Question
Question 11 Divide. Simplify your answer and write as a proper fraction, improper fraction, or whole number. \( \frac{2}{3} \div 4 \)
Ask by Hills Riley. in the United States
Jan 22,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The simplified answer is \( \frac{1}{6} \).
Solution
To divide \( \frac{2}{3} \) by 4 and simplify the result, follow these steps:
1. **Rewrite the Division as a Multiplication:**
Dividing by a number is the same as multiplying by its reciprocal. So, dividing by 4 is the same as multiplying by \( \frac{1}{4} \).
\[
\frac{2}{3} \div 4 = \frac{2}{3} \times \frac{1}{4}
\]
2. **Multiply the Fractions:**
Multiply the numerators (top numbers) together and the denominators (bottom numbers) together.
\[
\frac{2 \times 1}{3 \times 4} = \frac{2}{12}
\]
3. **Simplify the Fraction:**
Find the greatest common divisor (GCD) of the numerator and the denominator to reduce the fraction to its simplest form. The GCD of 2 and 12 is 2.
\[
\frac{2 \div 2}{12 \div 2} = \frac{1}{6}
\]
4. **Final Answer:**
\[
\frac{2}{3} \div 4 = \frac{1}{6}
\]
The simplified answer is \( \frac{1}{6} \), which is a proper fraction.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
To divide \( \frac{2}{3} \) by 4, you can convert the whole number 4 into a fraction by writing it as \( \frac{4}{1} \). Then, remember that dividing by a fraction is the same as multiplying by its reciprocal. So, the expression becomes: \[ \frac{2}{3} \div \frac{4}{1} = \frac{2}{3} \times \frac{1}{4} = \frac{2 \times 1}{3 \times 4} = \frac{2}{12} \] Now, simplify \( \frac{2}{12} \) by dividing both the numerator and the denominator by 2: \[ \frac{2 \div 2}{12 \div 2} = \frac{1}{6} \] So, the simplified answer is \( \frac{1}{6} \).
