{13}{2} = \frac{13 \times 5}{2 \times 5} = \frac{65}{10} \)
3. Now we can add the fractions:
\[
\frac{41}{10} + \frac{65}{10} = \frac{41 + 65}{10} = \frac{106}{10}
\]
4. Convert \( \frac{106}{10} \) back to a mixed number:
- \( 106 \div 10 = 10 \) remainder \( 6 \), so \( \frac{106}{10} = 10 \frac{6}{10} = 10 \frac{3}{5} \)
**Answer:** \( 10 \frac{3}{5} \)
---
### Summary of Answers
1. \( 3 \frac{1}{8} \)
2. \( 8 \frac{7}{30} \)
3. \( 10 \frac{3}{5} \)
### Problem 1: \( 1 \frac{7}{8} + 1 \frac{1}{4} \)
1. Convert the mixed numbers to improper fractions.
- \( 1 \frac{7}{8} = \frac{8 \times 1 + 7}{8} = \frac{15}{8} \)
- \( 1 \frac{1}{4} = \frac{4 \times 1 + 1}{4} = \frac{5}{4} \)
2. Find a common denominator. The least common multiple of 8 and 4 is 8. We convert \( \frac{5}{4} \) to eighths.
- \( \frac{5}{4} = \frac{5 \times 2}{4 \times 2} = \frac{10}{8} \)
3. Now we can add the fractions:
\[
\frac{15}{8} + \frac{10}{8} = \frac{15 + 10}{8} = \frac{25}{8}
\]
4. Convert \( \frac{25}{8} \) back to a mixed number:
- \( 25 \div 8 = 3 \) remainder \( 1 \), so \( \frac{25}{8} = 3 \frac{1}{8} \)
**Answer:** \( 3 \frac{1}{8} \)
---
### Problem 2: \( 2 \frac{2}{5} + 5 \frac{5}{6} \)
1. Convert the mixed numbers to improper fractions.
- \( 2 \frac{2}{5} = \frac{5 \times 2 + 2}{5} = \frac{12}{5} \)
- \( 5 \frac{5}{6} = \frac{6 \times 5 + 5}{6} = \frac{35}{6} \)
2. Find a common denominator. The least common multiple of 5 and 6 is 30. We convert both fractions:
- \( \frac{12}{5} = \frac{12 \times 6}{5 \times 6} = \frac{72}{30} \)
- \( \frac{35}{6} = \frac{35 \times 5}{6 \times 5} = \frac{175}{30} \)
3. Now we can add the fractions:
\[
\frac{72}{30} + \frac{175}{30} = \frac{72 + 175}{30} = \frac{247}{30}
\]
4. Convert \( \frac{247}{30} \) back to a mixed number:
- \( 247 \div 30 = 8 \) remainder \( 7 \), so \( \frac{247}{30} = 8 \frac{7}{30} \)
**Answer:** \( 8 \frac{7}{30} \)
---
### Problem 3: \( 4 \frac{1}{10} + 6 \frac{1}{2} \)
1. Convert the mixed numbers to improper fractions.
- \( 4 \frac{1}{10} = \frac{10 \times 4 + 1}{10} = \frac{41}{10} \)
- \( 6 \frac{1}{2} = \frac{2 \times 6 + 1}{2} = \frac{13}{2} \)
2. Find a common denominator. The least common multiple of 10 and 2 is 10. We convert \( \frac{13}{2} \) to tenths:
- \( \frac{13}{2} = \frac{13 \times 5}{2 \times 5} = \frac{65}{10} \)
3. Now we can add the fractions:
\[
\frac{41}{10} + \frac{65}{10} = \frac{41 + 65}{10} = \frac{106}{10}
\]
4. Convert \( \frac{106}{10} \) back to a mixed number:
- \( 106 \div 10 = 10 \) remainder \( 6 \), so \( \frac{106}{10} = 10 \frac{6}{10} = 10 \frac{3}{5} \)
**Answer:** \( 10 \frac{3}{5} \)
---
### Summary of Answers
1. \( 3 \frac{1}{8} \)
2. \( 8 \frac{7}{30} \)
3. \( 10 \frac{3}{5} \)