Question
4. \( \begin{array}{l}7 \frac{8}{12} \\ -2 \frac{3}{12} \\ \text { 8. } 5 \frac{2}{8}-3 \frac{7}{8}\end{array} \)
Ask by Newton Johnston. in the United States
Mar 12,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The answers are:
1. \( 5 \frac{5}{12} \)
2. \( 1 \frac{3}{8} \)
Solution
Let's solve the problems step by step.
### Problem 1: \( 7 \frac{8}{12} - 2 \frac{3}{12} \)
1. **Convert mixed numbers to improper fractions:**
- For \( 7 \frac{8}{12} \):
\[
7 \frac{8}{12} = \frac{7 \times 12 + 8}{12} = \frac{84 + 8}{12} = \frac{92}{12}
\]
- For \( 2 \frac{3}{12} \):
\[
2 \frac{3}{12} = \frac{2 \times 12 + 3}{12} = \frac{24 + 3}{12} = \frac{27}{12}
\]
2. **Subtract the improper fractions:**
\[
\frac{92}{12} - \frac{27}{12} = \frac{92 - 27}{12} = \frac{65}{12}
\]
3. **Convert back to a mixed number:**
\[
\frac{65}{12} = 5 \frac{5}{12}
\]
### Problem 2: \( 5 \frac{2}{8} - 3 \frac{7}{8} \)
1. **Convert mixed numbers to improper fractions:**
- For \( 5 \frac{2}{8} \):
\[
5 \frac{2}{8} = \frac{5 \times 8 + 2}{8} = \frac{40 + 2}{8} = \frac{42}{8}
\]
- For \( 3 \frac{7}{8} \):
\[
3 \frac{7}{8} = \frac{3 \times 8 + 7}{8} = \frac{24 + 7}{8} = \frac{31}{8}
\]
2. **Subtract the improper fractions:**
\[
\frac{42}{8} - \frac{31}{8} = \frac{42 - 31}{8} = \frac{11}{8}
\]
3. **Convert back to a mixed number:**
\[
\frac{11}{8} = 1 \frac{3}{8}
\]
### Final Answers:
1. \( 7 \frac{8}{12} - 2 \frac{3}{12} = 5 \frac{5}{12} \)
2. \( 5 \frac{2}{8} - 3 \frac{7}{8} = 1 \frac{3}{8} \)
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Mind Expander
To tackle these arithmetic problems involving mixed numbers, it helps to convert them into improper fractions. For instance, \( 7 \frac{8}{12} \) becomes \( \frac{88}{12} \) and \( 2 \frac{3}{12} \) becomes \( \frac{27}{12} \). Subtracting \( 2 \frac{3}{12} \) from \( 7 \frac{8}{12} \) gives you \( \frac{61}{12} \) or \( 5 \frac{1}{12} \). For the second problem, convert \( 5 \frac{2}{8} \) to \( \frac{42}{8} \) and \( 3 \frac{7}{8} \) to \( \frac{31}{8} \). Subtracting these gives you \( \frac{11}{8} \), which can be simplified to \( 1 \frac{3}{8} \).