Answer :
To solve the problem of dividing the fractions [tex]\(\frac{2}{5}\)[/tex] by [tex]\(\frac{6}{14}\)[/tex], we can follow these steps:
1. Understand Division of Fractions: To divide two fractions, we multiply the first fraction by the reciprocal (or inverse) of the second fraction.
2. Find the Reciprocal of the Second Fraction: The reciprocal of [tex]\(\frac{6}{14}\)[/tex] is [tex]\(\frac{14}{6}\)[/tex].
3. Set Up the Multiplication: Now multiply [tex]\(\frac{2}{5}\)[/tex] by [tex]\(\frac{14}{6}\)[/tex]:
[tex]\[
\frac{2}{5} \times \frac{14}{6}
\][/tex]
4. Multiply the Numerators and Denominators:
- Numerators: [tex]\(2 \times 14 = 28\)[/tex]
- Denominators: [tex]\(5 \times 6 = 30\)[/tex]
So, the fraction after multiplication is [tex]\(\frac{28}{30}\)[/tex].
5. Simplify the Fraction: We can simplify [tex]\(\frac{28}{30}\)[/tex] by finding the greatest common divisor (GCD) of 28 and 30, which is 2. Divide both the numerator and the denominator by 2:
[tex]\[
\frac{28 \div 2}{30 \div 2} = \frac{14}{15}
\][/tex]
Therefore, the answer is [tex]\(\frac{14}{15}\)[/tex]. The correct option is C.
1. Understand Division of Fractions: To divide two fractions, we multiply the first fraction by the reciprocal (or inverse) of the second fraction.
2. Find the Reciprocal of the Second Fraction: The reciprocal of [tex]\(\frac{6}{14}\)[/tex] is [tex]\(\frac{14}{6}\)[/tex].
3. Set Up the Multiplication: Now multiply [tex]\(\frac{2}{5}\)[/tex] by [tex]\(\frac{14}{6}\)[/tex]:
[tex]\[
\frac{2}{5} \times \frac{14}{6}
\][/tex]
4. Multiply the Numerators and Denominators:
- Numerators: [tex]\(2 \times 14 = 28\)[/tex]
- Denominators: [tex]\(5 \times 6 = 30\)[/tex]
So, the fraction after multiplication is [tex]\(\frac{28}{30}\)[/tex].
5. Simplify the Fraction: We can simplify [tex]\(\frac{28}{30}\)[/tex] by finding the greatest common divisor (GCD) of 28 and 30, which is 2. Divide both the numerator and the denominator by 2:
[tex]\[
\frac{28 \div 2}{30 \div 2} = \frac{14}{15}
\][/tex]
Therefore, the answer is [tex]\(\frac{14}{15}\)[/tex]. The correct option is C.
