College

Add: [tex]\frac{1}{15} + \frac{12}{25}[/tex]

Give your answer in reduced terms.

[tex]\square[/tex]

Answer :

To add the fractions [tex]\(\frac{1}{15}\)[/tex] and [tex]\(\frac{12}{25}\)[/tex], you should follow these steps:

1. Find a Common Denominator:
The denominators in the fractions are 15 and 25. To add these fractions, we need to find a common denominator. The least common multiple (LCM) of 15 and 25 is 75.

2. Convert Each Fraction to an Equivalent Fraction with the Common Denominator:
- For [tex]\(\frac{1}{15}\)[/tex], you need to convert it to a fraction with the denominator of 75. Multiply both the numerator and the denominator by 5:
[tex]\[
\frac{1}{15} = \frac{1 \times 5}{15 \times 5} = \frac{5}{75}
\][/tex]
- For [tex]\(\frac{12}{25}\)[/tex], convert it using the same denominator. Multiply both the numerator and the denominator by 3:
[tex]\[
\frac{12}{25} = \frac{12 \times 3}{25 \times 3} = \frac{36}{75}
\][/tex]

3. Add the Equivalent Fractions:
Now that both fractions have the same denominator, you can simply add the numerators:
[tex]\[
\frac{5}{75} + \frac{36}{75} = \frac{5 + 36}{75} = \frac{41}{75}
\][/tex]

4. Simplify if Necessary:
The fraction [tex]\(\frac{41}{75}\)[/tex] is already in its simplest form because 41 and 75 have no common factors other than 1.

So, [tex]\(\frac{1}{15} + \frac{12}{25} = \frac{41}{75}\)[/tex].