Question
\( 1 \leftarrow \begin{array}{l}\frac{10}{32} \div \frac{5}{8} \\ \frac{10}{32} \div \frac{5}{8}=\square \\ \text { (Type a whole number or a simplified fraction.) }\end{array} \)
Ask by Wells Perkins. in the United States
Jan 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\(\frac{1}{2}\)
Solution
To solve the division of two fractions:
\[
\frac{10}{32} \div \frac{5}{8}
\]
Follow these steps:
1. **Rewrite the Division as Multiplication:**
Dividing by a fraction is the same as multiplying by its reciprocal.
\[
\frac{10}{32} \div \frac{5}{8} = \frac{10}{32} \times \frac{8}{5}
\]
2. **Simplify Before Multiplying:**
- Simplify \(\frac{10}{32}\):
\[
\frac{10}{32} = \frac{5}{16} \quad (\text{divided numerator and denominator by } 2)
\]
- Now multiply:
\[
\frac{5}{16} \times \frac{8}{5}
\]
3. **Cancel Common Factors:**
- The 5 in the numerator and denominator cancels out.
\[
\frac{\cancel{5}}{16} \times \frac{8}{\cancel{5}} = \frac{8}{16}
\]
4. **Simplify the Final Fraction:**
\[
\frac{8}{16} = \frac{1}{2}
\]
**Answer:** \(\frac{1}{2}\)
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Simplify this solution The Deep Dive
To solve \( \frac{10}{32} \div \frac{5}{8} \), we first invert the second fraction and change the division to multiplication: \[ \frac{10}{32} \times \frac{8}{5} \] Now, multiply the numerators and denominators: \[ \frac{10 \times 8}{32 \times 5} = \frac{80}{160} \] Simplifying \( \frac{80}{160} \) gives \( \frac{1}{2} \). So, the answer is \( \frac{1}{2} \). When working with fractions, remember to always check for simplification throughout the process. A common mistake is to forget to invert the divisor, which can lead to incorrect results. Double-checking your work with the simplest numbers can help avoid this!
