High School

Subtract the following fractions:

[tex]\frac{12}{25} - \frac{2}{5}[/tex]

Remember to get a common denominator first, subtract, then simplify if possible.

Answer :

To subtract the fractions [tex]\(\frac{12}{25}\)[/tex] and [tex]\(\frac{2}{5}\)[/tex], follow these steps:

1. Find a common denominator:
The denominators here are 25 and 5. The least common denominator (LCD) between 25 and 5 is 25.

2. Convert the fractions:
Since [tex]\(\frac{12}{25}\)[/tex] already has the denominator 25, we'll focus on converting [tex]\(\frac{2}{5}\)[/tex].

Multiply both the numerator and denominator of [tex]\(\frac{2}{5}\)[/tex] by 5 to get the common denominator of 25:
[tex]\[
\frac{2}{5} = \frac{2 \times 5}{5 \times 5} = \frac{10}{25}
\][/tex]

3. Subtract the fractions:
Now that both fractions have a common denominator, subtract the second fraction from the first:
[tex]\[
\frac{12}{25} - \frac{10}{25} = \frac{12 - 10}{25} = \frac{2}{25}
\][/tex]

4. Simplify the result (if possible):
The fraction [tex]\(\frac{2}{25}\)[/tex] is already in its simplest form, as 2 and 25 have no common factors other than 1.

Therefore, the answer to [tex]\(\frac{12}{25} - \frac{2}{5}\)[/tex] is [tex]\(\frac{2}{25}\)[/tex].