Question
Find \( \frac{3}{4} \div \frac{3}{10} \). Simplify the answer and write as a mixed number, if possible. \( \frac{9}{40} \) \( \frac{10}{4} \) \( \frac{2}{5} \) \( 2 \frac{1}{2} \)
Ask by Hilton Simpson. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The answer is \( 2 \frac{1}{2} \).
Solution
To solve \( \frac{3}{4} \div \frac{3}{10} \), follow these steps:
1. **Understand Division of Fractions:**
Dividing by a fraction is the same as multiplying by its reciprocal. So,
\[
\frac{3}{4} \div \frac{3}{10} = \frac{3}{4} \times \frac{10}{3}
\]
2. **Multiply the Fractions:**
\[
\frac{3}{4} \times \frac{10}{3} = \frac{3 \times 10}{4 \times 3} = \frac{30}{12}
\]
3. **Simplify the Fraction:**
\[
\frac{30}{12} = \frac{5}{2} = 2 \frac{1}{2}
\]
(Here, \( \frac{5}{2} \) is converted to a mixed number by dividing 5 by 2, which equals 2 with a remainder of 1, hence \( 2 \frac{1}{2} \)).
**Therefore, the simplified answer is:**
**\( 2 \frac{1}{2} \)**
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
To find \( \frac{3}{4} \div \frac{3}{10} \), you can multiply by the reciprocal of the second fraction. This gives you: \[ \frac{3}{4} \times \frac{10}{3} \] The threes cancel out, leading to: \[ \frac{10}{4} \] Now simplify \( \frac{10}{4} \) by dividing both the numerator and denominator by 2: \[ \frac{10 \div 2}{4 \div 2} = \frac{5}{2} \] Next, convert \( \frac{5}{2} \) to a mixed number: \[ 5 \div 2 = 2 \quad \text{with a remainder of } 1 \] This means: \[ \frac{5}{2} = 2 \frac{1}{2} \] So the answer is \( 2 \frac{1}{2} \).
