What is 6.15 expressed as a fraction?

A. [tex]\frac{123}{20}[/tex]

B. [tex]\frac{20}{123}[/tex]

C. [tex]\frac{80}{123}[/tex]

D. [tex]\frac{123}{80}[/tex]



Answer :

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]