Answer :
To find the quotient of [tex]\(\frac{14}{15} \div 3.8\)[/tex], follow these steps:
1. Understand the Division: Dividing by a number is the same as multiplying by its reciprocal. So, [tex]\(\frac{14}{15} \div 3.8\)[/tex] is the same as [tex]\(\frac{14}{15} \times \frac{1}{3.8}\)[/tex].
2. Convert to Fraction: The number 3.8 can be written as a fraction. Since 3.8 is equal to [tex]\(\frac{38}{10}\)[/tex], we can use the reciprocal of this fraction.
[tex]\[
\frac{1}{3.8} = \frac{1}{\frac{38}{10}} = \frac{10}{38}
\][/tex]
3. Simplify the Reciprocal Fraction: Simplify [tex]\(\frac{10}{38}\)[/tex] by finding the greatest common divisor (GCD) of 10 and 38, which is 2. Divide both the numerator and the denominator by 2.
[tex]\[
\frac{10}{38} = \frac{10 \div 2}{38 \div 2} = \frac{5}{19}
\][/tex]
4. Multiply the Fractions: Now multiply [tex]\(\frac{14}{15}\)[/tex] by the simplified reciprocal [tex]\(\frac{5}{19}\)[/tex].
[tex]\[
\frac{14}{15} \times \frac{5}{19} = \frac{14 \times 5}{15 \times 19} = \frac{70}{285}
\][/tex]
5. Simplify the Result: Find the GCD of 70 and 285. The GCD is 5. Divide both the numerator and the denominator by 5.
[tex]\[
\frac{70}{285} = \frac{70 \div 5}{285 \div 5} = \frac{14}{57}
\][/tex]
So, the final quotient is:
[tex]\[
\boxed{\frac{14}{57}}
\][/tex]
1. Understand the Division: Dividing by a number is the same as multiplying by its reciprocal. So, [tex]\(\frac{14}{15} \div 3.8\)[/tex] is the same as [tex]\(\frac{14}{15} \times \frac{1}{3.8}\)[/tex].
2. Convert to Fraction: The number 3.8 can be written as a fraction. Since 3.8 is equal to [tex]\(\frac{38}{10}\)[/tex], we can use the reciprocal of this fraction.
[tex]\[
\frac{1}{3.8} = \frac{1}{\frac{38}{10}} = \frac{10}{38}
\][/tex]
3. Simplify the Reciprocal Fraction: Simplify [tex]\(\frac{10}{38}\)[/tex] by finding the greatest common divisor (GCD) of 10 and 38, which is 2. Divide both the numerator and the denominator by 2.
[tex]\[
\frac{10}{38} = \frac{10 \div 2}{38 \div 2} = \frac{5}{19}
\][/tex]
4. Multiply the Fractions: Now multiply [tex]\(\frac{14}{15}\)[/tex] by the simplified reciprocal [tex]\(\frac{5}{19}\)[/tex].
[tex]\[
\frac{14}{15} \times \frac{5}{19} = \frac{14 \times 5}{15 \times 19} = \frac{70}{285}
\][/tex]
5. Simplify the Result: Find the GCD of 70 and 285. The GCD is 5. Divide both the numerator and the denominator by 5.
[tex]\[
\frac{70}{285} = \frac{70 \div 5}{285 \div 5} = \frac{14}{57}
\][/tex]
So, the final quotient is:
[tex]\[
\boxed{\frac{14}{57}}
\][/tex]
