To convert the decimal number 6.15 into a fraction, follow these steps:
1. Identify the given decimal number: We start with 6.15.
2. Understand the structure of the number: The number 6.15 can be expressed as:
[tex]\[
6 + 0.15
\][/tex]
3. Convert the fractional part to a fraction:
- [tex]\(0.15\)[/tex] is the same as [tex]\(\frac{15}{100}\)[/tex].
4. Simplify the fraction [tex]\(\frac{15}{100}\)[/tex]:
- Divide the numerator and the denominator by their greatest common divisor (GCD), which is 5:
[tex]\[
\frac{15 \div 5}{100 \div 5} = \frac{3}{20}
\][/tex]
5. Combine the whole number part with the fractional part:
- Express 6 as a fraction: [tex]\(\frac{6 \cdot 20}{20} = \frac{120}{20}\)[/tex].
- Add the two fractions:
[tex]\[
\frac{120}{20} + \frac{3}{20} = \frac{120 + 3}{20} = \frac{123}{20}
\][/tex]
Therefore, 6.15 expressed as a fraction is:
[tex]\[
\frac{123}{20}
\][/tex]
Upon examining the provided options:
- [tex]\(\frac{123}{20}\)[/tex]
- [tex]\(\frac{20}{123}\)[/tex]
- [tex]\(\frac{80}{123}\)[/tex]
- [tex]\(\frac{123}{80}\)[/tex]
The correct fraction is:
[tex]\[\boxed{\frac{123}{20}}\][/tex]
