To find the quotient of the given division problem [tex]\( \frac{6}{13.8} \)[/tex], we can follow these detailed steps:
1. Understand the Problem: We need to divide 6 by 13.8.
2. Set Up the Division:
The problem can be written as:
[tex]\[
6 \div 13.8
\][/tex]
3. Simplify the Denominator (if needed):
Notice that 13.8 can be expressed as a fraction over 10:
[tex]\[
13.8 = \frac{138}{10}
\][/tex]
So, the division problem can be rewritten using fractions:
[tex]\[
6 \div \frac{138}{10}
\][/tex]
When dividing by a fraction, we multiply by its reciprocal:
[tex]\[
6 \times \frac{10}{138}
\][/tex]
4. Simplify the Multiplication:
Simplify the fraction [tex]\( \frac{10}{138} \)[/tex] first:
[tex]\[
\frac{10}{138} = \frac{5}{69}
\][/tex]
So, our division problem now looks like:
[tex]\[
6 \times \frac{5}{69}
\][/tex]
Multiply the numerator and the numerator, and the denominator and the denominator:
[tex]\[
6 \times 5 = 30
\][/tex]
[tex]\[
1 \times 69 = 69
\][/tex]
Thus, the expression becomes:
[tex]\[
\frac{30}{69}
\][/tex]
5. Simplify the Fraction:
Both 30 and 69 can be divided by their greatest common divisor (GCD), which is 3.
[tex]\[
\frac{30 \div 3}{69 \div 3} = \frac{10}{23}
\][/tex]
6. Convert the Fraction to Decimal Form:
Divide 10 by 23 to find the decimal form:
[tex]\[
\frac{10}{23} = 0.43478260869565216
\][/tex]
By following these steps accurately, we find that:
[tex]\[
6 \div 13.8 = 0.43478260869565216
\][/tex]
