What is 1/4 divided by 3/8? (fractions)
The Correct Answer and Explanation is:
To solve the problem of dividing the fraction ( \frac{1}{4} ) by ( \frac{3}{8} ), we follow the rule of multiplying by the reciprocal. Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of a fraction is obtained by flipping its numerator and denominator. Therefore, the reciprocal of ( \frac{3}{8} ) is ( \frac{8}{3} ).
The mathematical expression can be set up as follows:
[
\frac{1}{4} \div \frac{3}{8} = \frac{1}{4} \times \frac{8}{3}
]
Next, we multiply the fractions. To multiply fractions, we multiply the numerators together and the denominators together:
- Numerators: ( 1 \times 8 = 8 )
- Denominators: ( 4 \times 3 = 12 )
Now, we can write the resulting fraction:
[
\frac{1}{4} \times \frac{8}{3} = \frac{8}{12}
]
The fraction ( \frac{8}{12} ) can be simplified. To simplify a fraction, we find the greatest common divisor (GCD) of the numerator and the denominator. The GCD of 8 and 12 is 4. We divide both the numerator and the denominator by 4:
[
\frac{8 \div 4}{12 \div 4} = \frac{2}{3}
]
Thus, ( \frac{1}{4} \div \frac{3}{8} ) simplifies to ( \frac{2}{3} ).
In conclusion, the answer to the division of ( \frac{1}{4} ) by ( \frac{3}{8} ) is ( \frac{2}{3} ). This process highlights the importance of understanding how to manipulate fractions, particularly how to divide them using the reciprocal method and simplify results to their lowest terms. Mastering these concepts is crucial in mathematics, especially in algebra and higher-level math where fractions are frequently encountered.